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Make a CSPICE plane from a normal vector and a point.
PLANES
Variable I/O Description -------- --- -------------------------------------------------- normal, point I A normal vector and a point defining a plane. plane O A CSPICE plane structure representing the plane.
normal, point are, respectively, a normal vector and point that define a plane in three-dimensional space. normal need not be a unit vector. Let the symbol < a, b > indicate the inner product of vectors a and b; then the geometric plane is the set of vectors x in three-dimensional space that satisfy < x - point, normal > = 0.
plane is a CSPICE plane structure that represents the geometric plane defined by point and normal.
None.
CSPICE geometry routines that deal with planes use the `plane' data type to represent input and output planes. This data type makes the subroutine interfaces simpler and more uniform. The CSPICE routines that produce CSPICE planes from data that define a plane are: nvc2pl_c ( Normal vector and constant to plane ) nvp2pl_c ( Normal vector and point to plane ) psv2pl_c ( Point and spanning vectors to plane ) The CSPICE routines that convert CSPICE planes to data that define a plane are: pl2nvc_c ( Plane to normal vector and constant ) pl2nvp_c ( Plane to normal vector and point ) pl2psv_c ( Plane to point and spanning vectors ) Any of these last three routines may be used to convert this routine's output, plane, to another representation of a geometric plane.
1) Project a vector v orthogonally onto a plane defined by point and normal. proj is the projection we want; it is the closest vector in the plane to v. nvp2pl_c ( normal, point, &plane ); vprjp_c ( v, &plane, proj ); 2) Given a point in a plane and a normal vector, find the distance of the plane from the origin. We make a `plane' from the point and normal, then convert the plane to a unit normal and constant. The output constant is (according to the specification of pl2nvc_c) the distance of the plane from the origin. nvp2pl_c ( normal, point, &plane ); pl2nvc_c ( &plane, normal, constant );
None.
1) If the input vector normal is the zero vector, the error SPICE(ZEROVECTOR) is signaled.
None.
N.J. Bachman (JPL)
[1] `Calculus and Analytic Geometry', Thomas and Finney.
-CSPICE Version 1.0.0, 05-MAR-1999 (NJB)
normal vector and point to plane