vproj_c |

Table of contents## Procedurevproj_c ( Vector projection, 3 dimensions ) void vproj_c ( ConstSpiceDouble a[3], ConstSpiceDouble b[3], SpiceDouble p[3] ) ## AbstractCompute the projection of one 3-dimensional vector onto another 3-dimensional vector. ## Required_ReadingNone. ## KeywordsVECTOR ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- a I The vector to be projected. b I The vector onto which `a' is to be projected. p O The projection of `a' onto `b'. ## Detailed_Inputa is a double precision, 3-dimensional vector. This vector is to be projected onto the vector `b'. b is a double precision, 3-dimensional vector. This vector is the vector which receives the projection. ## Detailed_Outputp is a double precision, 3-dimensional vector containing the projection of `a' onto `b'. (`p' is necessarily parallel to `b'.) If `b' is the zero vector then `p' will be returned as the zero vector. `p' may overwrite either `a' or `b'. ## ParametersNone. ## ExceptionsError free. ## FilesNone. ## ParticularsGiven any vectors `a' and `b', there is a unique decomposition of `a' as a sum v + p such that `v', the dot product of `v' and `b', is zero, and the dot product of `p' with `b' is equal the product of the lengths of `p' and `b'. `p' is called the projection of `a' onto `b'. It can be expressed mathematically as dot(a,b) -------- * b dot(b,b) (This is not necessarily the prescription used to compute the projection. It is intended only for descriptive purposes.) ## ExamplesThe numerical results shown for this example may differ across platforms. The results depend on the SPICE kernels used as input, the compiler and supporting libraries, and the machine specific arithmetic implementation. 1) Define two sets of vectors and compute the projection of each vector of the first set on the corresponding vector of the second set. Example code begins here. /. Program vproj_ex1 ./ #include <stdio.h> #include "SpiceUsr.h" int main( ) { /. Local parameters. ./ #define NDIM 3 #define SETSIZ 4 /. Local variables. ./ SpiceDouble pvec [NDIM]; SpiceInt i; /. Define the two vector sets. ./ SpiceDouble seta [SETSIZ][NDIM] = { {6.0, 6.0, 6.0}, {6.0, 6.0, 6.0}, {6.0, 6.0, 0.0}, {6.0, 0.0, 0.0} }; SpiceDouble setb [SETSIZ][NDIM] = { { 2.0, 0.0, 0.0}, {-3.0, 0.0, 0.0}, { 0.0, 7.0, 0.0}, { 0.0, 0.0, 9.0} }; /. Calculate the projection ./ for ( i = 0; i < SETSIZ; i++ ) { ## Restrictions1) An implicit assumption exists that `a' and `b' are specified in the same reference frame. If this is not the case, the numerical result has no meaning. ## Literature_References[1] G. Thomas and R. Finney, "Calculus and Analytic Geometry," 7th Edition, Addison Wesley, 1988. ## Author_and_InstitutionJ. Diaz del Rio (ODC Space) W.L. Taber (JPL) E.D. Wright (JPL) ## Version-CSPICE Version 1.0.1, 01-NOV-2021 (JDR) Edited the header to comply with NAIF standard. Added complete example to the -Examples section. Added entry to -Restrictions section. -CSPICE Version 1.0.0, 08-FEB-1998 (EDW) (WLT) ## Index_Entries3-dimensional vector projection |

Fri Dec 31 18:41:15 2021