vprjpi_c |

Table of contents## Procedurevprjpi_c ( Vector projection onto plane, inverted ) void vprjpi_c ( ConstSpiceDouble vin [3], ConstSpicePlane * projpl, ConstSpicePlane * invpl, SpiceDouble vout [3], SpiceBoolean * found ) ## AbstractFind the vector in a specified plane that maps to a specified vector in another plane under orthogonal projection. ## Required_ReadingPLANES ## KeywordsGEOMETRY MATH PLANE VECTOR ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- vin I The projected vector. projpl I Plane containing `vin'. invpl I Plane containing inverse image of `vin'. vout O Inverse projection of `vin'. found O Flag indicating whether `vout' could be calculated. ## Detailed_Inputvin, projpl, invpl are, respectively, a 3-vector, a SPICE plane containing the vector, and a SPICE plane containing the inverse image of the vector under orthogonal projection onto `projpl'. ## Detailed_Outputvout is the inverse orthogonal projection of `vin'. This is the vector lying in the plane `invpl' whose orthogonal projection onto the plane `projpl' is `vin'. `vout' is valid only when `found' (defined below) is SPICETRUE. Otherwise, `vout' is undefined. found indicates whether the inverse orthogonal projection of `vin' could be computed. `found' is SPICETRUE if so, SPICEFALSE otherwise. ## ParametersNone. ## Exceptions1) If the normal vector of either input plane does not have unit length (allowing for round-off error), the error SPICE(NONUNITNORMAL) is signaled by a routine in the call tree of this routine. 2) If the geometric planes defined by `projpl' and `invpl' are orthogonal, or nearly so, the inverse orthogonal projection of `vin' may be undefined or have magnitude too large to represent with double precision numbers. In either such case, `found' will be set to SPICEFALSE. 3) Even when `found' is SPICETRUE, `vout' may be a vector of extremely large magnitude, perhaps so large that it is impractical to compute with it. It's up to you to make sure that this situation does not occur in your application of this routine. ## FilesNone. ## ParticularsProjecting a vector orthogonally onto a plane can be thought of as finding the closest vector in the plane to the original vector. This "closest vector" always exists; it may be coincident with the original vector. Inverting an orthogonal projection means finding the vector in a specified plane whose orthogonal projection onto a second specified plane is a specified vector. The vector whose projection is the specified vector is the inverse projection of the specified vector, also called the "inverse image under orthogonal projection" of the specified vector. This routine finds the inverse orthogonal projection of a vector onto a plane. Related routines are vprjp_c, which projects a vector onto a plane orthogonally, and vproj_c, which projects a vector onto another vector orthogonally. ## Examples1) Suppose vin = ( 0.0, 1.0, 0.0 ), and that projpl has normal vector projn = ( 0.0, 0.0, 1.0 ). Also, let's suppose that invpl has normal vector and constant invn = ( 0.0, 2.0, 2.0 ) invc = 4.0. Then vin lies on the y-axis in the x-y plane, and we want to find the vector vout lying in invpl such that the orthogonal projection of vout the x-y plane is vin. Let the notation < a, b > indicate the inner product of vectors a and b. Since every point x in invpl satisfies the equation < x, (0.0, 2.0, 2.0) > = 4.0, we can verify by inspection that the vector ( 0.0, 1.0, 1.0 ) is in invpl and differs from vin by a multiple of projn. So ( 0.0, 1.0, 1.0 ) must be vout. To find this result using CSPICE, we can create the SPICE planes projpl and invpl using the code fragment nvp2pl_c ( projn, vin, &projpl ); nvc2pl_c ( invn, invc, &invpl ); and then perform the inverse projection using the call ## Restrictions1) It is recommended that the input planes be created by one of the CSPICE routines nvc2pl_c ( Normal vector and constant to plane ) nvp2pl_c ( Normal vector and point to plane ) psv2pl_c ( Point and spanning vectors to plane ) In any case each input plane must have a unit length normal vector and a plane constant consistent with the normal vector. ## Literature_References[1] G. Thomas and R. Finney, "Calculus and Analytic Geometry," 7th Edition, Addison Wesley, 1988. ## Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) ## Version-CSPICE Version 1.1.1, 25-AUG-2021 (JDR) (NJB) Edited the header to comply with NAIF standard. Added entry #1 to -Exceptions section, and entry #1 to -Restrictions. -CSPICE Version 1.1.0, 05-APR-2004 (NJB) Computation of LIMIT was re-structured to avoid run-time underflow warnings on some platforms. -CSPICE Version 1.0.0, 05-MAR-1999 (NJB) ## Index_Entriesvector projection onto plane inverted |

Fri Dec 31 18:41:15 2021