pltvol_c |

Table of contents## Procedurepltvol_c ( Compute volume of plate model ) SpiceDouble pltvol_c ( SpiceInt nv, ConstSpiceDouble vrtces[][3], SpiceInt np, ConstSpiceInt plates[][3] ) ## AbstractCompute the volume of a three-dimensional region bounded by a collection of triangular plates. ## Required_ReadingDSK ## KeywordsDSK GEOMETRY MATH TOPOGRAPHY ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- nv I Number of vertices. vrtces I Array of vertices. np I Number of triangular plates. plates I Array of plates. The function returns the volume of the spatial region bounded by the plates. ## Detailed_Inputnv is the number of vertices comprising the plate model. vrtces is an array containing the plate model's vertices. Elements vrtces[i-1][0] vrtces[i-1][1] vrtces[i-1][2] are, respectively, the X, Y, and Z components of the ith vertex, where `i' ranges from 1 to `nv'. This routine doesn't associate units with the vertices. np is the number of triangular plates comprising the plate model. plates is an array containing 3-tuples of integers representing the model's plates. The elements of `plates' are vertex indices. The vertex indices are 1-based: vertices have indices ranging from 1 to `nv'. The elements plates[i-1][0] plates[i-1][1] plates[i-1][2] are, respectively, the indices of the vertices comprising the ith plate. Note that the order of the vertices of a plate is significant: the vertices must be ordered in the positive (counterclockwise) sense with respect to the outward normal direction associated with the plate. In other words, if `v1', `v2', `v3' are the vertices of a plate, then ( v2 - v1 ) x ( v3 - v2 ) points in the outward normal direction. Here "x" denotes the vector cross product operator. ## Detailed_OutputThe function returns the volume of the spatial region bounded by the plates. If the components of the vertex array have length unit L, then the output volume has units 3 L ## ParametersNone. ## Exceptions1) The input plate model must define a spatial region with a boundary. This routine does not check the inputs to verify this condition. See the -Restrictions section below. 2) If the number of vertices is less than 4, the error SPICE(TOOFEWVERTICES) is signaled by a routine in the call tree of this routine. 3) If the number of plates is less than 4, the error SPICE(TOOFEWPLATES) is signaled by a routine in the call tree of this routine. 4) If any plate contains a vertex index outside of the range [1, nv] the error SPICE(INDEXOUTOFRANGE) is signaled by a routine in the call tree of this routine. ## FilesNone. ## ParticularsThis routine computes the volume of a spatial region bounded by a set of triangular plates. If the plate set does not actually form the boundary of a spatial region, the result of this routine is invalid. Examples: Valid inputs ------------ Tetrahedron Box Tiled ellipsoid Two disjoint boxes Invalid inputs -------------- Single plate Tiled ellipsoid with one plate removed Two boxes with intersection having positive volume ## ExamplesThe numerical results shown for this example may differ across platforms. The results depend on the SPICE kernels used as input (if any), the compiler and supporting libraries, and the machine specific arithmetic implementation. 1) Compute the volume of the pyramid defined by the four triangular plates whose vertices are the 3-element subsets of the set of vectors ( 0, 0, 0 ) ( 1, 0, 0 ) ( 0, 1, 0 ) ( 0, 0, 1 ) Example code begins here. /. Program pltvol_ex1 Compute the volume of a plate model representing the pyramid with one vertex at the origin and the other vertices coinciding with the standard basis vectors. ./ #include <stdio.h> #include "SpiceUsr.h" int main() { /. Local constants ./ #define NVERT 4 #define NPLATE 4 /. Local variables ./ SpiceDouble vol; /. Let the notation < A, B > denote the dot product of vectors A and B. The plates defined below lie in the following planes, respectively: Plate 1: { P : < P, (-1, 0, 0) > = 0 } Plate 2: { P : < P, ( 0, -1, 0) > = 0 } Plate 3: { P : < P, ( 0, 0, -1) > = 0 } Plate 4: { P : < P, ( 1, 1, 1) > = 1 } ./ SpiceDouble vrtces[NVERT ][3] = { { 0.0, 0.0, 0.0 }, { 1.0, 0.0, 0.0 }, { 0.0, 1.0, 0.0 }, { 0.0, 0.0, 1.0 } }; SpiceInt plates[NPLATE][3] = { { 1, 4, 3 }, { 1, 2, 4 }, { 1, 3, 2 }, { 2, 3, 4 } }; vol = ## Restrictions1) The plate collection must describe a surface and enclose a volume such that the divergence theorem (see [1]) is applicable. ## Literature_References[1] T. Apostol, "Calculus, Vol. II," John Wiley & Sons, 1969. ## Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) ## Version-CSPICE Version 1.0.1, 13-APR-2021 (JDR) Edited the header to comply with NAIF standard. -CSPICE Version 1.0.0, 24-OCT-2016 (NJB) ## Index_Entriescompute plate model volume |

Fri Dec 31 18:41:10 2021