/** * Returns the sub-solar latitude/longitude in universal coordinates (0-360 * positive east, ocentric) * * @param lat Sub-solar latitude * * @param lon Sub-solar longitude */ void Spice::SubSolarPoint (double &lat, double &lon) { NaifStatus::CheckErrors(); if (p_et == -DBL_MAX) { std::string msg = "You must call SetEphemerisTime first"; throw iException::Message(iException::Programmer,msg,_FILEINFO_); } SpiceDouble uuB[3],dist; unorm_c (p_uB,uuB,&dist); SpiceDouble a = p_radii[0]; SpiceDouble b = p_radii[1]; SpiceDouble c = p_radii[2]; SpiceDouble originB[3]; originB[0] = originB[1] = originB[2] = 0.0; SpiceBoolean found; SpiceDouble subB[3]; surfpt_c (originB,uuB,a,b,c,subB,&found); SpiceDouble mylon,mylat; reclat_c (subB,&a,&mylon,&mylat); lat = mylat * 180.0 / Isis::PI; lon = mylon * 180.0 / Isis::PI; if (lon < 0.0) lon += 360.0; NaifStatus::CheckErrors(); }
/** * Returns the sub-spacecraft latitude/longitude in universal coordinates * (0-360 positive east, ocentric) * * @param lat Sub-spacecraft latitude * * @param lon Sub-spacecraft longitude */ void Spice::SubSpacecraftPoint (double &lat, double &lon) { NaifStatus::CheckErrors(); if (p_et == -DBL_MAX) { std::string msg = "You must call SetEphemerisTime first"; throw iException::Message(iException::Programmer,msg,_FILEINFO_); } SpiceDouble usB[3],dist; std::vector<double> vsB = p_bodyRotation->ReferenceVector(p_instrumentPosition->Coordinate()); SpiceDouble sB[3]; sB[0] = vsB[0]; sB[1] = vsB[1]; sB[2] = vsB[2]; unorm_c (sB,usB,&dist); SpiceDouble a = p_radii[0]; SpiceDouble b = p_radii[1]; SpiceDouble c = p_radii[2]; SpiceDouble originB[3]; originB[0] = originB[1] = originB[2] = 0.0; SpiceBoolean found; SpiceDouble subB[3]; surfpt_c (originB,usB,a,b,c,subB,&found); SpiceDouble mylon,mylat; reclat_c (subB,&a,&mylon,&mylat); lat = mylat * 180.0 / Isis::PI; lon = mylon * 180.0 / Isis::PI; if (lon < 0.0) lon += 360.0; NaifStatus::CheckErrors(); }
/** Compute undistorted focal plane coordinate from ground position using current Spice from SetImage call * * This method will compute the undistorted focal plane coordinate for * a ground position, using the current Spice settings (time and kernels) * without resetting the current point values for lat/lon/radius/x/y. * * @param lat planetocentric latitude in degrees * @param lon planetocentric longitude in degrees * @param radius local radius in m * * @return conversion was successful */ bool CameraGroundMap::GetXY(const double lat, const double lon, const double radius, std::vector<double> &lookJ) { // Check for Sky images if ( p_camera->IsSky() ) { return false; } // Should a check be added to make sure SetImage has been called??? // Compute the look vector in body-fixed coordinates double pB[3]; // Point on surface latrec_c( radius/1000.0, lon*Isis::PI/180.0, lat*Isis::PI/180.0, pB); // Get spacecraft vector in body-fixed coordinates SpiceRotation *bodyRot = p_camera->BodyRotation(); std::vector<double> sB = bodyRot->ReferenceVector(p_camera->InstrumentPosition()->Coordinate()); std::vector<double> lookB(3); for (int ic=0; ic<3; ic++) lookB[ic] = pB[ic] - sB[ic]; // Check for point on back of planet by checking to see if surface point is viewable (test emission angle) // During iterations, we may not want to do the back of planet test??? double upsB[3],upB[3],dist; vminus_c ( (SpiceDouble *) &lookB[0], upsB); unorm_c (upsB, upsB, &dist); unorm_c (pB, upB, &dist); double angle = vdot_c(upB, upsB); double emission; if (angle > 1) { emission = 0; } else if (angle < -1) { emission = 180.; } else { emission = acos (angle) * 180.0 / Isis::PI; } if (fabs(emission) > 90.) return false; // Get the look vector in the camera frame and the instrument rotation lookJ.resize(3); lookJ = p_camera->BodyRotation()->J2000Vector( lookB ); return true; }
/** * Computes and returns emission angle in degrees given the observer position. * * Emission Angle: The angle between the surface normal vector at the * intersection point and a vector from the intersection point to the * spacecraft. The emission angle varies from 0 degrees when the spacecraft is * viewing the sub-spacecraft point (nadir viewing) to 90 degrees when the * intercept is tangent to the surface of the target body. Thus, higher values * of emission angle indicate more oblique viewing of the target. * * @param sB: Spacecraft position in body-fixed coordinates * * @return Emmision angle in decimal degrees * */ double PlaneShape::emissionAngle(const std::vector<double> & sB) { SpiceDouble pB[3]; // surface intersection in body-fixed coordinates SpiceDouble psB[3]; // vector from spacecraft to surface intersection SpiceDouble upsB[3]; // unit vector from spacecraft to surface intersection SpiceDouble dist; // vector magnitude // Get vector from center of body to surface point pB[0] = surfaceIntersection()->GetX().kilometers(); pB[1] = surfaceIntersection()->GetY().kilometers(); pB[2] = surfaceIntersection()->GetZ().kilometers(); // Get vector from surface intersect point to observer and normalize it vsub_c((ConstSpiceDouble *) &sB[0], pB, psB); unorm_c(psB, upsB, &dist); // temporary normal vector SpiceDouble n[3]; n[0] = 0.0; n[1] = 0.0; n[2] = 1.0; // flip normal if observer is "below" the plane, assuming that the target // body north pole defines the "up" direction if (sB[2] < 0.0) n[2] = -n[2]; // dot product of surface normal and observer-surface intersection vector double angle = vdot_c(n, upsB); if (angle > 1.0) return 0.0; if (angle < -1.0) return 180.0; return acos(angle) * RAD2DEG; }
/** * Computes and returns incidence angle in degrees given the sun position. * * Incidence Angle: The incidence angle provides a measure of the lighting * condition at the surface intersection point. The angle between the surface * normal vector at the intersection point and a vector from the intersection * point to the sun. The incidence angle varies from 0 degrees when the * intersection point coincides with the sub-solar point to 90 degrees when * the intersection point is at the terminator (i.e., in the shadowed or dark * portion of the target body). Thus, higher values of incidence angles * indicate the existence of a greater number of surface shadows. * * @param uB: Sun position in body-fixed coordinates * * @return Incidence angle in decimal degrees * */ double PlaneShape::incidenceAngle(const std::vector<double> &uB) { SpiceDouble pB[3]; // surface intersection in body-fixed coordinates SpiceDouble puB[3]; // vector from sun to surface intersection SpiceDouble upuB[3]; // unit vector from sun to surface intersection SpiceDouble dist; // vector magnitude // Get vector from center of body to surface point pB[0] = surfaceIntersection()->GetX().kilometers(); pB[1] = surfaceIntersection()->GetY().kilometers(); pB[2] = surfaceIntersection()->GetZ().kilometers(); // Get vector from surface intersect point to sun and normalize it vsub_c((SpiceDouble *) &uB[0], pB, puB); unorm_c(puB, upuB, &dist); // temporary normal vector SpiceDouble n[3]; n[0] = 0.0; n[1] = 0.0; n[2] = 1.0; // flip normal if sun is "below" the plane, assuming that the target // body north pole defines the "up" direction if (uB[2] < 0.0) n[2] = -n[2]; double angle = vdot_c((SpiceDouble *) &n[0], upuB); if (angle > 1.0) return 0.0; if(angle < -1.0) return 180.0; return acos(angle) * RAD2DEG; }
void dvhat_c ( ConstSpiceDouble s1 [6], SpiceDouble sout[6] ) /* -Brief_I/O VARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- s1 I State to be normalized. sout O Unit vector s1 / |s1|, and its time derivative. -Detailed_Input s1 This is any double precision state. If the position component of the state is the zero vector, this routine will detect it and will not attempt to divide by zero. -Detailed_Output sout sout is a state containing the unit vector pointing in the direction of position component of s1 and the derivative of the unit vector with respect to time. sout may overwrite s1. -Parameters None. -Exceptions Error free. 1) If s1 represents the zero vector, then the position component of sout will also be the zero vector. The velocity component will be the velocity component of s1. -Files None. -Particulars Let s1 be a state vector with position and velocity components p and v respectively. From these components one can compute the unit vector parallel to p, call it u and the derivative of u with respect to time, du. This pair (u,du) is the state returned by this routine in sout. -Examples Any numerical results shown for this example may differ between platforms as the results depend on the SPICE kernels used as input and the machine specific arithmetic implementation. Suppose that 'state' gives the apparent state of a body with respect to an observer. This routine can be used to compute the instantaneous angular rate of the object across the sky as seen from the observers vantage. #include "SpiceUsr.h" #include <stdio.h> #include <math.h> int main() { SpiceDouble et; SpiceDouble ltime; SpiceDouble omega; SpiceDouble state [6]; SpiceDouble ustate [6]; SpiceChar * epoch = "Jan 1 2009"; SpiceChar * target = "MOON"; SpiceChar * frame = "J2000"; SpiceChar * abcorr = "LT+S"; SpiceChar * obsrvr = "EARTH BARYCENTER"; /. Load SPK, PCK, and LSK kernels, use a meta kernel for convenience. ./ furnsh_c ( "standard.tm" ); /. Define an arbitrary epoch, convert the epoch to ephemeris time. ./ str2et_c ( epoch, &et ); /. Calculate the state of the moon with respect to the earth-moon barycenter in J2000, corrected for light time and stellar aberration at ET. ./ spkezr_c ( target, et, frame, abcorr, obsrvr, state, <ime ); /. Calculate the unit vector of STATE and the derivative of the unit vector. ./ dvhat_c ( state, ustate ); /. Calculate the instantaneous angular velocity from the magnitude of the derivative of the unit vector. v = r x omega ||omega|| = ||v|| for r . v = 0 ----- ||r|| ||omega|| = ||v|| for ||r|| = 1 ./ omega = vnorm_c( &ustate[3] ); printf( "Instantaneous angular velocity, rad/sec %.10g\n", omega ); return 0; } The program outputs: Instantaneous angular velocity, rad/sec 2.48106658e-06 -Restrictions None. -Literature_References None. -Author_and_Institution W.L. Taber (JPL) E.D. Wright (JPL) -Version -CSPICE Version 1.0.1, 06-MAY-2010 (EDW) Reordered header sections to proper NAIF convention. Minor edit to code comments eliminating typo. -CSPICE Version 1.0.0, 07-JUL-1999 (EDW) -Index_Entries State of a unit vector parallel to a state vector -& */ { /* Begin dvhat_c */ /* Local variables */ SpiceDouble length; SpiceDouble posin [3]; SpiceDouble posout[3]; SpiceDouble velin [3]; SpiceDouble velout[3]; /* We'll do this the obvious way for now. Unpack the input vector into two working vectors. */ posin[0] = s1[0]; posin[1] = s1[1]; posin[2] = s1[2]; velin[0] = s1[3]; velin[1] = s1[4]; velin[2] = s1[5]; /* Get the position portion of the output state and the length of the input position. */ unorm_c ( posin, posout, &length ); if ( length == 0. ) { /* If the length of the input position is zero, just copy the input velocity to the output velocity. */ vequ_c ( velin, velout ); } else { /* Otherwise the derivative of the unit vector is just the component of the input velocity perpendicular to the input position, scaled by the reciprocal of the length of the input position. */ vperp_c ( velin , posout, velout ); vscl_c ( 1./length, velout, velout ); } /* Pack everything and return. Hazar! */ sout[0] = posout[0]; sout[1] = posout[1]; sout[2] = posout[2]; sout[3] = velout[0]; sout[4] = velout[1]; sout[5] = velout[2]; } /* End dvhat_c */
void npedln_c ( SpiceDouble a, SpiceDouble b, SpiceDouble c, ConstSpiceDouble linept[3], ConstSpiceDouble linedr[3], SpiceDouble pnear[3], SpiceDouble * dist ) /* -Brief_I/O Variable I/O Description -------- --- -------------------------------------------------- a I Length of ellipsoid's semi-axis in the x direction b I Length of ellipsoid's semi-axis in the y direction c I Length of ellipsoid's semi-axis in the z direction linept I Point on line linedr I Direction vector of line pnear O Nearest point on ellipsoid to line dist O Distance of ellipsoid from line -Detailed_Input a, b, c are the lengths of the semi-axes of a triaxial ellipsoid which is centered at the origin and oriented so that its axes lie on the x-, y- and z- coordinate axes. a, b, and c are the lengths of the semi-axes that point in the x, y, and z directions respectively. linept linedr are, respectively, a point and a direction vector that define a line. The line is the set of vectors linept + t * linedr where t is any real number. -Detailed_Output pnear is the point on the ellipsoid that is closest to the line, if the line doesn't intersect the ellipsoid. If the line intersects the ellipsoid, pnear will be a point of intersection. If linept is outside of the ellipsoid, pnear will be the closest point of intersection. If linept is inside the ellipsoid, pnear will not necessarily be the closest point of intersection. dist is the distance of the line from the ellipsoid. This is the minimum distance between any point on the line and any point on the ellipsoid. If the line intersects the ellipsoid, dist is zero. -Parameters None. -Exceptions If this routine detects an error, the output arguments nearp and dist are not modified. 1) If the length of any semi-axis of the ellipsoid is non-positive, the error SPICE(INVALIDAXISLENGTH) is signaled. 2) If the line's direction vector is the zero vector, the error SPICE(ZEROVECTOR) is signaled. 3) 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. 4) If the input ellipsoid is extremely flat or needle-shaped and has its shortest axis close to perpendicular to the input line, numerical problems could cause this routine's algorithm to fail, in which case the error SPICE(DEGENERATECASE) is signaled. -Files None. -Particulars For any ellipsoid and line, if the line does not intersect the ellipsoid, there is a unique point on the ellipsoid that is closest to the line. Therefore, the distance dist between ellipsoid and line is well-defined. The unique line segment of length dist that connects the line and ellipsoid is normal to both of these objects at its endpoints. If the line intersects the ellipsoid, the distance between the line and ellipsoid is zero. -Examples 1) We can find the distance between an instrument optic axis ray and the surface of a body modelled as a tri-axial ellipsoid using this routine. If the instrument position and pointing unit vector in body-fixed coordinates are linept = ( 1.0e6, 2.0e6, 3.0e6 ) and linedr = ( -4.472091234e-1 -8.944182469e-1, -4.472091234e-3 ) and the body semi-axes lengths are a = 7.0e5 b = 7.0e5 c = 6.0e5, then the call to npedln_c npedln_c ( a, b, c, linept, linedr, pnear, &dist ); yields a value for pnear, the nearest point on the body to the optic axis ray, of ( -.16333110792340931E+04, -.32666222157820771E+04, .59999183350006724E+06 ) and a value for dist, the distance to the ray, of .23899679338299707E+06 (These results were obtained on a PC-Linux system under gcc.) In some cases, it may not be clear that the closest point on the line containing an instrument boresight ray is on the boresight ray itself; the point may lie on the ray having the same vertex as the boresight ray and pointing in the opposite direction. To rule out this possibility, we can make the following test: /. Find the difference vector between the closest point on the ellipsoid to the line containing the boresight ray and the boresight ray's vertex. Find the angular separation between this difference vector and the boresight ray. If the angular separation does not exceed pi/2, we have the nominal geometry. Otherwise, we have an error. ./ vsub_c ( pnear, linept, diff ); sep = vsep_c ( diff, linedr ); if ( sep <= halfpi_c() ) { [ perform normal processing ] } else { [ handle error case ] } -Restrictions None. -Literature_References None. -Author_and_Institution N.J. Bachman (JPL) -Version -CSPICE Version 1.1.0, 01-JUN-2010 (NJB) Added touchd_ calls to tests for squared, scaled axis length underflow. This forces rounding to zero in certain cases where it otherwise might not occur due to use of extended registers. -CSPICE Version 1.0.1, 06-DEC-2002 (NJB) Outputs shown in header example have been corrected to be consistent with those produced by this routine. -CSPICE Version 1.0.0, 03-SEP-1999 (NJB) -Index_Entries distance between line and ellipsoid distance between line of sight and body nearest point on ellipsoid to line -& */ { /* Begin npedln_c */ /* Local variables */ SpiceBoolean found [2]; SpiceBoolean ifound; SpiceBoolean xfound; SpiceDouble oppdir [3]; SpiceDouble mag; SpiceDouble normal [3]; SpiceDouble prjpt [3]; SpiceDouble prjnpt [3]; SpiceDouble pt [2][3]; SpiceDouble scale; SpiceDouble scla; SpiceDouble scla2; SpiceDouble sclb; SpiceDouble sclb2; SpiceDouble sclc; SpiceDouble sclc2; SpiceDouble sclpt [3]; SpiceDouble udir [3]; SpiceEllipse cand; SpiceEllipse prjel; SpiceInt i; SpicePlane candpl; SpicePlane prjpl; /* Static variables */ /* Participate in error tracing. */ chkin_c ( "npedln_c" ); /* The algorithm used in this routine has two parts. The first part handles the case where the input line and ellipsoid intersect. Our procedure is simple in that case; we just call surfpt_c twice, passing it first one ray determined by the input line, then a ray pointing in the opposite direction. The second part of the algorithm handles the case where surfpt_c doesn't find an intersection. Finding the nearest point on the ellipsoid to the line, when the two do not intersect, is a matter of following four steps: 1) Find the points on the ellipsoid where the surface normal is normal to the line's direction. This set of points is an ellipse centered at the origin. The point we seek MUST lie on this `candidate' ellipse. 2) Project the candidate ellipse onto a plane that is normal to the line's direction. This projection preserves distance from the line; the nearest point to the line on this new ellipse is the projection of the nearest point to the line on the candidate ellipse, and these two points are exactly the same distance from the line. If computed using infinite-precision arithmetic, this projection would be guaranteed to be non-degenerate as long as the input ellipsoid were non-degenerate. This can be verified by taking the inner product of the scaled normal to the candidate ellipse plane and the line's unitized direction vector (these vectors are called normal and udir in the code below); the inner product is strictly greater than 1 if the ellipsoid is non-degenerate. 3) The nearest point on the line to the projected ellipse will be contained in the plane onto which the projection is done; we find this point and then find the nearest point to it on the projected ellipse. The distance between these two points is the distance between the line and the ellipsoid. 4) Finally, we find the point on the candidate ellipse that was projected to the nearest point to the line on the projected ellipse that was found in step 3. This is the nearest point on the ellipsoid to the line. Glossary of Geometric Variables a, b, c Input ellipsoid's semi-axis lengths. point Point of intersection of line and ellipsoid if the intersection is non-empty. candpl Plane containing candidate ellipse. normal Normal vector to the candidate plane candpl. cand Candidate ellipse. linept, linedr, Point and direction vector on input line. udir Unitized line direction vector. prjpl Projection plane; the candidate ellipse is projected onto this plane to yield prjel. prjel Projection of the candidate ellipse cand onto the projection plane prjel. prjpt Projection of line point. prjnpt Nearest point on projected ellipse to projection of line point. pnear Nearest point on ellipsoid to line. */ /* We need a valid normal vector. */ unorm_c ( linedr, udir, &mag ); if ( mag == 0. ) { setmsg_c( "Line direction vector is the zero vector. " ); sigerr_c( "SPICE(ZEROVECTOR)" ); chkout_c( "npedln_c" ); return; } if ( ( a <= 0. ) || ( b <= 0. ) || ( c <= 0. ) ) { setmsg_c ( "Semi-axis lengths: a = #, b = #, c = #." ); errdp_c ( "#", a ); errdp_c ( "#", b ); errdp_c ( "#", c ); sigerr_c ( "SPICE(INVALIDAXISLENGTH)" ); chkout_c ( "npedln_c" ); return; } /* Scale the semi-axes lengths for better numerical behavior. If squaring any one of the scaled lengths causes it to underflow to zero, we cannot continue the computation. Otherwise, scale the viewing point too. */ scale = maxd_c ( 3, a, b, c ); scla = a / scale; sclb = b / scale; sclc = c / scale; scla2 = scla*scla; sclb2 = sclb*sclb; sclc2 = sclc*sclc; if ( ( (SpiceDouble)touchd_(&scla2) == 0. ) || ( (SpiceDouble)touchd_(&sclb2) == 0. ) || ( (SpiceDouble)touchd_(&sclc2) == 0. ) ) { setmsg_c ( "Semi-axis too small: a = #, b = #, c = #. " ); errdp_c ( "#", a ); errdp_c ( "#", b ); errdp_c ( "#", c ); sigerr_c ( "SPICE(DEGENERATECASE)" ); chkout_c ( "npedln_c" ); return; } /* Scale linept. */ sclpt[0] = linept[0] / scale; sclpt[1] = linept[1] / scale; sclpt[2] = linept[2] / scale; /* Hand off the intersection case to surfpt_c. surfpt_c determines whether rays intersect a body, so we treat the line as a pair of rays. */ vminus_c ( udir, oppdir ); surfpt_c ( sclpt, udir, scla, sclb, sclc, pt[0], &(found[0]) ); surfpt_c ( sclpt, oppdir, scla, sclb, sclc, pt[1], &(found[1]) ); for ( i = 0; i < 2; i++ ) { if ( found[i] ) { *dist = 0.0; vequ_c ( pt[i], pnear ); vscl_c ( scale, pnear, pnear ); chkout_c ( "npedln_c" ); return; } } /* Getting here means the line doesn't intersect the ellipsoid. Find the candidate ellipse CAND. NORMAL is a normal vector to the plane containing the candidate ellipse. Mathematically the ellipse must exist, since it's the intersection of an ellipsoid centered at the origin and a plane containing the origin. Only numerical problems can prevent the intersection from being found. */ normal[0] = udir[0] / scla2; normal[1] = udir[1] / sclb2; normal[2] = udir[2] / sclc2; nvc2pl_c ( normal, 0., &candpl ); inedpl_c ( scla, sclb, sclc, &candpl, &cand, &xfound ); if ( !xfound ) { setmsg_c ( "Candidate ellipse could not be found." ); sigerr_c ( "SPICE(DEGENERATECASE)" ); chkout_c ( "npedln_c" ); return; } /* Project the candidate ellipse onto a plane orthogonal to the line. We'll call the plane prjpl and the projected ellipse prjel. */ nvc2pl_c ( udir, 0., &prjpl ); pjelpl_c ( &cand, &prjpl, &prjel ); /* Find the point on the line lying in the projection plane, and then find the near point PRJNPT on the projected ellipse. Here PRJPT is the point on the line lying in the projection plane. The distance between PRJPT and PRJNPT is DIST. */ vprjp_c ( sclpt, &prjpl, prjpt ); npelpt_c ( prjpt, &prjel, prjnpt, dist ); /* Find the near point pnear on the ellipsoid by taking the inverse orthogonal projection of prjnpt; this is the point on the candidate ellipse that projects to prjnpt. Note that the output dist was computed in step 3 and needs only to be re-scaled. The inverse projection of pnear ought to exist, but may not be calculable due to numerical problems (this can only happen when the input ellipsoid is extremely flat or needle-shaped). */ vprjpi_c ( prjnpt, &prjpl, &candpl, pnear, &ifound ); if ( !ifound ) { setmsg_c ( "Inverse projection could not be found." ); sigerr_c ( "SPICE(DEGENERATECASE)" ); chkout_c ( "npedln_c" ); return; } /* Undo the scaling. */ vscl_c ( scale, pnear, pnear ); *dist *= scale; chkout_c ( "npedln_c" ); } /* End npedln_c */