/* -Procedure pltar_c ( Compute area of plate set ) -Abstract Compute the total area of a collection of triangular plates. -Disclaimer THIS SOFTWARE AND ANY RELATED MATERIALS WERE CREATED BY THE CALIFORNIA INSTITUTE OF TECHNOLOGY (CALTECH) UNDER A U.S. GOVERNMENT CONTRACT WITH THE NATIONAL AERONAUTICS AND SPACE ADMINISTRATION (NASA). THE SOFTWARE IS TECHNOLOGY AND SOFTWARE PUBLICLY AVAILABLE UNDER U.S. EXPORT LAWS AND IS PROVIDED "AS-IS" TO THE RECIPIENT WITHOUT WARRANTY OF ANY KIND, INCLUDING ANY WARRANTIES OF PERFORMANCE OR MERCHANTABILITY OR FITNESS FOR A PARTICULAR USE OR PURPOSE (AS SET FORTH IN UNITED STATES UCC SECTIONS 2312-2313) OR FOR ANY PURPOSE WHATSOEVER, FOR THE SOFTWARE AND RELATED MATERIALS, HOWEVER USED. IN NO EVENT SHALL CALTECH, ITS JET PROPULSION LABORATORY, OR NASA BE LIABLE FOR ANY DAMAGES AND/OR COSTS, INCLUDING, BUT NOT LIMITED TO, INCIDENTAL OR CONSEQUENTIAL DAMAGES OF ANY KIND, INCLUDING ECONOMIC DAMAGE OR INJURY TO PROPERTY AND LOST PROFITS, REGARDLESS OF WHETHER CALTECH, JPL, OR NASA BE ADVISED, HAVE REASON TO KNOW, OR, IN FACT, SHALL KNOW OF THE POSSIBILITY. RECIPIENT BEARS ALL RISK RELATING TO QUALITY AND PERFORMANCE OF THE SOFTWARE AND ANY RELATED MATERIALS, AND AGREES TO INDEMNIFY CALTECH AND NASA FOR ALL THIRD-PARTY CLAIMS RESULTING FROM THE ACTIONS OF RECIPIENT IN THE USE OF THE SOFTWARE. -Required_Reading None. -Keywords DSK GEOMETRY MATH */ #include "SpiceUsr.h" #include "SpiceZfc.h" #include "SpiceZst.h" #undef pltar_c SpiceDouble pltar_c ( SpiceInt nv, ConstSpiceDouble vrtces [][3], SpiceInt np, ConstSpiceInt plates [][3] ) /* -Brief_I/O Variable 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 total area of the set of plates. -Detailed_Input nv is the number of vertices comprising the plate set. 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 set. plates is an array containing 3-tuples of integers representing the set of 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_Output The function returns the total area of the input set of plates. Each plate contributes the area of the triangle defined by the plate's vertices. If the components of the vertex array have length unit L, then the output area has units 2 L -Parameters None. -Exceptions 1) If the number of plates is less than 0, the error SPICE(BADPLATECOUNT) is signaled. 2) If the number of plates is positive and the number of vertices is less than 3, the error SPICE(TOOFEWVERTICES) is signaled. 3) If any plate contains a vertex index outside of the range [1, nv] the error SPICE(INDEXOUTOFRANGE) will be signaled. -Files None. -Particulars This routine computes the total area of a set of triangular plates. The plates need not define a closed surface. Examples of valid plate sets: Tetrahedron Box Tiled ellipsoid Tiled ellipsoid with one plate removed Two disjoint boxes Two boxes with intersection having positive volume Single plate Empty plate set -Examples The numerical results shown for these examples 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 area 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 EX1 ./ /. Compute the area of a plate model representing the pyramid with one vertex at the origin and the other vertices coinciding with the standard basis vectors. ./ #include #include "SpiceUsr.h" int main() { /. Local constants ./ #define NVERT 4 #define NPLATE 4 /. Local variables ./ SpiceDouble area; /. 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 } }; area = pltar_c( NVERT, vrtces, NPLATE, plates ); printf ( "Expected area = (3 + sqrt(3)) / 2\n" " = 0.23660254037844384e+01\n" ); printf ( "Computed area = %24.17e\n", area ); return ( 0 ); } When this program was executed on a PC/Linux/gcc/64-bit platform, the output was: Expected area = (3 + SQRT(3)) / 2 = 0.23660254037844384E+01 Computed area = 2.3660254037844384 -Restrictions None. -Literature_References None. -Author_and_Institution N.J. Bachman (JPL) -Version -CSPICE Version 1.0.0, 24-OCT-2016 (NJB) -Index_Entries compute plate model area -& */ { /* Begin pltar_c */ /* Local variables */ SpiceDouble retval; /* Participate in error tracing. */ chkin_c ( "pltar_c" ); retval = (SpiceDouble) pltar_ ( ( integer * ) &nv, ( doublereal * ) vrtces, ( integer * ) &np, ( integer * ) plates ); chkout_c ( "pltar_c" ); return ( retval ); } /* End pltar_c */