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: http://www.stsci.edu/~sontag/spicedocs/cspice/nvp2pl_c.html
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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