inelpl_c |

Table of contents## Procedureinelpl_c ( Intersection of ellipse and plane ) void inelpl_c ( ConstSpiceEllipse * ellips, ConstSpicePlane * plane, SpiceInt * nxpts, SpiceDouble xpt1[3], SpiceDouble xpt2[3] ) ## AbstractFind the intersection of an ellipse and a plane. ## Required_ReadingELLIPSES PLANES ## KeywordsELLIPSE GEOMETRY MATH ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- ellips I A SPICE ellipse. plane I A SPICE plane. nxpts O Number of intersection points of plane and ellipse. xpt1, xpt2 O Intersection points. ## Detailed_Inputellips is a SPICE ellipse. The ellipse is allowed to be degenerate: one or both semi-axes may have zero length. plane is a SPICE plane. The intersection of plane and ellipse is sought. ## Detailed_Outputnxpts is the number of points of intersection of the geometric plane and ellipse represented by `plane' and `ellips'. `nxpts' may take the values 0, 1, 2 or -1. The value -1 indicates that the ellipse consists of more than one point lies in the plane, so the number of intersection points is infinite. When the ellipse consists of a single point and lies in the plane, `nxpts' is set to 1. xpt1, xpt2 are the points of intersection of the input plane and ellipse. If there is only one intersection point, both xpt1 and xpt2 contain that point. If the number of intersection points is zero or infinite, the contents of xpt1 and xpt2 are undefined. ## ParametersNone. ## Exceptions1) If the input plane is invalid, the error SPICE(INVALIDPLANE) is signaled. The input plane must be a SPICE plane: the normal vector must be non-zero and the constant must be non-negative. 2) If the input ellipse has non-orthogonal axes, the error SPICE(INVALIDELLIPSE) is signaled. 3) The input ellipse is allowed to be a line segment or a point; these cases are not considered to be errors. If the ellipse consists of a single point and lies in the plane, the number of intersection points is set to 1 (rather than -1) and the output arguments `xpt1' and `xpt2' are assigned the value of the ellipse's center. ## FilesNone. ## ParticularsThis routine computes the intersection set of a non-degenerate plane with a possibly degenerate ellipse. The ellipse is allowed to consist of a line segment or a point. A plane may intersect an ellipse in 0, 1, 2, or infinitely many points. For there to be an infinite set of intersection points, the ellipse must lie in the plane and consist of more than one ## Examples1) If we want to find the angle of some ray above the limb of an ellipsoid, where the angle is measured in a plane containing the ray and a "down" vector, we can follow the procedure given below. We assume the ray does not intersect the ellipsoid. The result we seek is called angle, imaginatively enough. We assume that all vectors are given in body-fixed coordinates. #include "SpiceUsr.h" . . . /. Find the limb of the ellipsoid as seen from the point observ. Here a, b, and c are the lengths of the semi-axes of the ellipsoid. The limb is returned as a SpiceEllipse. ./ edlimb_c ( a, b, c, observ, &limb ); /. The ray direction vector is raydir, so the ray is the set of points observ + t * raydir where t is any non-negative real number. The `down' vector is just -observ. The vectors observ and raydir are spanning vectors for the plane we're interested in. We can use psv2pl_c to represent this plane by a SPICE plane. ./ psv2pl_c ( observ, observ, raydir, &plane ); /. Find the intersection of the plane defined by observ and raydir with the limb. ./ ## RestrictionsNone. ## Literature_ReferencesNone. ## Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) ## Version-CSPICE Version 2.1.1, 24-AUG-2021 (JDR) Edited the header to comply with NAIF standard. Removed non-standard header section "Revisions", moving its contents to the relevant entry in -Version section. -CSPICE Version 2.1.0, 07-OCT-2011 (NJB) Relaxed ellipse semi-axes orthogonality test limit SEPLIM from 1.D-12 TO 1.D-9 radians. The angular separation of the axes of the input ellipse must not differ from pi/2 radians by more than this limit. -CSPICE Version 2.0.0, 14-JAN-2008 (NJB) Bug fix: the routine's specification and behavior have been updated so the routine now returns a meaningful result for the case of an ellipse consisting of a single point. In this case, if an intersection is found, the number of intersection points is set to 1 and both intersection arguments are set equal to the ellipse's center. Bug fix: in the degenerate case where the input ellipse is a line segment of positive length, and this segment intersects the plane, the number of intersection points is set to 1 rather than 2. Invalid input planes and ellipses are now diagnosed. Error handling code has been added to trap errors that had been erroneously passed off to lower level routines for diagnosis. -CSPICE Version 1.0.0, 28-AUG-2001 (NJB) ## Index_Entriesintersection of ellipse and plane |

Fri Dec 31 18:41:08 2021