Index Page DSK Required Reading

## Table of Contents

       DSK Required Reading
          Abstract
             Purpose
             Intended Audience
             References
          Introduction
       DSK Software
          High-Level DSK-Enabled Geometry Functions
          DSK File Loading and Unloading
          DSK Utility Functions
          DSK Type 2 Functions
          DLA and DAS Functions
          Surface Name and ID Conversion Functions
          SPICE Toolkit DSK Utility Programs
          Non-SPICE Toolkit DSK Utility Programs
       DSK Concepts
          Shapes and Surfaces
          Surface IDs
             Defining Surface Name-ID Mappings
          Segments
             DLA and DSK Descriptors
             Reference Frames
             Coordinate Systems and Spatial Coverage
             Spatial coverage: Dimensions
             Spatial coverage: Gaps and Padding
             Time Bounds
             Data Types
             Data Classes
          Data Competition and Priority
          Greedy Algorithms
             Greedy Ray-Segment Boundary Intercepts
             DSK Type 2 Plate Expansion
             Additional Greedy Algorithms
             DSK Tolerances
             Drawbacks
             Access to DSK Tolerances and Margin Values
       DSK Files
          DAS Files
          DLA Files
          DSK File Format
       DSK Type 2: Triangular Plate Model
          Type 2 Shape Data
             Vertices
             Plates
          Type 2 Ancillary Information
          Pointers and Offsets
          DSK Type 2 Segment Parameters
          Spatial Index: Voxel-Plate Mapping
             Fine Voxel Grid
             Fine Voxel Scale
             Coarse Voxel Grid
             Purpose of the Coarse Voxel Grid
             Voxel-Plate Pointer Array
             Voxel-Plate Association Array
             Size of the Voxel-Plate Association Array
          Spatial Index: Vertex-Plate Mapping
             Structure of the Vertex-Plate Mapping
             Size of the Vertex-Plate Mapping Array
          Layout of DSK Type 2 Segments
             DSK Type 2 Integer Segment Component
             DSK Type 2 Double Precision Segment Component
             Coordinate System Parameters
       Common Problems
          Slow DSK Computations
          Non-Portable and Unstable Results
          Non-Convex and Multi-Valued Surfaces
          DSK File Creation Errors
             MKDSK Setup File Errors
             Data Errors
             Segment Coverage Errors
             Poor Data Distribution Across Segments
       Appendix A --- Revision History
             2017 APR 05 by N. J. Bachman.
       Appendix B --- DSK Subsystem Limits
          General Limits
          DSK Type 2 Segment Limits

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# DSK Required Reading

Last revised on 2017 APR 05 by N. J. Bachman.

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## Abstract

The Digital Shape Kernel (DSK) subsystem is the component of SPICE concerned with detailed shape models for extended objects.

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### Purpose

This document is a reference guide for the SPICE DSK subsystem. Here you'll find

`--` A discussion of the DSK subsystem's software. This includes the API (application programming interface) functions---these are the functions that may be called directly by SPICE-based user application code---and the SPICE utility programs that work with DSK files.

`--` Discussions of DSK concepts

`--` A description of the DSK file format

`--` Discussion of problems that may arise when using the DSK subsystem

The DSK subsystem does not deal with triaxial ellipsoid shape models; these models are usually provided by PCK files. See the PCK Required Reading, pck.req, for further information.

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### Intended Audience

This document addresses the needs of several groups of SPICE users. Users looking for a basic discussion of the capabilities of the SPICE DSK subsystem should read the introduction below. Users planning to write application code using the DSK subsystem may benefit from reading the entire document, possibly excepting the description of the details of DSK type 2, but in any case should read the ``DSK Concepts'' chapter. Users planning to create DSK files are encouraged to read the entire document.

This document assumes you already have a strong understanding of SPICE concepts and terminology.

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### References

The references listed below provide essential background for programmers intending to use the DSK subsystem. They also document DSK utility programs.

`1.` DAS Required Reading (das.req)

`2.` DLA Required Reading (dla.req)

`3.` NAIF Integer ID Codes (naif_ids.req)

`4.` Frames Required Reading (frames.req)

`5.` Convert User's Guide (convert.ug)

`6.` DSKBRIEF User's Guide

`7.` MKDSK User's Guide

`8.` DSKEXP User's Guide

`9.` DLACAT User's Guide.

`10.` BINGO User's Guide.

`11.` SPICE Tutorials. Thes are available on the NAIF web site at

                https://naif.jpl.nasa.gov/naif/tutorials.html

The programs

       DLACAT
       BINGO

are utilities that are not part of the SPICE Toolkit, but that operate on DSK files. They are available on the NAIF web site at

       https://naif.jpl.nasa.gov/naif/utilities.html

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## Introduction

The Digital Shape Kernel (DSK) subsystem is the component of SPICE concerned with detailed shape models for extended objects. These objects typically are solar system bodies such as planets, dwarf planets, natural satellites, asteroids, and comet nuclei. DSK data can represent the shapes of such objects, as well as local topography, such as that in the vicinity of a rover or a tracking station.

DSK data also can represent shapes of artificial objects such as spacecraft components, or represent abstractions such as the subset of a target body's surface that has a property of interest.

The DSK subsystem comprises software, the DSK file format specification, and documentation.

The primary purpose of the DSK subsystem is to enable SPICE-based applications to conveniently and efficiently use detailed shape data in geometry computations performed by SPICE functions. DSK data enable these functions to produce more accurate results than those obtainable using triaxial ellipsoid shape models. See the section below titled ``High-Level DSK-Enabled Geometry Routines'' for details.

The DSK implementation ensures that shape data used by SPICE are accompanied by all of the attribute information necessary for correct, programmatic use of the data---including, but not limited to, reference frames, central bodies, coordinate systems, spatial coverage bounds, and time bounds of applicability. The DSK format enables data to be augmented by indexes, or other pre-computed parameters, that greatly enhance the speed of common geometric computations, such as those of ray-surface intercepts.

DSK data sets can be distributed across multiple DSK files; this is normal for large data sets. Such sets of files can be ``loaded'' (made available for read access by CSPICE software) concurrently; CSPICE software will select data from the appropriate files as needed to perform computations.

The DSK file format facilitates storage, transmission, and archival of shape data. It allows the data to be annotated with free-form descriptive comments, also called ``metadata.''

DSK documentation uses the term ``data type'' to refer to types of mathematical shape representations, associated DSK file formats, and software. The DSK subsystem is designed to accommodate multiple data types, and to enable high-level SPICE geometry software to function independently of these types.

Currently there is only one DSK data type, which represents the shape of an object by a set of triangular plates. This representation is called a ``tessellated plate model'' or ``triangular plate model.'' The DSK documentation refers to this type as ``DSK type 2.''

Support for digital elevation models (DEMs) will be added in a later version of the SPICE Toolkit; one or more new DSK data types will be developed to support such data.

Because many popular file formats for shape data exist, and because it is impractical for these formats to be used directly by SPICE for geometric computations, the DSK subsystem supports conversion of a variety of text-based shape data file formats to DSK format; it also supports conversion of DSK files to a variety of text formats.

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# DSK Software

Below we list the CSPICE functions that either work directly with DSK files or that support DSK usage. We also briefly describe the CSPICE utility programs that work with DSK files.

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## High-Level DSK-Enabled Geometry Functions

High-level SPICE geometry functions constitute the principal application programming interface to the DSK subsystem. The functions described here are supported in all language versions of the SPICE Toolkit.

All of these routines perform computations that involve a target body. All can model the shape of that body using data provided by DSK files. Many of the functions can use triaxial ellipsoid models as well.

These functions have extensive header documentation. Each header describes all input and output arguments and includes one or more example programs accompanied by example meta-kernels and corresponding program outputs.

dskxsi_c
  Ray-surface intercept with source information: compute a ray-surface intercept using data provided by multiple loaded DSK segments. Return information about the source of the data defining the surface on which the intercept was found: DSK handle, DLA and DSK descriptors, and DSK data type-dependent parameters. [Compare with sincpt_c.]

dskxv_c
  Vectorized ray-surface intercept: compute ray-surface intercepts for a set of rays, using data provided by multiple loaded DSK segments. [Compare with sincpt_c.]

gfoclt_c
  Occultation search: determine time intervals when an observer sees one target occulted by, or in transit across, another.

illumf_c
  Illumination angles: compute the illumination angles---phase, incidence, and emission---at a specified point on a target body. Return logical flags indicating whether the surface point is visible from the observer's position and whether the surface point is illuminated.

latsrf_c
  Compute surface points specified by longitudes and latitudes: map an array of planetocentric longitude/latitude coordinate pairs to surface points on a specified target body.

limbpt_c
  Find limb points on a target body: the limb is the set of points of tangency on the target of rays emanating from the observer. The caller specifies half-planes bounded by the observer-target center vector in which to search for limb points.

occult_c
  Occultation state: determine the occultation condition (not occulted, partially, etc.) of one target relative to another target as seen by an observer at a given time.

sincpt_c
  Ray-surface intercept: for a given observer, target, and ray direction, find the nearest intersection to the observer of the ray and target body's surface, optionally corrected for light time and stellar aberration.

srfnrm_c
  Surface normal vectors: map an array of surface points on a specified target body to the corresponding unit length outward surface normal vectors.

subpnt_c
  Sub-observer point: compute the rectangular coordinates of the sub-observer point on a target body at a specified epoch, optionally corrected for light time and stellar aberration.

subslr_c
  Sub-solar point: compute the rectangular coordinates of the sub-solar point on a target body at a specified epoch, optionally corrected for light time and stellar aberration.

termpt_c
  Find terminator points on a target body: the terminator is the set of points of tangency on the target body of planes tangent to both this body and to a light source. The caller specifies half-planes, bounded by the illumination source center-target center vector, in which to search for terminator points.

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## DSK File Loading and Unloading

DSK files are loaded and unloaded by the same functions used for all other SPICE kernels:

furnsh_c
  Load a SPICE kernel. DSK files can be loaded directly by furnsh_c; they also can be referenced in a meta-kernel which can be loaded by furnsh_c. The latter method is usually preferable; see the ``Intro to Kernels'' tutorial on the NAIF web site.

unload_c
  Unload a SPICE kernel. unload_c can unload both DSK files and meta-kernels.

kclear_c
  Unload all SPICE kernels and clear the kernel pool.

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## DSK Utility Functions

DSK utility functions perform functions other than geometry computations.

Functions for DSK file creation:

dskopn_c
  Open a new DSK file for subsequent write operations.

dskcls_c
  Close a DSK file.

Also see the data type-specific segment writing functions below.

Function for fetching DSK segment attributes:

dskgd_c
  Return the DSK descriptor from a DSK segment identified by a DAS handle and DLA descriptor.

Functions for determining objects covered by DSK files:

dskobj_c
  Find the set of body ID codes of all objects for which data are provided in a specified DSK file.

dsksrf_c
  Find the set of surface ID codes for all surfaces associated with a given body in a specified DSK file.

Functions for fetching and adjusting DSK tolerances:

dskgtl_c
  Retrieve the value of a specified DSK tolerance or margin parameter.

dskstl_c
  Set the value of a specified DSK tolerance or margin parameter.

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## DSK Type 2 Functions

The DSK functions specific to data type 2 are:

dskb02_c
  Return bookkeeping data from a DSK type 2 segment.

dskd02_c
  Fetch double precision data from a DSK type 2 segment. To fetch vertex data, see dskv02_c.

dski02_c
  Fetch integer data from a DSK type 2 segment. To fetch plate data, see dskp02_c. To fetch vertex and plate counts, see dskz02_c.

dskmi2_c
  Make a spatial index for a DSK type 2 segment.

dskn02_c
  Compute the outward unit normal vector for a specified plate in a DSK type 2 segment.

dskp02_c
  Fetch triangular plates from a DSK type 2 segment.

dskrb2_c
  Determine range bounds for a set of triangular plates to be stored in a DSK type 2 segment.

dskv02_c
  Fetch vertices from a DSK type 2 segment.

dskw02_c
  Write a DSK type 2 segment to a DSK file.

dskz02_c
  Return plate count and vertex count of a DSK type 2 segment.

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## DLA and DAS Functions

DSK files are instances of DLA files, which in turn are instances of DAS files. See the chapter ``DSK Files'' for further information.

Some lower-level functionality is provided by functions of the DLA and DAS subsystems. The routines below support linear traversal of the doubly linked list---also called ``searching'' the list---of DSK segments within a DSK file:

dasopr_c
  Open a DAS file for reading.

dascls_c
  Close a DAS file.

dlabfs_c
  Begin a forward segment search in a DLA file.

dlafns_c
  Find the segment following a specified segment in a DLA file.

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## Surface Name and ID Conversion Functions

The routines below map surface names to surface IDs and vice versa.

srfc2s_c
  Translate a surface ID code, together with a body ID code, to the corresponding surface name.

srfcss_c
  Translate a surface ID code, together with a body string, to the corresponding surface name.

srfs2c_c
  Translate a surface string, together with a body string, to the corresponding surface ID code.

srfscc_c
  Translate a surface string, together with a body ID code, to the corresponding surface ID code.

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## SPICE Toolkit DSK Utility Programs

The DSK utility programs included in the SPICE Toolkit are

DSKBRIEF
  Display summaries of one or more DSK files. See the DSKBRIEF User's Guide, dskbrief.ug.

MKDSK
  Create a DSK file from shape data provided in a text file. See the MKDSK User's Guide, mkdsk.ug.

DSKEXP
  ``Export'' (write) DSK data to one or more text files. See the DSKEXP User's Guide, dskexp.ug.

COMMNT
  Read, extract, append to, or delete the contents of a DSK file's comment area. See the COMMNT User's Guide, commnt.ug.

TOBIN, TOXFR
  Convert a transfer format DSK file to binary format, and vice versa. See the user's guide ``Converting and Porting SPICE Binary Data Files,'' convert.ug.

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## Non-SPICE Toolkit DSK Utility Programs

The utility programs below are not part of the SPICE Toolkit, but are available, as is their documentation, from the NAIF server.

BINGO
  Convert a binary DSK file from IEEE little-endian format to IEEE big-endian format, or vice versa.

DLACAT
  Concatenate DLA files (DSK files are instances of DLA files) into a single file.

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# DSK Concepts

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## Shapes and Surfaces

The terms ``shape data,'' ``surface data,'' and ``topography'' are generally used as synonyms in DSK documentation. The term ``surface,'' when applied to DSK data, refers solely to the geometric form of the surface---never to associated properties such as albedo or chemical composition.

The term ``surfaces'' is also used to refer to DSK data sets themselves, particularly when there are multiple data sets, differing in some aspects, that provide data for a given body. For example, Mars topography data sets based on MGS MOLA data might be referred to as the ``64 pixels/degree surface'' or the ``128 pixels/degree surface.''

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## Surface IDs

To facilitate run-time selection of DSK data, SPICE provides DSK segments with a second identifying attribute in addition to the ``central body'': the ``surface ID code'' (or ``surface ID''). Different DSK data sets for a given body may be assigned distinct surface IDs.

At run time, calls from user applications to CSPICE functions can restrict the DSK data used to those from specified surfaces. For example, a user application might direct the CSPICE sub-observer point function subpnt_c to to use a high-resolution surface for a spacecraft altitude computation, versus a low-resolution surface for plotting the spacecraft's ground track.

Because surface IDs enable SPICE applications to select data from among those available in loaded DSK files, it is not necessary for applications to repeatedly load and unload DSK files to control which shape data are used for a given body and computation. Applications normally can load at start-up all of the DSK data for a given body, then select the data to be used on a per-computation basis.

Avoiding repetitive DSK loading tends to improve an application's computation speed. This is because after any change to the set of loaded DSK files, the DSK subsystem must perform some bookkeeping computations before DSK-based computations can be performed. Degradation of overall execution speed due to these computations is slight as long as they're performed infrequently.

SPICE surface IDs are associated with surface names; these associations are made via assignments in SPICE text kernels. Surface name-ID associations are made for specific bodies: the combination of a body name or body ID and surface name can be mapped to a surface ID code, and the combination of a body name or body ID and a surface ID code can be mapped to a surface name.

A given surface ID code can be re-used for different bodies without ambiguity. For a given body, it's important for users to coordinate assignment of surface names and surface IDs.

The CSPICE functions for converting between surface IDs and surface names are listed in the section ``Surface Name and ID Conversion Functions'' above.

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### Defining Surface Name-ID Mappings

Surface name-to-ID mappings may be defined at run time by loading text kernels containing kernel variable assignments of the form

       NAIF_SURFACE_NAME += ( <surface name 1>, ... )
       NAIF_SURFACE_CODE += ( <surface code 1>, ... )
       NAIF_SURFACE_BODY += ( <body code 1>,    ... )

Above, the Ith elements of the lists on the assignments' right hand sides together define the Ith surface name/ID mapping.

The same effect can be achieved using assignments formatted as follows:

       NAIF_SURFACE_NAME += <surface name 1>
       NAIF_SURFACE_CODE += <surface code 1>
       NAIF_SURFACE_BODY += <body code 1>

       NAIF_SURFACE_NAME += <surface name 2>
       NAIF_SURFACE_CODE += <surface code 2>
       NAIF_SURFACE_BODY += <body code 2>

          ...

Note the use of the

       +=

operator; this operator appends to rather than overwrites the kernel variable named on the left hand side of the assignment.

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## Segments

Data in every DSK file are grouped into one or more subsets called ``segments.'' DSK segments are implemented as DLA segments, also called ``arrays.'' Each DSK segment has double precision and integer components.

Each DSK segment contains data for some or all of the surface of a single body object. This object is called the ``body,'' ``central body,'' or ``center,'' even though it need not be a natural solar system body.

Within a segment, the data have the following attributes in common:

`--` Body

`--` Surface

`--` Reference frame

`--` Coordinate system

`--` Coordinate system parameters, if applicable (for example, planetodetic equatorial radius and flattening coefficient)

`--` Spatial coverage bounds

`--` Time bounds

`--` Data type

`--` Data class

These attributes are discussed in the following sections.

When DSK files are loaded via one or more calls to furnsh_c, all segments from those files become available to the DSK subsystem for use in computations. At run time, when a request for shape data for a specified body is made to the DSK subsystem, all segments for that body can be considered as possible sources of data to satisfy the request.

For small DSK data sets, such as low-resolution shape models for asteroids, a single segment can suffice to store all of the data for the model. Large DSK data sets typically consist of tens or hundreds of segments distributed over multiple DSK files. Normally all segments for a given body can be loaded at one time. The limit on the total number of DSK segments for all bodies that can be loaded is given in Appendix B.

DSK utilities typically create or operate on segments:

`--` MKDSK creates a single-segment DSK file

`--` DSKBRIEF displays summary information for groups of segments having common attributes, or for individual segments

`--` DSKEXP exports data from DSK segments to separate output files

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### DLA and DSK Descriptors

Lower-level CSPICE DSK functions refer to DSK segments by means of data structures called DLA and DSK ``descriptors.''

The DLA descriptor of a DSK segment indicates the location of the segment's data in the DSK file containing that segment. DLA descriptors contain DAS base addresses and sizes of the double precision and integer components of the associated segments. DLA descriptors are integer arrays.

User applications can locate all segments in a DSK file by calling the DLA ``begin forward search'' routine dlabfs_c, then repeatedly calling the DLA ``find next segment'' routine dlafns_c. See the API documentation of those functions for details and code examples.

The DSK descriptor of a DSK segment contains the segment's attribute information; these are the attributes listed above. User applications can determine attributes of a DSK segment by obtaining the DLA descriptor of the segment, then calling the CSPICE function dskgd_c to obtain the segment's DSK descriptor.

See the chapter ``DSK Files'' for details.

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### Reference Frames

Each DSK segment has an associated reference frame. That frame is fixed to the central body. The center of the frame need not be the central body. For example, a segment containing data for Mars could use a topocentric reference frame centered at a specified surface point on Mars.

Within a DSK segment, all shape data are expressed relative to that segment's reference frame.

For example, if a segment containing data for Phobos uses the IAU_PHOBOS body-fixed frame, and if the segment contains vertices of triangular plates, the coordinates of those vertices are expressed in the IAU_PHOBOS reference frame.

The set of DSK segments to be used in a computation for a given body need not be associated with a single reference frame, but using data from mixed frames should be done cautiously. It is up to the user to combine data in ways that make sense.

For example, Mars data expressed in the Mars-centered IAU_MARS frame can be used together with Mars data expressed in one or more Mars topocentric frames.

On the other hand, it doesn't make sense to combine earth data expressed in the ITRF93 frame with data expressed in the IAU_EARTH frame, because those frames have some relative rotation. The same is true for data expressed in the IAU_MOON and MOON_ME frames: even though these are realizations of the same reference frame, the approximation error in the IAU_MOON frame is time-dependent, so these frames have relative rotation.

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### Coordinate Systems and Spatial Coverage

For the purpose of segment selection, the spatial coverage of a DSK segment is considered to be three-dimensional: it is a region of space within which the segment provides data for the associated body.

The supported coordinate systems are:

`--` Latitudinal (planetocentric)

`--` Planetodetic

`--` Rectangular

Planetocentric coordinates are appropriate for most natural bodies.

Planetodetic coordinates should be used only for large bodies having surfaces well approximated by spheroids.

Rectangular coordinates may be appropriate for data sets expressed in topocentric reference frames, for artificial structures, and for extremely irregular natural bodies.

A segment's coordinate system is used to represent the segment's coverage bounds.

For example, a DSK segment that uses the Phobos planetocentric coordinate system and IAU_PHOBOS reference frame might contain surface data for Phobos within the spatial region

       Planetocentric latitude:    -90 to  +90 degrees
       Planetocentric longitude:  -180 to +180 degrees
       Radius:                       0 to   10 km

Here the planetocentric coordinate system's equatorial plane is the X-Y plane of the IAU_PHOBOS frame. The prime meridian of the coordinate system lies in the frame's X-Z plane and intersects the +X axis of the frame.

Another example: a DSK segment that uses a Mars planetodetic coordinate system might contain surface data for Mars within the spatial region

       Planetodetic latitude:   -30 to +30 degrees
       Planetodetic longitude:  +60 to +90 degrees
       Altitude:                -10 to +20 km

Here the planetodetic coordinate system's equatorial plane is the X-Y plane of the segment's reference frame, for example the IAU_MARS frame. The prime meridian of the coordinate system lies in the frame's X-Z plane and intersects the +X axis of the frame. The altitude is measured relative to a reference spheroid, the size and shape parameters of which are contained in the segment.

A third example: a DSK segment that contains data for a horizon mask for a tracking station might use rectangular coordinates and a topocentric frame having axis directions

       X: north
       Y: west
       Z: up

The region covered by the segment might be

       X:   -0.5 to +0.5 km
       Y:   -0.5 to +0.5 km
       Z:   -0.2 to +0.2 km

In this case the horizon mask need not model the topography surrounding the station; it can simply model obscuration due to the topography. So the coverage region need not extend to the horizon; it can be contained in a small box enclosing the station.

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### Spatial coverage: Dimensions

The coverage bounds of a segment enable the DSK subsystem to rapidly determine whether the segment may be applicable for a given geometric computation such as a ray-surface intercept. For this purpose, it is convenient to consider the coverage of a segment to be three-dimensional.

For many applications, it is more natural to consider the spatial coverage of a segment to be two-dimensional. This is true when the surface represented by the segment can be expressed as a function that maps a two-dimensional region to radius or height values. For example, surface height relative to a reference spheroid can be a function of planetodetic longitude and latitude. In a topocentric frame, the Z coordinate of a surface can be a function of the X and Y coordinates.

In cases where a surface is viewed as a function of two coordinates, those coordinates are called the ``domain coordinates.'' In some DSK documentation, the terms ``horizontal'' or ``tangential'' coordinates may be used as synonyms.

The DSKBRIEF summary utility displays spatial coverage in three dimensions for individual segments. It treats spatial coverage as two-dimensional for the purpose of displaying combined coverage of multiple segments, and for displaying gaps within that combined coverage. For such displays, coverage and gaps will be displayed as longitude-latitude rectangles in the planetocentric or planetodetic systems, or as X-Y rectangles in the rectangular system.

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### Spatial coverage: Gaps and Padding

In general, the spatial bounds of a DSK segment don't imply that there is complete coverage of the domain coordinates within those bounds; spatial coverage can have gaps. In some cases this is an inevitable consequence of the shape of the body: for example, if the coordinate system is rectangular and the body is a torus lying on the X-Y plane, there will be no data for some (X,Y) coordinates.

Spatial coverage gaps also can occur due to the way data are grouped in segments by a DSK file's creator. Normally DSK file creators should ensure that segments don't have coverage gaps that users would not expect. Coverage gaps can cause geometric computations to fail at run time.

The concept of spatial coverage gaps normally applies to a segment's domain coordinates, such as longitude and latitude. It is also possible for a surface's maximum or minimum height, radius, or Z coordinate to be, respectively, strictly less than or strictly greater than the corresponding upper or lower bound. The term ``gap'' usually does not apply to such differences; these differences usually have no impact on computations.

Data for a segment need not be confined to the spatial region delimited by the spatial bounds. DSK creators can include in DSK segments ``padding'' data that extend slightly beyond the segments' spatial bounds. Padding data can ensure that coverage implied by a segment's domain coordinate bounds is really present.

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### Time Bounds

Segments in a DSK file provide data for a time interval determined by the DSK file's creator.

For a surface having a shape that evolves over a time span of interest, multiple versions of the surface corresponding to different time intervals can be created. When a computation is performed for a particular time, only segments providing data for time intervals that include that time will be considered.

In many cases the surface represented by a DSK segment is considered to be constant with respect to time, so the start and stop time bounds may be set, respectively, to values far in the past and future (for example, plus or minus one century) relative to the time range for which the segment is expected to be used.

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### Data Types

The DSK subsystem supports multiple forms of mathematical representations of shape data. For each such form, there is a corresponding DSK segment type and set of functions that can access segments of that type. Collectively the form of representation, the segment structure and associated software are called a ``DSK data type.''

DSK data type 2 represents body shapes using collections of triangular plates. Another DSK data type, not yet implemented, will represent surfaces as digital elevation models (DEMs).

The CSPICE system's high-level geometry functions operate without reference to the data types of DSK segments providing shape data to these routines. These routines require lower-level, type-dependent routines to provide functionality that is common across all DSK data types, such as ``find the intercept of a ray with the surface defined by a segment,'' or ``return the unit length outward normal vector at a specified point on the surface defined by a segment.''

Some CSPICE functions perform functions specific to particular data types. For example, the functions dskv02_c and dskp02_c return, respectively, vertices and plates from a type 2 segment.

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### Data Classes

The ``data class'' of a segment indicates aspects of the topology of the shape defined by that segment. There are currently two data classes:

`--` Class 1: single-valued surface. The surface is a single-valued function of the segment's domain coordinates.

`--` Class 2: arbitrary surface. Any surface for which there are multiple points for a given longitude and latitude, or for a given X and Y, belongs to class 2.

`` Surfaces that have features such as overhanging cliffs, arches, or caves belong to class 2.

`` Any DSK type 2 surface having an ``inward-facing'' plate---one for which the outward normal vector has negative dot product with any of the plate's vertices---is a class 2 surface.

`` The nucleus of the comet Churyumov-Gerasimenko is an example of a class 2 shape.

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## Data Competition and Priority

Two segments containing data for the same body, surface, location, and time are said to contain ``competing'' data. Segment priority is a scheme for determining which segment's data to use in case of competition.

Unlike the other SPICE binary kernel systems, the DSK subsystem does not necessarily make use of segment priority for a given computation. Instead, a user application can specify that a computation is ``unprioritized.'' This means that all loaded data for the given body and a specified list of surfaces are to be used together to represent the shape to be used in the computation.

When DSK data for different surfaces for one body are loaded concurrently, surface lists, which are inputs to CSPICE API functions that use DSK data, can be used to ensure that the correct set of DSK data are used for a given computation, and that none of the data compete. It is not necessary to load or unload DSK files to give the desired data top priority.

See the API documentation for any high-level CSPICE geometry function, for example sincpt_c, for a discussion of surface lists.

In the N0066 CSPICE Toolkit, all high-level geometry functions that work with DSK data support only unprioritized computations.

Although not currently used, the DSK subsystem does have a priority scheme: as in the SPICE SPK, CK, and binary PCK subsystems, when two segments from the same file compete, the one located later in the file (at higher addresses) takes precedence. When two segments from different files compete, the one from the file loaded later takes precedence.

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## Greedy Algorithms

A numerical problem affecting DSK computations is the possibility of ``false negatives'': finding no result when one should be expected. An example of this is not finding a ray-surface intercept when one clearly should exist.

The possibility of false negatives, at a minimum, complicates the design of user applications that depend on DSK data.

Aside from errors in DSK files themselves, the main cause of false negative results is round-off error.

Round-off error can cause a ray that should hit the common edge between two plates to be determined, according to double precision arithmetic, to miss both plates. Similarly, round-off error can cause a ray that should hit the common longitude boundary or latitude boundary shared by two DSK segments to hit neither segment boundary.

The DSK subsystem uses several techniques to avoid false negative results for ray-surface intercepts. These fall into the category of ``greedy algorithms'': they effectively treat segments and data as though they occupy not only the spatial regions implied by their boundaries, but the surrounding regions as well. (An examination of the default DSK ``greedy'' parameters will reveal that the greediness of DSK algorithms is a mild case. See ``Access to DSK Tolerances and Margin Values'' below.)

For example, when a ray-surface intercept computation is attempted, an intercept is considered to exist if the ray passes sufficiently close to the target---not only if it hits.

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### Greedy Ray-Segment Boundary Intercepts

In the discussion below, we refer to both ``segment boundaries'' and ``tangent surfaces.'' Both terms require definition:

Segment boundary
  This is the set of surfaces forming the boundary of the spatial region defined by the coordinate bounds in a segment's DSK descriptor. There are six such surfaces: for each one, one coordinate is at the segment's minimum or maximum value for that coordinate, and the other coordinates vary from their minimum to their maximum.

  For example, a segment using planetocentric latitudinal coordinates might have the longitude range 0:30 degrees, latitude range 0:45 degrees, and radius range 6300:6400 km. Then the segment's boundary on the sphere of radius 6400 km has longitude ranging from 0 to 30 degrees, and latitude ranging from 0 to 45 degrees.

Tangent surface
  This a ``level surface'' in geometric terms: a surface defined by setting one coordinate to a segment's minimum or maximum bound for that coordinate. For the segment above, the sphere of radius 6400 km is one such tangent surface. As in this example, the tangent surfaces may include areas that are not part of the segment's boundary.

One step in the ray-surface intercept computation is determination of the set of applicable segments that are hit by the ray. The segments that have the appropriate attributes are tested to see whether the ray hits the tangent surfaces defined by the coordinate ranges in the segments' DSK descriptors.

By default, when the ray's intersection with a segment's tangent surface is computed, if that intersection is close to the spatial region indicated by the segment's boundaries, an intersection with the segment is considered to exist. In the example we're using, a ray's intersection with the sphere of radius 6400 km that has longitude slightly greater than 30 degrees and latitude slightly greater than 45 degrees could be considered an intersection with the segment's boundary, if the longitude and latitude excursions are within margins.

The goal is to ensure that any segment that the ray might hit is considered for a more detailed intercept computation.

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### DSK Type 2 Plate Expansion

By default, to eliminate the problem of false negatives from ray-surface intercept computations, where the surface is defined by the data in a selected type 2 segment, the DSK type 2 ray-surface intercept computation expands plates slightly before attempting to compute the ray's intersection with them. The expansion is done by scaling up, by a factor slightly greater than 1, each of a plate's centroid-vertex vectors. The expanded plate lies in the plane of the original plate, its edges are parallel to those of the original plate, and its centroid coincides with that of the original plate.

The default plate expansion fraction is 1e-10. The expansion factor is

       1 + expansion_fraction

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### Additional Greedy Algorithms

Greedy algorithms are also used for

`--` Determining whether a ray-plate intercept, once found, is close enough to a segment's boundary to be considered inside the segment

`--` Determining whether a point is close enough to a plate to be considered to belong to that plate

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### DSK Tolerances

Some DSK tolerance parameters do not strictly support ``greedy'' behavior, but rather enhances the DSK software's usability. For example, there is a DSK parameter that is used to decide whether a longitude value is close enough to a segment's longitude range to be considered to lie within that range. Another tolerance parameter is used to decide whether angular values are valid. For example, a latitude that exceeds pi/2 radians by a positive number less than this tolerance is treated as though it were exactly pi/2.

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### Drawbacks

A possible negative consequence of greedy algorithms is that some results derived using them may be quite different from those derived without them.

For example, if a ray hits the edge of an expanded plate, and that plate has a maximum edge length of 1 km, then the ray might have missed the original plate by as much as 0.1 millimeters. After missing the original plate, the ray might hit the surface far from that plate, or it might miss the target altogether.

This issue, while it may appear serious, is a normal consequence of using finite precision arithmetic. A comparable difference in results might be observed were the computation without plate expansion performed on two different computer systems.

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### Access to DSK Tolerances and Margin Values

The greedy algorithms described above rely on tolerance parameters. These and other DSK tolerance and margin parameters are assigned default values in the header file SpiceDtl.h.

The parameters used for greedy algorithms are user-adjustable. Applications can call the functions dskgtl_c or dskstl_c to fetch or reset these parameters at run time.

It is recommended that the parameters be reset only by expert users.

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# DSK Files

The SPICE DSK file format is designed to support rapid access to large data sets. It is designed to be portable, and to support inclusion of documentation within DSK files.

The DSK file format is based on two lower-level SPICE file formats: the DSK format is a special case of the SPICE DLA format, which in turn is a special case of SPICE DAS format.

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## DAS Files

Most DSK properties are inherited from the ``Direct Access Segregated'' (DAS) specification. The properties visible to SPICE users are:

`--` Binary file format: integers and double precision numbers are stored in binary format for compactness and speed of read access.

`--` Direct access: data from any part of the file can be read in constant time, aside from latency of the storage medium.

`--` Array abstraction: the data portion of a DAS file appears to user application code as three arrays of contiguous data: one each of characters, integers, and double precision numbers. User applications can, for example, directly read the Nth double precision number from a DAS file. Fortran I/O features such as record numbers, record lengths, and logical units (or C emulations of these features) are hidden from the user application's view.

`--` Portability: DAS files can be transferred from IEEE big-endian to IEEE little-endian platforms, and vice-versa, requiring no modification to be readable on the target platform.

`` DAS files can be transferred to ANY platform on which CSPICE is supported; this is done by first converting the files to an ASCII ``transfer'' format on the source platform, moving the files, then converting the transfer format files to binary files on the target platform.

`--` Platform-independent buffering: DAS software buffers data read from DAS files using a built-in mechanism that's independent of any buffering mechanism provided by the host platform.

`--` Comment area: DAS files contain a data structure called the ``comment area''; this area can contain an arbitrary quantity of free-form, ASCII text. The comment area enables DAS file creators to include explanatory documentation in the files.

`` The SPICE Toolkit contains API functions to access the comment area. Also, the Toolkit contains a utility program, COMMNT, that can read, delete, or append to comments in the comment area.

See the DAS Required Reading das.req for details concerning the DAS subsystem and DAS file format.

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## DLA Files

The DLA file format organizes data into a doubly linked list of virtual segments. DLA functions enable application software to traverse such segment lists. Since the DSK file format is an instance of the DLA format, this traversal capability is inherited by the DSK subsystem.

DLA files indicate the DAS addresses and sizes of their segments' character, double precision, and integer components using data structures called ``DLA descriptors.'' The DLA segment descriptor members are:

       +---------------+
       | BACKWARD PTR  | Linked list backward pointer
       +---------------+
       | FORWARD PTR   | Linked list forward pointer
       +---------------+
       | BASE INT ADDR | Base DAS integer address
       +---------------+
       | INT COMP SIZE | Size of integer segment component
       +---------------+
       | BASE DP ADDR  | Base DAS d.p. address
       +---------------+
       | DP COMP SIZE  | Size of d.p. segment component
       +---------------+
       | BASE CHR ADDR | Base DAS character address
       +---------------+
       | CHR COMP SIZE | Size of character segment component
       +---------------+

The ``base address'' of a segment component of a given data type is the address, in the DAS address space of that type, preceding the first element of that component. All DAS addresses are 1-based.

DLA descriptors are used in the DSK subsystem to identify locations of the components of DSK segments within DSK files.

See the DLA Required Reading, dla.req, for details concerning the DLA subsystem and file format.

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## DSK File Format

For the majority of practical DSK applications, the DSK file format can be adequately understood using the following simplified model:

       +----------------------------------+
       |            File Record           |
       +----------------------------------+
       |            Comment Area          |
       +----------------------------------+
       |            Segment 1             |
       +----------------------------------+  -+
       |            ...                   |   |
       +----------------------------------+   | Optional
       |            Segment N             |   |
       +----------------------------------+  -+

That is, a DSK file contains some identification and bookkeeping information called a ``file record,'' it has a comment area, and it has one or more DSK segments containing shape data.

The segments are connected to each other as a doubly linked list, and the list can be traversed in forward or backward order. (In the N0066 Mice and Icy Toolkits, only forward traversal is supported.)

Each DSK segment has integer and double precision components. These components occupy, respectively, contiguous ranges of DAS integer and double precision addresses:

       +----------------------------------+
       |            Segment I             |  =
       +----------------------------------+

       +--------------+     +------------------+
       |              |     |                  |
       |  Segment I:  |     |    Segment I:    |
       |              |     |                  |
       |   Integer    |  +  |     Double       |
       |   Component  |     |     Precision    |
       |   (optional) |     |     Component    |
       |              |     |                  |
       +--------------+     |                  |
                            |                  |
                            +------------------+

The double precision component of a segment can be further expanded as:

       +------------------+
       |                  |
       |    Segment I:    |
       |                  |
       |     Double       |
       |     Precision    |   =
       |     Component    |
       |                  |
       |                  |
       +------------------+

       +--------------+     +------------------+
       |  Segment I:  |     |    Segment I:    |
       |              |     |                  |
       |  DSK Segment |  +  |     Double       |
       |  Descriptor  |     |     Precision    |
       +--------------+     |     Data         |
                            |     (optional)   |
                            |                  |
                            |  +  Bookkeeping  |
                            |     Information  |
                            |     (optional)   |
                            |                  |
                            +------------------+

The base addresses and sizes of a DSK segment's integer and double precision components are given by the segment's DLA descriptor. The DAS integer address range of a DSK segment is

       integer base address+1 : integer base address+
                                integer component size

Similarly, the DAS double precision address range of a DSK segment is

       d.p. base address+1 : d.p. base address+
                             d.p. component size

Low-level details of the general DSK file format, if not discussed in this document, can be obtained from the DAS Required Reading, das.req, and from the DLA Required Reading, dla.req.

An abstract view of a DSK segment---a view that ignores physical file layout and numeric data types---is

                   DSK segment =

       +-------------------------------------+
       |            DSK Descriptor           |
       +-------------------------------------+
       |      Type-specific shape data       |
       +-------------------------------------+
       | Type-specific ancillary information |
       +-------------------------------------+

DSK segments of all data types contain DSK descriptors.

Further details of the DSK segment's structure are data type-dependent. Currently there is just one DSK data type: type 2. It is discussed below.

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# DSK Type 2: Triangular Plate Model

The following discussion of shape data may be of interest to any DSK users. The discussion of type 2 ancillary information is quite detailed and likely is not of interest to most DSK users. It may be useful for DSK creators, especially those interested in optimizing performance.

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## Type 2 Shape Data

DSK type 2 represents shapes of objects as collections of triangular plates. This data type can model nearly any shape: the shape need not be smooth, connected, or continuously deformable to sphere.

Each triangular plate has three vertices: type 2 data consist of a set of vertices and a set of ``plates'' to which the vertices belong.

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### Vertices

Vertices are vectors in three-dimensional space: each vertex is represented by a double precision array consisting of the vertex's X, Y, and Z components, in that order.

The components of a vertex are expressed in the body-fixed reference frame of the DSK segment to which the vertex belongs. Each vertex represents an offset from the center of that reference frame.

The center of a type 2 segment's reference frame need not coincide with the body for which the segment provides data. For example, vertices for a DSK segment representing Mars topography might be expressed in a Mars topocentric frame; the vertices would then represent offsets from the Mars surface point at the center of that frame.

Within a type 2 segment, vertex components are always expressed in units of km, regardless of the units associated with the input data from which the segment was constructed.

Each vertex has an associated integer ID; vertex IDs range from 1 to NV, where NV is the number of vertices in the segment. This 1-based numbering scheme is used for all language versions of SPICE, so the vertex IDs in a DSK file match those used in SPICE DSK code on all platforms.

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### Plates

The term ``plate'' refers to both a planar surface with a triangular boundary in 3-dimensional space, and to a data structure.

As a data structure, a plate is a 3-tuple of integer vertex IDs that indicate which vertices belong to that plate.

Each plate has an associated ``outward normal'' direction: this direction is perpendicular to the plate. For surfaces that constitute boundaries of solid objects---for example, a sphere---the outward normal direction has the usual meaning: it points toward the exterior of the object. For other surfaces, for example a single plate, the outward normal direction may be an arbitrary choice.

The order of a plate's vertices implies the outward normal direction: if the vertices are

       V(1), V(2), V(3)

then the outward normal direction is

       ( V(2) - V(1) )  x  ( V(3) - V(2) )

where ``x'' denotes the vector cross product operator.

DSK creators must take vertex order into account when they define the plates of a DSK type 2 segment.

As the formula above shows, the outward normal direction is undefined if two or three vertices of a plate coincide; in this case the ``plate'' is actually a line segment or a point. Plates having these characteristics are termed ``degenerate.'' Even if all of a plate's vertices are distinct, the normal direction vector suffers great loss of precision if the angle between two plate edges is very close to zero.

Degenerate and nearly degenerate plates are allowed in type 2 segments, but it is strongly recommended that DSK creators exclude them from input data sets. Such plates can cause run-time failures of user applications performing functions that require outward normal directions to exist, for example computing emission and solar incidence angles.

Each plate has an associated integer ID; plate IDs range from 1 to NP, where NP is the number of plates in the segment. This 1-based numbering scheme is used for all language versions of SPICE, so the plate IDs in a DSK file match those used in SPICE DSK code on all platforms.

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## Type 2 Ancillary Information

Much of the ``added value'' provided by DSK type 2 segments derives from their spatial indexes: these enable rapid association between spatial regions and plates, and between vertices and plates.

A DSK type 2 spatial index consists of a ``voxel-plate mapping'' and optionally, a ``vertex-plate mapping,'' as well as various associated parameters.

All DSK type 2 segments contain a voxel-plate mapping. This mapping enables DSK type 2 software to rapidly determine which plates are near a specified ray or point.

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## Pointers and Offsets

In a DSK type 2 segment, integers that refer to locations of data or ancillary information are called ``pointers'' or ``offsets.'' In this context ``pointer'' is not a Fortran data type (Fortran 77 does not have a pointer type) but an indication of the role of the integer.

In a DSK type 2 segment, pointers and offsets are expressed relative to the DAS base addresses of that segment, or relative to the DAS addresses of other members of the segment. This ensures that the segment is ``relocatable'': it has no dependence on its absolute DAS addresses and can be moved or copied without corrupting its contents.

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## DSK Type 2 Segment Parameters

The DSK type 2 parameters are constant values stored in both the integer and double precision components of a DSK type 2 segment. These are distinct from parameters belonging to the segment's DSK descriptor.

A subset of these parameters refer to the segment's voxel grids. They are listed here; they are explained later in context.

The integer parameters are:

`--` Vertex count

`--` Plate count

`--` Fine voxel count (redundant, used for convenience)

`--` Fine voxel grid extents in the X, Y, and Z directions

`--` Coarse voxel scale

`--` Size of voxel-plate pointer array

`--` Size of voxel-plate association array

`--` Size of vertex-plate association array

The double precision parameters are:

`--` Fine voxel size (km)

`--` Vertex bounds in the X, Y, and Z directions (km)

`--` Voxel grid origin (3-vector, km)

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## Spatial Index: Voxel-Plate Mapping

The voxel-plate mapping associates regions of space with plates that intersect those regions.

The voxel-plate mapping plays a critical role in DSK geometry computations, because it enables plates relevant to computation to be located quickly:

`--` For ray-surface intercept computations, the voxel-plate mapping is used to quickly find the plates that are close enough to the ray to be tested for intersection.

`--` For association of an individual point with a plate, the voxel-plate mapping is used to quickly find plates that are close enough to the point so that inclusion of the point by those plates should be tested.

The voxel-plate mapping is implemented as a data structure comprising four sub-structures and several associated parameters. The sub-structures are

`--` The fine voxel grid (aka the ``fine grid'')

`--` The coarse voxel grid (aka the ``coarse grid'')

`--` The voxel-plate pointer array

`--` The voxel-plate association array

The structures refer to each other as shown in the following diagram:

       +---------------+
       |               |
       |               |
       |               |
       |               |                                  +-------------+
       |               |                                  |             |
       |               |                                  |             |
       |               |                                  |             |
       |               |                +-------------+   |             |
       |               |                |             |   |             |
       |               |   +--------+   |             |   |             |
       |               |   |        |   |             |   |             |
       |     Fine      |   | Coarse |   | Voxel-plate |   | Voxel-plate |
       |     voxel     |-->|  voxel |-->|   pointer   |-->| association |
       |     grid      |   |  grid  |   |    array    |   |    array    |
       |               |   |        |   |             |   |             |
       |               |   +--------+   |             |   |             |
       |               |                |             |   |             |
       |               |                +-------------+   |             |
       |               |                                  |             |
       |               |                                  |             |
       |               |                                  |             |
       |               |                                  +-------------+
       |               |
       |               |
       |               |
       +---------------+

The structures shown above enable DSK software to map a point in 3-dimensional space to a set of nearby plates as follows:

`1.` The fine voxel containing the point is identified. This is done by a constant-time arithmetic calculation.

`2.` The coarse voxel containing the fine voxel is identified. This is done by a constant-time address calculation.

`3.` The voxel-plate pointer corresponding to the fine voxel is identified. This is done by a constant-time address calculation.

`4.` The list of plates associated with the voxel is fetched. The time used by this process is linear with respect to the count of the voxel's associated plates.

These structures are described in detail in the following sections.

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### Fine Voxel Grid

The fine voxel grid is an array, also called a ``grid,'' of cubical regions in 3-dimensional space. The cubical regions are called ``fine voxels'' or simply ``voxels'' when the term is unambiguous. The overall shape of the grid is that of a box (a 3-dimensional solid having six rectangular sides).

The sides of the grid are aligned with the coordinate axes of the DSK segment's reference frame.

A segment's fine voxel grid contains all vertices in the segment (and therefore all plates); a small margin is used so that no plate contacts the grid's boundary. Thus no point on or outside of the grid's boundary can touch a plate.

The fine voxel grid is fully characterized by

`--` An origin. This is a 3-vector representing an offset from the reference frame's center. The origin is always placed at the minimum X, Y, and Z coordinates of the grid.

`--` A voxel size. This is the common edge length of the cubes making up the grid. Units are km. See the discussion of the ``fine voxel scale'' below.

`--` X, Y, and Z grid extents. These are the counts of the grid's fine voxels in the directions of the reference frame's coordinate axes.

The fine voxel grid is not implemented by a physical array; there is no storage cost associated with a large count of fine voxels. (There are consequences other than storage cost if the fine voxel size is too small: see the section below titled ``Size of the Voxel-Plate Association Array.'')

The diagram below shows the position of the fine voxel grid relative to its origin, the orientation of the grid relative to the reference frame's axes, and the relationship between the grid extents and the dimensions of the fine voxel grid.

In this diagram

`--` VGREXT is a 3-dimensional integer array containing the X, Y, and Z grid extents

`--` VOXSIZ is the fine voxel edge length, in km

`--` O represents the grid's origin

                            .------------.       ^ fine voxel count =
                           /            /|       | VGREXT(3)
                          /            / |       |
                         /            /  |       | length =
                        /            /   |       | VGREXT(3) * VOXSIZ (km)
        ^ +Z           /            /    .    .  v
        |    .        .------------.    /    /
        |   /         |            |   /    /
        |  /+Y        |            |  /    /  fine voxel count = VRGEXT(2)
        | /           |            | /    /
        |/            |            |/    /  length =
        *------->     O------------*    *   VGREXT(2) * VOXSIZ (km)
           +X
                      <------------>

       fine voxel count = VGREXT(1)
       length           = VGREXT(1) * VOXSIZ (km)

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### Fine Voxel Scale

The fine voxel scale is a parameter that relates the fine voxel size (referred to above as VOXSIZ) to the average extent of the plates in a DSK type 2 segment.

A plate's ``extent'' in the direction of coordinate axis i is the maximum value of coordinate i, taken over the plate's three vertices, minus the minimum value of coordinate i, also taken over the plate's three vertices. The average extent of a segment's plate set is the average of all the the plates' extents in the X, Y, and Z directions.

The fine voxel scale maps the plate set's extents to a voxel size by:

       VOXSIZ  = file_voxel_scale * average_plate_extent

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### Coarse Voxel Grid

The coarse voxel grid is a data structure that represents the same spatial region as the fine voxel grid. Unlike the fine grid, the coarse grid is implemented by an array in the DSK segment. The term ``coarse voxel grid'' may refer to either the spatial region or the data structure, depending on context.

The voxels of the coarse grid are cubes of identical size. The edge length of the coarse voxels is an integer multiple of the fine voxels' edge length. Let CGRSCL represent this multiple; then each coarse voxel contains

             3
       CGRSCL

fine voxels.

We use the term ``parent'' to refer to the unique coarse voxel that contains a specified fine voxel.

Each extent of the fine voxel grid is

       CGRSCL

times the corresponding extent of the coarse grid.

The diagram below shows the relationship between the coarse voxel grid's extents and edge lengths. The integer array VGREXT, as above, contains the extents of the fine voxel grid. The parameter VOXSIZ contains the fine voxels' edge length.

             .------------.       ^  coarse voxel count =
            /            /|       |  VGREXT(3) / CGRSCL
           /            / |       |
          /            /  |       |  length =
         /            /   |       |  VGREXT(3) * VOXSIZ (km)
        /            /    .    .  v
       .------------.    /    /
       |            |   /    /  coarse voxel count = VRGEXT(2)/CGRSCL
       |            |  /    /
       |            | /    / length =
       |            |/    /  VGREXT(2) * VOXSIZ (km)
       *------------*    *

       <------------>

       coarse voxel count = VGREXT(1) / CGRSCL
       length             = VGREXT(1) * VOXSIZ (km)

In the description below, the term ``integer'' refers to an element of the DAS integer address space.

The DSK integer array representing the coarse voxel grid has one element for each coarse voxel. If any plates intersect the spatial region corresponding to a coarse voxel, the corresponding coarse voxel grid array element contains a pointer into the voxel-plate pointer array. If no plates intersect that spatial region, the voxel contains the value zero, which represents a null pointer. (Caution: for reasons of backward compatibility, the values zero and -1 are used in different parts of DSK type 2 segments indicate null pointers.)

Note that during the construction of a spatial index, plate-voxel ``intersection'' may be determined using a margin so that plates very near a voxel are considered to intersect it. This is the case for DSK type 2 segments created by dskw02_c and by MKDSK.

A non-null pointer in a given coarse voxel is a 1-based index of a pointer set within the voxel-plate pointer array. The pointer set indicates the locations of plate lists associated with the fine voxels having the coarse voxel as a parent.

The maximum coarse voxel count within a segment, SPICE_DSK02_MAXCGR, is set to

       100000

This value cannot be changed in any future version of SPICE.

The value is small enough to make it practical for DSK type 2 software to buffer the entire coarse voxel grid in memory.

In all DSK type 2 segments, SPICE_DSK02_MAXCGR integers are allocated for the coarse voxel grid, even if the grid is smaller.

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### Purpose of the Coarse Voxel Grid

Below, the term ``empty'' means ``not intersected by any plates.''

The coarse voxel grid allows type 2 segments to avoid storing pointers for all fine voxels, since only fine voxels belonging to non-empty coarse voxels require pointers. Since in many practical cases, the majority of coarse voxels are empty, this often greatly reduces the required number of pointers.

The coarse voxel grid also tends to reduce the number of physical file reads necessary to determine the plate set relevant to a given computation, since DSK type 2 software often can use it to quickly determine that a given fine voxel is empty, without looking up a voxel-plate pointer and then a plate list for that voxel. Any fine voxel that belongs to an empty coarse voxel is empty as well, and typically the majority of empty fine voxels do belong to empty coarse voxels.

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### Voxel-Plate Pointer Array

The voxel-plate pointer array contains a contiguous set of pointers for each non-empty coarse voxel. There is one pointer for each fine voxel having the associated coarse voxel as a parent. Each such ``pointer'' is a 1-based index in the voxel-plate association array of the start of the plate list corresponding to a fine voxel. Null pointers in this structure are indicated by the value -1.

The pointer set for a given coarse voxel contains one pointer for each fine voxel having that coarse voxel as a parent, so there are

             3
       CGRSCL

pointers in each set.

Let NNECVX indicate the number of non-empty coarse voxels. Then the voxel-plate pointer array has the form:

       +---------------------+
       |  pointer set 1      |
       +---------------------+
                 ...
       +---------------------+
       |  pointer set NNECVX | (number of non-empty coarse voxels)
       +---------------------+

The mapping from the coarse voxel grid to pointer sets in the voxel-plate pointer array is determined by the segment's data, the voxel grid parameters, and the order in which the data are processed. As indicated in the following diagram, no particular relationship should be assumed to exist between a non-empty coarse voxel's coordinates in the coarse grid and the position of its pointer set in the voxel-plate pointer array:

       Coarse voxel grid            Voxel-plate pointer array

                                     +--------------------------------+
                                  .->| pointer set for coarse voxel v |
                                 /   +--------------------------------+
                                /
       +----------------+      /
       |   NULL         |     /
       +----------------+    /
       | coarse voxel u |--./                       ...
       +----------------+  /\
       | coarse voxel v |-*  \
       +----------------+     \
            ...                \     +--------------------------------+
       +----------------+       *--> | pointer set for coarse voxel u |
       |   NULL         |            +--------------------------------+
       +----------------+                           ...
       | coarse voxel w |--.
       +----------------+   \        +--------------------------------+
       |   NULL         |    *-----> | pointer set for coarse voxel w |
       +----------------+            +--------------------------------+

Above, the letters

       u, v, w

indicate arbitrary voxel indices. The positions of the null values were selected for this example. They're not representative of an actual DSK segment.

Within the voxel-plate pointer array, each pointer set has the form:

       +-----------+
       |  pointer  | voxel 1
       +-----------+
            ...
       +-----------+
       |  pointer  | voxel CGRSCL**3
       +-----------+

Each pointer corresponds to a fine voxel in the coarse voxel associated with the pointer set. Treating the fine voxels in this coarse voxel as a 1-dimensional array, the first fine voxel maps to the first pointer, and so on. The ordering of the fine voxels is Fortran-style, so a fine voxel with 1-based indices (I, J, K) relative to its parent coarse voxel has the one-dimensional index

                                           2
       I   +  (J-1)*CGRSCL  +  (K-1)*CGRSCL

The fine voxel with coordinates (1, 1, 1) relative to the parent coarse voxel is located in parent voxel's corner having minimum X, Y, and Z values in the Cartesian coordinate system associated with the segment's reference frame.

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### Voxel-Plate Association Array

The voxel-plate association array contains, for each non-empty fine voxel, a list of plate IDs identifying the plates that intersect that voxel, and a plate count.

Let NNEFVX be the total number of non-empty fine voxels in the fine grid. Let

       v_1, v_2, ..., v_NNEFVX

indicate NNEFVX indices of non-empty fine voxels in arbitrary order. The voxel-plate association array has the form:

       +-------------------------+
       | List for voxel v_1      |
       +-------------------------+
       | List for voxel v_2      |
       +-------------------------+
                   ...
       +-------------------------+
       | List for voxel v_NNEFVX | (number of non-empty fine voxels)
       +-------------------------+

Let N be the number of plates in the plate list for voxel v_i. Let

       p_1, p_2, ..., p_N

be the plate IDs of these plates. The plate list for the fine voxel at index v_i has the form

       +--------------------+
       | List count = N     |
       +--------------------+
       | Plate ID p_1       |
       +--------------------+
                ...
       +--------------------+
       | Plate ID p_N       |
       +--------------------+

The mapping from a pointer in the voxel-plate pointer array to a plate list in the voxel-plate association array is determined by the segment's data, the voxel grid parameters, and the order in which the data are processed. As indicated in the following diagram, no particular relationship should be assumed to exist between the position of a pointer in the voxel-plate pointer array and the position of the corresponding plate list in the voxel-plate association array:

       Voxel-plate                     Voxel-plate association array
       pointer array
                                     +-------------------------------+
                                  .->| plate list for voxel u_2      |
                                 /   +-------------------------------+
                                /
                               /
         pointer set u        /
       +----------------+    /
       | voxel u_1      |--./                       ...
       +----------------+  /\
       | voxel u_2      |-*  \
       +----------------+     \
             ...               \     +-------------------------------+
       +----------------+       *--->| plate list for voxel u_1      |
       |   NULL         |            +-------------------------------+
       +----------------+                           ...
       | voxel u_n      |--.
       +----------------+   \        +-------------------------------+
       |   NULL         |    *------>| plate list for voxel u_n      |
       +----------------+            +-------------------------------+

               3
         CGRSCL  elements

Above, the letter ``u'' indicates an arbitrary pointer set in the voxel-plate pointer array, which contains NNECVX such sets. The positions of the null values were selected for this example. They're not representative of an actual DSK segment.

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### Size of the Voxel-Plate Association Array

This section likely is of interest only to DSK creators.

Other than the optional vertex-plate association array, the voxel-plate association array is the largest ancillary data structure in a DSK type 2 segment. The size, in units of integers, of this array is affected by the fine voxel scale, which is a user-selectable parameter. For a given plate and vertex set, the size of fine voxels varies in proportion to the fine voxel scale.

Let NVOXPL be the size, in units of integers, of the voxel-plate association array; as above, let NNEFVX be the total count of non-empty fine voxels; let NP be the segment's plate count. A lower bound on NVOXPL is

       NNEFVX + NP

This number reflects the plate counts for the plate lists of each non-empty fine voxel, plus the presence of each plate ID on at least one list.

Normally, a large number of plates cross voxel boundaries and so have their IDs on multiple lists. Hence NVOXPL is normally larger than the lower bound shown above.

Reducing the fine voxel size improves the discrimination of the fine grid, which can improve the efficiency of algorithms that must operate on plates associated with a specified spatial region. For example, in the ray-surface intercept computation, the count of plates associated with voxels intersected by the ray will usually decrease as the voxel size is reduced.

However, as the fine voxel size is reduced, more plates cross voxel boundaries---such plates are on the plate list of each voxel they touch---and NVOXPL increases. The memory required to hold the spatial index increases as well; it may become too large to allow a program calling dskw02_c (the utility MKDSK is one such program) to run successfully. If a DSK segment with a very large value of NVOXPL is successfully created, its large size may have a detrimental effect on disk access time.

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## Spatial Index: Vertex-Plate Mapping

Recall that a ``plate'' is a 3-tuple of integer vertex IDs. Given a vertex ID, the vertex-plate mapping enables DSK software to quickly find the plates that include that vertex ID as one of their own. This enables geometric algorithms to quickly find the plates that lie close to a given plate.

Currently (as of the time of release of the N0066 SPICE Toolkit) there are no CSPICE routines that rely on the vertex-plate mapping. Creation of this mapping is therefore optional. Both the DSK type 2 writer function dskw02_c and the utility program MKDSK enable users to indicate whether to create a vertex-plate mapping in an output DSK segment.

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### Structure of the Vertex-Plate Mapping

The vertex-plate mapping consists of two arrays in DAS integer address space: the vertex-plate pointer array and the vertex-plate association array. Elements of the former array refer to positions in the latter:

                           +--------------+
                           |              |
                           |              |
       +---------------+   |              |
       |               |   |              |
       |               |   |              |
       |               |   |              |
       | Vertex-plate  |-->| Vertex-plate |
       | pointer array |   | association  |
       |               |   |   array      |
       |               |   |              |
       +---------------+   |              |
                           |              |
                           |              |
                           +--------------+

Let NV be the number of vertices in the segment. Then the vertex-plate pointer array contains NV elements, and the ith element indicates the plate list associated with vertex i.

The vertex-plate association array contains a plate list for each vertex:

       +----------------------+
       | List for vertex v_1  |
       +----------------------+
       | List for vertex v_2  |
       +----------------------+
                 ...
       +----------------------+
       | List for vertex v_NV |
       +----------------------+

Let N be the number of plates in the plate list for vertex i. Let

       p_1, p_2, ..., p_N

be the plate IDs of these plates. The plate list for vertex i has the form

       +--------------------+
       | List count = N     |
       +--------------------+
       | Plate ID p_1       |
       +--------------------+
                ...
       +--------------------+
       | Plate ID p_N       |
       +--------------------+

The mapping from a vertex to a plate list in the vertex-plate association array is determined by the segment's data, the voxel grid parameters, and the order in which the data are processed. No particular relationship should be assumed to exist between a vertex ID and the position of the corresponding plate list in the vertex-plate association array.

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### Size of the Vertex-Plate Mapping Array

This section likely is of interest only to DSK creators.

Let NV be a DSK type 2 segment's vertex count, and let NP be the segment's plate count. Then the size, in units of integers, of the vertex-plate pointer array is

       NV

and the size of the vertex-plate association array is

       NV  +  3*NP

The latter value is due to the facts that

`--` Each plate ID is on exactly three lists

`--` There is a list for each of the NV vertices

`--` Each list contains a plate count

The potentially large size of the vertex-plate association array makes the optional vertex-plate mapping a good candidate for omission when a DSK type 2 segment is created.

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## Layout of DSK Type 2 Segments

Below we describe the organization of integer and double precision data and ancillary information in DSK type 2 segments.

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### DSK Type 2 Integer Segment Component

The layout in DAS integer address space of the integer items in a DSK type 2 segment is:

          +-----------------+
          | NV              |   number of vertices
          +-----------------+
          | NP              |   number of plates
          +-----------------+
          | NVXTOT          |   total number of voxels
          +-----------------+
          | VGREXT          |   voxel grid extents, 3 integers
          +-----------------+
          | CGRSCL          |   coarse voxel grid scale
          +-----------------+
          | VOXNPT          |   size of voxel-plate pointer list
          +-----------------+
          | VOXNPL          |   size of voxel-plate association list
          +-----------------+
          | VTXNPL          |   size of vertex-plate association list
          +-----------------+
          | PLATES          |   NP 3-tuples of vertex IDs
          +-----------------+
          | VOXPTR          |   voxel-plate pointer array, variable size
          +-----------------+
          | VOXPLT          |   voxel-plate association list, variable size
          +-----------------+
          | VTXPTR          |   vertex-plate pointer array, 0 or
          |                 |   NV integers
          +-----------------+
          | VTXPLT          |   vertex-plate association list,
          |                 |   0 or NV + 3*NP integers
          +-----------------+
          | CGRPTR          |   coarse grid pointers,
          |                 |   SPICE_DSK02_MAXCGR integers
          +-----------------+

The sizes of all variable-size items are stored at known locations, so the starting position of any item can be calculated. Parameters specifying offsets of the items from the segment's base integer address are declared in SpiceDSK.h. The segment's base integer address is available from the segment's DLA descriptor.

CSPICE provides the low-level utility function dski02_c to fetch any of the items shown above. Plates and the plate count may be fetched more conveniently using the routines dskp02_c and dskz02_c.

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### DSK Type 2 Double Precision Segment Component

The layout in DAS double precision address space of the double precision items in a DSK type 2 segment is:

          +-------------------+
          | DSK descriptor    |  SPICE_DSK_DSCSIZ d.p. values
          +-------------------+
          | Vertex bounds     |  6 d.p. values (min/max for each component)
          +-------------------+
          | Voxel grid origin |  3 d.p. values
          +-------------------+
          | Fine voxel size   |  1 d.p. value
          +-------------------+
          | Vertices          |  3*NV d.p. values
          +-------------------+

The parameter SPICE_DSK_DSCSIZ is declared in SpiceDSK.h.

CSPICE provides the low-level utility function dskd02_c to fetch any of the items shown above. Vertices and the vertex count may be fetched more conveniently using the routines dskv02_c and dskz02_c.

The DSK segment descriptor layout is:

          +---------------------+
          | Surface ID code     |
          +---------------------+
          | Center ID code      |
          +---------------------+
          | Data class code     |
          +---------------------+
          | Data type           |
          +---------------------+
          | Ref frame code      |
          +---------------------+
          | Coord sys code      |
          +---------------------+
          | Coord sys parameters|  10 d.p. values
          +---------------------+
          | Min coord 1         |
          +---------------------+
          | Max coord 1         |
          +---------------------+
          | Min coord 2         |
          +---------------------+
          | Max coord 2         |
          +---------------------+
          | Min coord 3         |
          +---------------------+
          | Max coord 3         |
          +---------------------+
          | Start time          |
          +---------------------+
          | Stop time           |
          +---------------------+

The DSK descriptor of a DSK segment may be fetched using the function dskgd_c.

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### Coordinate System Parameters

The coordinate system parameter section of a DSK descriptor always contains 10 elements.

The contents of this section are dependent on the coordinate system. For planetodetic coordinates, the contents are:

          +------------------------+
          | Equatorial radius (km) |
          +------------------------+
          | Flattening coefficient |
          +------------------------+
          | <undefined>            | 8 d.p. values
          +------------------------+

These parameters define the axes of a reference ellipsoid. The length of the polar axis is

         polar_axis = (1 - flattening_coefficient) * equatorial_axis

For planetocentric latitudinal and rectangular coordinates, all elements are undefined.

DSK subsystem computations involving a DSK segment always use the coordinate parameters stored in that segment. These parameters may differ from those specified in a text PCK used by the same application program, or from those specified in a different segment for the same body.

It is not necessarily an error for different sets of coordinate parameters to be used in a computation, but DSK users should be aware of which parameters are used for which purpose.

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# Common Problems

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## Slow DSK Computations

Depending on the computation and the DSK data used, DSK-based geometry computations can range from imperceptibly slower to orders of magnitude slower than those using triaxial ellipsoid shape models.

SPICE users can speed up DSK computations by several means:

`1.` Store DSK files on a fast medium, such as a solid-state drive.

`` Most DSK applications perform a large number of physical file reads, so speeding up these operations has a large effect on overall speed.

`` For applications using large data sets, the speed of the storage medium can be the dominant factor affecting overall program execution speed.

`2.` Use the lowest-resolution shape model that's suitable for the computation.

`` For example, for a small target body, generation of graphics overlays for limbs, terminators, and subspacecraft points may require a type 2 shape model with only a few thousand plates.

`` Large data sets generally result in slower data access performance. This is due to both slower access to the storage medium, and to the fact that, for some DSK data types, DSK software must perform more operations to find data of interest in a large data set than in a small one. This latter point applies to DSK data type 2.

`3.` Choose the proper computation method for the problem.

`` For example, for a ray-surface intercept computation where there are multiple rays for a given observer, target, and observation time, if it's valid to use the same aberration corrections for all of the rays, then the lower-level routine dskxv_c will perform the computation far faster than sincpt_c.

`` Another example: for large target bodies having shapes that are well approximated by ellipsoids, limb and terminator points might be sufficiently accurate if computed using the ``GUIDED'' rather than the ``TANGENT'' method. See the API documentation of limbpt_c and termpt_c for further information.

`` Another example: for an illumination angle computation, a low-resolution surface may, in some cases, yield smoother and more meaningful results than a high-resolution surface.

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## Non-Portable and Unstable Results

Round-off errors can cause valid yet unexpected results due to the fact that round-off errors can differ from one computer platform (this term refers not only to hardware but to math libraries and even compilation options) to the next. For example:

`--` A ray-surface intercept computation, given identical inputs, may result in an intercept on one platform and a miss on another.

`--` The ID of the plate on which a given ray hits a target body may change from one platform to the next.

`` This situation is not hard to contrive in test software: a program designed to aim rays at a type 2 segment's plate edges and vertices can demonstrate it.

`--` The altitude of an observer above the surface, given identical inputs to the computation, might change drastically from one platform to the next.

``Unstable'' results are those that vary greatly in response to small changes in input values. A small difference in input times, with all other inputs equal, can make the difference between a ray-surface intersection and non-intersection, or between spacecraft altitude measured relative to a plateau vs terrain at the base of a cliff.

These problems are best avoided at the time application software is designed: software developers must account for the effects of round-off error.

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## Non-Convex and Multi-Valued Surfaces

Non-convex surfaces can thwart logic that is valid for triaxial ellipsoid models. For example, at a given point on a non-convex surface, for a specified observer, an emission angle of less than 90 degrees doesn't necessarily imply that the point is visible from the observer. Similarly, a solar incidence angle of less than 90 degrees doesn't necessarily imply the point is illuminated by the sun.

Even a slight deviation from convexity can change numerical results considerably from those obtained using a triaxial ellipsoid model. For example, depending on whether there is a mountain in the foreground or whether the intercept lies in a valley (oriented in the general direction of the ray's projection on the surface), the range from an observer to a ray-surface intercept point can be much shorter or longer than the distance to the ray's intercept on the target body's reference ellipsoid.

Non-convex surfaces can, in some cases, render some geometric quantities undefined or unusable. For example, the nearest surface point to a given point, not on the surface, can have multiple solutions, all in substantially different directions from the given point. Another example: the origin of a body-fixed reference frame for an object may be outside of the object--- a surface modeling a planetary ring would have this property.

Multi-valued surfaces are those for which, for a given latitude and longitude, or for a given (X,Y) value, there are multiple radius or height values. These surfaces can occur due to presence of topographic features such as cliffs, caves, and arches. They can also occur due to the large-scale shape of an object, as is the case for the nucleus of the comet Churyumov-Gerasimenko.

Multi-valued surfaces invite new categories of errors not possible with single-valued, non-convex surfaces. For example, for a given observer position, the sub-observer point can vary depending on the observer's altitude. Software meant for use with single-valued surfaces, for example the function latsrf_c, may yield incorrect results for such cases.

Multi-valued surfaces can yield discontinuities in derived quantities that are well-behaved when an ellipsoid is used to model the target's shape. For example, when an observing spacecraft overflies a cliff, the observer's altitude can change discontinuously. If the sub-spacecraft point is corrected for light time, the light time algorithm may converge slowly or not at all.

Again, these problems are best solved by designing application software to avoid assumptions appropriate only for ellipsoids.

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## DSK File Creation Errors

The variety of possible DSK file creation errors is limited only by the fact that inputs to the process contain a finite number of bytes. We'll mention only some of the common ones.

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### MKDSK Setup File Errors

While MKDSK can check for obviously invalid values, there are some values that it either cannot or does not check:

`--` Central body ID code

`--` Surface ID code

`--` Central body reference frame---is it the one to which the data are actually referenced?

`--` Segment coordinate bounds---are they compatible with the data?

`--` Angular and distance units

MKDSK does place a copy of the setup file in the comment area of the output DSK file, so users can check it.

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### Data Errors

Some data properties are allowed by MKDSK and dskw02_c, but result in DSK segments that may be unsuitable for some computations. These include:

`--` Degenerate plates. Some plate generation algorithms can create plates that have zero-length edges (in fact, MKDSK can be induced to do this). Such plates can be written to a DSK segment, but they will cause failure of algorithms that need to compute the outward normal vectors of plates.

`--` Missing data. Missing data can cause failure of some algorithms such as the sub-observer point computation.

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### Segment Coverage Errors

It is possible for DSK creators to create segments that don't have the coverage claimed in the segments' DSK descriptors and intended by the creator to be present.

This is an easy error to make when a large data set is distributed across multiple DSK files. The DSK creator may assume that the original plate set, partitioned among various files, will yield the same coverage as if all plates were stored in a single segment. Not so---each segment can only provide the coverage its DSK descriptor claims it has, so if a plate needed by a segment to provide coverage near, but within, that segment's boundary is allocated to a different segment, the first segment's coverage will have a gap.

An artificial, but simple, example of this is a tessellation of a sphere, using triangular plates. Suppose that the surface is partitioned into a 6 x 12 grid of segments, each covering a 30 degree by 30 degree region of planetocentric longitude and latitude. Suppose each segment contains 225 pairs of plates such that each pair covers a longitude-latitude rectangle having angular extent 2 degrees by 2 degrees, so each segment is ``covered'' by 450 plates.

Consider the segment covering the coordinate rectangle

       Planetocentric longitude (deg):    0 to +30
       Planetocentric latitude  (deg):  +30 to +60

For each plate having two vertices on the segment's southern boundary, the edge of that plate connecting those vertices has latitude greater than 30 degrees everywhere but at the vertices themselves. At the midpoint of that edge, the latitude is actually about 30.00378 degrees.

A ray aimed from an exterior vertex to the center of the sphere will miss the surface if the longitude of the vertex is 15 degrees and latitude of the vertex is above 30 degrees but less than the latitude of the edge's midpoint.

The solution is to create each segment using ``padding''---additional plates extending slightly beyond the segment's southern boundary, so no ray emanating from the origin and hitting the sphere within the segment's longitude-latitude coverage can miss all of the segment's plates.

The same problem exists for all southern segment latitude boundaries having positive latitude, and for all northern segment latitude boundaries having negative latitude. All of these boundaries require padding in order to achieve the intended coverage.

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### Poor Data Distribution Across Segments

It's possible to create DSK segments that are technically valid but that give rise to very slow run-time performance.

A seemingly attractive choice that can lead to this problem is partitioning a large data set into a small number of files, each of which contains a large number of plates.

Type 2 segments can contain 10000000 or more plates (see Appendix B), but as a segment's plate count increases, the speed of DSK ray-surface intercept computations decreases.

Experience indicates that DSK ray-surface intercepts exhibit an ``economy of small scale'' phenomenon, whereby spreading data across multiple, small segments tends to improve performance. This is true only up to a point: as the number of segments grows, the amount of time spent reading new data when switching from one segment to another grows. At some point this overhead becomes a significant drag on performance.

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# Appendix A --- Revision History

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### 2017 APR 05 by N. J. Bachman.

Initial release.

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# Appendix B --- DSK Subsystem Limits

The limits shown here apply to the N0066 CSPICE Toolkit.

See the file

       SpiceDSK.h

for declarations of public parameters defining DSK limits.

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## General Limits

`--` Maximum number of loaded DSK files: 5000

`` The practical limit is lower, since the total number of kernels of all types that can be loaded is 5000.

`--` Maximum number of loaded DSK segments: 10000

`` Note that the DSK subsystem, unlike the SPK, CK, and binary PCK subsystems, does not search kernels for segments in ``search without buffering'' mode. Thus instead of suffering greatly degraded performance, a user's application will receive a CSPICE error signal if an attempt is made to load too many segments.

`--` Maximum number of surfaces in a surface list: 100

`` This applies to surface lists in calls to the CSPICE APIs that use them.

`--` Maximum number of surface name-ID pairs that can be defined at run time: 2003

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## DSK Type 2 Segment Limits

For all platforms:

Maximum number of coarse voxels:
  100000

Maximum number of fine voxels:
  100000000

For the platforms

       PC-64BIT-MS_C
       PC-CYGWIN-64BIT-GCC_C
       PC-CYGWIN-64BIT-GFORTRAN
       PC-CYGWIN-GFORTRAN
       PC-CYGWIN_C
       PC-MS_C
       PC-WINDOWS-64BIT-IFORT
       PC-WINDOWS-IFORT
       SUN-SOLARIS
       SUN-SOLARIS-64BIT-GCC_C
       SUN-SOLARIS-64BIT-NATIVE_C
       SUN-SOLARIS-GCC_C
       SUN-SOLARIS-NATIVE_C

the following limits apply:

Maximum number of plates:
  10000000

Maximum number of vertices:
  5000002

For all others, the limits are:

Maximum number of plates:
  32000000

Maximum number of vertices:
  16000002