/*
* Sets up the polygons, runs the overlap computation, and returns the area of overlap.
*/
double computeOverlap(double *ilon, double *ilat, double *olon, double *olat,
int energyMode, double refArea, double *areaRatio) {
int i;
double thisPixelArea;
*areaRatio = 1.;
if (energyMode) {
nv = 0;
for (i = 0; i < 4; ++i)
SaveVertex(&P[i]);
thisPixelArea = Girard();
*areaRatio = thisPixelArea / refArea;
}
nv = 0;
if (DEBUG >= 4) {
printf("Input (P):\n");
for (i = 0; i < 4; ++i)
printf("%10.6f %10.6f\n", ilon[i], ilat[i]);
printf("\nOutput (Q):\n");
for (i = 0; i < 4; ++i)
printf("%10.6f %10.6f\n", olon[i], olat[i]);
printf("\n");
fflush(stdout);
}
for (i = 0; i < 4; ++i) {
P[i].x = cos(ilon[i]) * cos(ilat[i]);
P[i].y = sin(ilon[i]) * cos(ilat[i]);
P[i].z = sin(ilat[i]);
}
for (i = 0; i < 4; ++i) {
Q[i].x = cos(olon[i]) * cos(olat[i]);
Q[i].y = sin(olon[i]) * cos(olat[i]);
Q[i].z = sin(olat[i]);
}
ComputeIntersection(P, Q);
return (Girard());
}
double computeOverlap(double *ilon, double *ilat,
double *olon, double *olat,
int energyMode, double refArea, double *areaRatio)
{
int i;
double thisPixelArea;
pi = atan(1.0) * 4.;
dtr = pi / 180.;
*areaRatio = 1.;
if(energyMode)
{
nv = 0;
for(i=0; i<4; ++i)
SaveVertex(&P[i]);
thisPixelArea = Girard();
*areaRatio = thisPixelArea / refArea;
}
nv = 0;
if(debug >= 4)
{
printf("\n-----------------------------------------------\n\nAdding pixel (%d,%d) to pixel (%d,%d)\n\n",
inRow, inColumn, outRow, outColumn);
printf("Input (P):\n");
for(i=0; i<4; ++i)
printf("%10.6f %10.6f\n", ilon[i], ilat[i]);
printf("\nOutput (Q):\n");
for(i=0; i<4; ++i)
printf("%10.6f %10.6f\n", olon[i], olat[i]);
printf("\n");
fflush(stdout);
}
for(i=0; i<4; ++i)
{
P[i].x = cos(ilon[i]*dtr) * cos(ilat[i]*dtr);
P[i].y = sin(ilon[i]*dtr) * cos(ilat[i]*dtr);
P[i].z = sin(ilat[i]*dtr);
}
for(i=0; i<4; ++i)
{
Q[i].x = cos(olon[i]*dtr) * cos(olat[i]*dtr);
Q[i].y = sin(olon[i]*dtr) * cos(olat[i]*dtr);
Q[i].z = sin(olat[i]*dtr);
}
ComputeIntersection(P, Q);
return(Girard());
}
double Girard()
{
int i, j, ibad;
double area;
double lon, lat;
Vec side[16];
double ang [16];
Vec tmp;
double pi, dtr, sumang, cosAng, sinAng;
pi = atan(1.0) * 4.;
dtr = pi / 180.;
sumang = 0.;
if(nv < 3)
return(0.);
if(debug >= 4)
{
for(i=0; i<nv; ++i)
{
lon = atan2(V[i].y, V[i].x)/dtr;
lat = asin(V[i].z)/dtr;
printf("Girard(): %3d [%13.6e,%13.6e,%13.6e] -> (%10.6f,%10.6f)\n",
i, V[i].x, V[i].y, V[i].z, lon, lat);
fflush(stdout);
}
}
for(i=0; i<nv; ++i)
{
Cross (&V[i], &V[(i+1)%nv], &side[i]);
(void) Normalize(&side[i]);
}
for(i=0; i<nv; ++i)
{
Cross (&side[i], &side[(i+1)%nv], &tmp);
sinAng = Normalize(&tmp);
cosAng = -Dot(&side[i], &side[(i+1)%nv]);
/* Remove center point of colinear segments */
ang[i] = atan2(sinAng, cosAng);
if(debug >= 4)
{
if(i==0)
printf("\n");
printf("Girard(): angle[%d] = %13.6e -> %13.6e (from %13.6e / %13.6e)\n", i, ang[i], ang[i] - pi/2., sinAng, cosAng);
fflush(stdout);
}
if(ang[i] > pi - 0.0175) /* Direction changes of less than */
{ /* a degree can be tricky */
ibad = (i+1)%nv;
if(debug >= 4)
{
printf("Girard(): ---------- Corner %d bad; Remove point %d -------------\n",
i, ibad);
fflush(stdout);
}
--nv;
for(j=ibad; j<nv; ++j)
{
V[j].x = V[j+1].x;
V[j].y = V[j+1].y;
V[j].z = V[j+1].z;
}
return(Girard());
}
sumang += ang[i];
}
area = sumang - (nv-2.)*pi;
if(mNaN(area) || area < 0.)
area = 0.;
if(debug >= 4)
{
printf("\nGirard(): area = %13.6e [%d]\n\n", area, nv);
fflush(stdout);
}
return(area);
}
/*
* Use Girard's theorem to compute the area of a sky polygon.
*/
double Girard() {
int i, j, ibad;
double area;
double lon, lat;
Vec side[16];
double ang[16];
Vec tmp;
double sumang, cosAng, sinAng;
sumang = 0;
if (nv < 3)
return 0;
if (DEBUG >= 4) {
for (i = 0; i < nv; ++i) {
lon = atan2(V[i].y, V[i].x) / DEG_TO_RADIANS;
lat = asin(V[i].z) / DEG_TO_RADIANS;
printf("Girard(): %3d [%13.6e,%13.6e,%13.6e] -> (%10.6f,%10.6f)\n", i,
V[i].x, V[i].y, V[i].z, lon, lat);
fflush(stdout);
}
}
for (i = 0; i < nv; ++i) {
Cross(&V[i], &V[(i + 1) % nv], &side[i]);
Normalize(&side[i]);
}
for (i = 0; i < nv; ++i) {
Cross(&side[i], &side[(i + 1) % nv], &tmp);
sinAng = Normalize(&tmp);
cosAng = -Dot(&side[i], &side[(i + 1) % nv]);
// Remove center point of colinear segments
ang[i] = atan2(sinAng, cosAng);
if (DEBUG >= 4) {
if (i == 0)
printf("\n");
printf("Girard(): angle[%d] = %13.6e -> %13.6e (from %13.6e / %13.6e)\n",
i, ang[i], ang[i] - M_PI / 2., sinAng, cosAng);
fflush(stdout);
}
// Direction changes of less than a degree can be tricky
if (ang[i] > M_PI - 0.0175) {
ibad = (i + 1) % nv;
if (DEBUG >= 4) {
printf("Girard(): ---------- Corner %d bad; "
"Remove point %d -------------\n",
i, ibad);
fflush(stdout);
}
--nv;
for (j = ibad; j < nv; ++j) {
V[j].x = V[j + 1].x;
V[j].y = V[j + 1].y;
V[j].z = V[j + 1].z;
}
return (Girard());
}
sumang += ang[i];
}
area = sumang - (nv - 2.) * M_PI;
if (mNaN(area) || area < 0.)
area = 0.;
if (DEBUG >= 4) {
printf("\nGirard(): area = %13.6e [%d]\n\n", area, nv);
fflush(stdout);
}
return area;
}
