Find the limb of a triaxial ellipsoid, viewed from a specified point.
Variable I/O Description -------- --- -------------------------------------------------- a I Length of ellipsoid semi-axis lying on the x-axis. b I Length of ellipsoid semi-axis lying on the y-axis. c I Length of ellipsoid semi-axis lying on the z-axis. viewpt I Location of viewing point. limb O Limb of ellipsoid as seen from viewing point.
a, b, c are the lengths of the semi-axes of a triaxial ellipsoid. The ellipsoid is centered at the origin and oriented so that its axes lie on the x, y and z axes. a, b, and c are the lengths of the semi-axes that point in the x, y, and z directions respectively. viewpt is a point from which the ellipsoid is viewed. viewpt must be outside of the ellipsoid.
limb is a CSPICE ellipse that represents the limb of the ellipsoid.
The limb of a body, as seen from a viewing point, is the boundary of the portion of the body's surface that is visible from that viewing point. In this definition, we consider a surface point to be `visible' if it can be connected to the viewing point by a line segment that doen't pass through the body. This is a purely geometrical definition that ignores the matter of which portions of the surface are illuminated, or whether the view is obscured by any additional objects. If a body is modelled as a triaxial ellipsoid, the limb is always an ellipse. The limb is determined by its center, a semi-major axis vector, and a semi-minor axis vector. We note that the problem of finding the limb of a triaxial ellipsoid is mathematically identical to that of finding its terminator, if one makes the simplifying assumption that the terminator is the limb of the body as seen from the vertex of the umbra. So, this routine can be used to solve this simplified version of the problem of finding the terminator.
1) We'd like to find the apparent limb of Jupiter, corrected for light time and stellar aberration, as seen from a spacecraft's position at time ET. /. Find the viewing point in Jupiter-fixed coordinates. To do this, find the apparent position of Jupiter as seen from the spacecraft in Jupiter-fixed coordinates and negate this vector. In this case we'll use light time and stellar aberration corrections to arrive at the apparent limb. jstat is the Jupiter's state (position and velocity) as seen from the spacecraft. scpos is the spacecraft's position relative to Jupiter. ./ spkez_c( jupid, et, "IAU_JUPITER", "LT+S", scid, scstat, <); vminus_c ( scstat, scpos ); /. Get Jupiter's semi-axis lengths. ./ bodvcd_c ( jupid, "RADII", 3, &n, rad ); /. Find the apparent limb. limb is a CSPICE ellipse representing the limb. ./ edlimb_c ( rad, rad, rad, scpos, &limb ); /. lcentr, smajor, and sminor are the limb's center, semi-major axis, and semi-minor axis. ./ el2cgv_c ( &limb, center, smajor, sminor );
1) If the length of any semi-axis of the ellipsoid is non-positive, the error DEGENERATECASE is signaled. limb is not modified. 2) If the length of any semi-axis of the ellipsoid is zero after the semi-axis lengths are scaled by the reciprocal of the magnitude of the longest semi-axis and then squared, the error SPICE(DEGENERATECASE) is signaled. limb is not modified. 3) If the viewing point viewpt is inside the ellipse, the error SPICE(INVALIDPOINT) is signaled. limb is not modified. 4) If the geometry defined by the input ellipsoid and viewing point is so extreme that the limb cannot be found, the error SPICE(DEGENERATECASE) is signaled. 5) If the shape of the ellipsoid and the viewing geometry are such that the limb is an excessively flat ellipsoid, the limb may be a degenerate ellipse. You must determine whether this possibility poses a problem for your application.
N.J. Bachman (JPL)
-CSPICE Version 1.0.1, 24-OCT-2005 (NJB) Header update: reference to bodvar_c was replaced with reference to bodvcd_c. -CSPICE Version 1.0.0, 13-JUN-1999 (NJB)