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computeTriClip_kernel.cu
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computeTriClip_kernel.cu
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#include "optical_clipping_common.h"
#include <cutil_inline.h>
#include <cutil_math.h>
#include <math.h>
#include <math_constants.h>
extern "C" {
__device__ __host__ float vectorNorm(float point[]) {
return sqrtf(point[0]*point[0]+point[1]*point[1]);
}
__device__ __host__ float vecMag(float vec[]) {
return sqrtf(vec[0]*vec[0] + vec[1]*vec[1]);
}
__device__ __host__ float polygonArea(float x[], float y[], int len) {
float sum = 0;
int l;
for (l=0; l<len-1; l++) {
sum = sum + x[l]*y[l+1] - y[l]*x[l+1];
}
sum = sum + x[l]*y[0] - y[l]*x[0];
return 0.5*sum;
}
// Can be made parallel in CUDA
__device__ __host__ void projPointOnLine(float *point, float *line, float *projPoint) {
// line: x y dx dy
// point: x y
float dx, dy, tp;
dx = line[2];
dy = line[3];
tp = ((point[1] - line[1])*dy + (point[0] - line[0])*dx) / (dx*dx+dy*dy);
projPoint[0] = line[0] + tp*dx;
projPoint[1] = line[1] + tp*dy;
}
__device__ __host__ int isPointOnEdge(float *point, float * edge) {
// extract computation tolerance
float tol = 1e-14;
float x0 = edge[0];
float y0 = edge[1];
float dx = edge[2]-x0;
float dy = edge[3]-y0;
float xp = point[0];
float yp = point[1];
// test if point is located on supporting line
int b1 = fabsf((xp-x0)*dy - (yp-y0)*dx)/(dx*dx+dy*dy)<tol;
// check if point is located between edge bounds
int ind = fabsf(dx)>abs(dy);
float t;
if (ind)
t = (xp-x0)/dx;
else
t = (yp-y0)/dy;
return t>-tol & t-1<tol & b1;
}
__device__ __host__ int isPointOnEdgeTol(float *point, float * edge, float tol) {
float x0 = edge[0];
float y0 = edge[1];
float dx = edge[2]-x0;
float dy = edge[3]-y0;
float xp = point[0];
float yp = point[1];
// test if point is located on supporting line
int b1 = fabsf((xp-x0)*dy - (yp-y0)*dx)/(dx*dx+dy*dy)<tol;
// check if point is located between edge bounds
int ind = fabsf(dx)>fabsf(dy);
float t;
if (ind)
t = (xp-x0)/dx;
else
t = (yp-y0)/dy;
return t>-tol & t-1<tol & b1;
}
__device__ __host__ float distancePoints(float *p1, float *p2) {
float dx = p1[0]-p2[0], dy = p1[1]-p2[1];
return sqrtf(dx*dx + dy*dy);
}
__device__ __host__ void intersectLines(float *line1, float*line2, float *point) {
float x1 = line1[0];
float y1 = line1[1];
float dx1 = line1[2];
float dy1 = line1[3];
float x2 = line2[0];
float y2 = line2[1];
float dx2 = line2[2];
float dy2 = line2[3];
// indices of parallel lines
int par = fabsf(dx1*dy2-dx2*dy1)<1e-14;
// indices of colinear lines
int col = fabsf((x2-x1)*dy1-(y2-y1)*dx1)<1e-14 & par ;
if (par && !col) {
#if !defined(__CUDA_ARCH__)
point[0] = NAN;
point[1] = NAN;
#else
point[0] = CUDART_NAN_F;
point[1] = CUDART_NAN_F;
#endif
return;
} else if (col) {
#if !defined(__CUDA_ARCH__)
point[0] = INFINITY;
point[1] = INFINITY;
#else
point[0] = CUDART_INF_F;
point[1] = CUDART_INF_F;
#endif
return;
}
float x0,y0;
x0 = ((y2-y1)*dx1*dx2 + x1*dy1*dx2 - x2*dy2*dx1) / (dx2*dy1-dx1*dy2) ;
y0 = ((x2-x1)*dy1*dy2 + y1*dx1*dy2 - y2*dx2*dy1) / (dx1*dy2-dx2*dy1) ;
point[0] = x0;
point[1] = y0;
}
__device__ __host__ void intersectLineEdgeTol(float line[], float edge[], float *inter, float tol ) {
float x0 = line[0];
float y0 = line[1];
float dx1 = line[2];
float dy1 = line[3];
float x1 = edge[0];
float y1 = edge[1];
float x2 = edge[2];
float y2 = edge[3];
float dx2 = x2-x1;
float dy2 = y2-y1;
int par = fabsf(dx1*dy2-dx2*dy1)< 1e-14;
int col = fabsf((x1-x0)*dy1-(y1-y0)*dx1)<1e-14 & par ;
float xi,yi;
if (par && !col) {
#if !defined(__CUDA_ARCH__)
inter[0] = NAN;
inter[1] = NAN;
#else
inter[0] = CUDART_NAN_F;
inter[1] = CUDART_NAN_F;
#endif
return;
} else if (col) {
#if !defined(__CUDA_ARCH__)
inter[0] = INFINITY;
inter[1] = INFINITY;
#else
inter[0] = CUDART_INF_F;
inter[1] = CUDART_INF_F;
#endif
return;
}
xi = ((y1-y0)*dx1*dx2 + x0*dy1*dx2 - x1*dy2*dx1) / (dx2*dy1-dx1*dy2) ;
yi = ((x1-x0)*dy1*dy2 + y0*dx1*dy2 - y1*dx2*dy1) / (dx1*dy2-dx2*dy1) ;
float point[2];
point[0] = xi;
point[1] = yi;
if (isPointOnEdgeTol(point, edge, tol)) {
inter[0] = xi;
inter[1] = yi;
return;
}
#if !defined(__CUDA_ARCH__)
inter[0] = NAN;
inter[1] = NAN;
#else
inter[0] = CUDART_NAN_F;
inter[1] = CUDART_NAN_F;
#endif
}
__device__ __host__ float dotProd(float v1[], float v2[]) {
return v1[0]*v2[0] + v1[1]*v2[1];
}
// dot prod with perpendicular v2
__device__ __host__ float dotPerp(float v1[], float v2[]) {
return v1[0]*v2[1] + v1[1]*(-v2[0]);
}
__device__ __host__ void normalizeVec(float vec[]) {
float mag = vecMag(vec);
vec[0] /=mag;
vec[1] /=mag;
}
__device__ __host__ void IntrLine2Segment(float *line, float *seg, float *inter ) {
// The intersection of two lines is a solution to P0+s0*D0 = P1+s1*D1.
// Rewrite this as s0*D0 - s1*D1 = P1 - P0 = Q. If D0.Dot(Perp(D1)) = 0,
// the lines are parallel. Additionally, if Q.Dot(Perp(D1)) = 0, the
// lines are the same. If D0.Dot(Perp(D1)) is not zero, then
// s0 = Q.Dot(Perp(D1))/D0.Dot(Perp(D1))
// produces the point of intersection. Also,
// s1 = Q.Dot(Perp(D0))/D0.Dot(Perp(D1))
// The segment is represented as (1-s)*P0+s*P1, where P0 and P1 are the
// endpoints of the segment and 0 <= s <= 1.
//
// Some algorithms involving segments might prefer a centered
// representation similar to how oriented bounding boxes are defined.
// This representation is C+t*D, where C = (P0+P1)/2 is the center of
// the segment, D = (P1-P0)/Length(P1-P0) is a unit-length direction
// vector for the segment, and |t| <= e. The value e = Length(P1-P0)/2
// is the 'extent' (or radius or half-length) of the segment.
float segCenter[2];
segCenter[0] = (seg[0] + seg[2])/2.0;
segCenter[1] = (seg[1] + seg[3])/2.0;
float originDiff[2];
originDiff[0] = segCenter[0] - line[0];
originDiff[1] = segCenter[1] - line[1];
float lineDir[2];
lineDir[0] = line[2];
lineDir[1] = line[3];
float segDir[2];
segDir[0] = seg[2] - seg[0];
segDir[1] = seg[3] - seg[1];
float segMag = vecMag(segDir);
float D0DotPerpD1 = dotPerp(lineDir, segDir);
if (D0DotPerpD1 > 1e-14) {
float invD0DotPerpD1 = 1.0/D0DotPerpD1;
float diffDotPerpD0 = dotPerp(originDiff, lineDir);
float diffDotPerpD1 = dotPerp(originDiff, segDir);
float s0 = diffDotPerpD1*invD0DotPerpD1;
float s1 = diffDotPerpD0*invD0DotPerpD1;
float segExt = segMag/2;
if (s1 <= segExt) {
inter[0] = line[0] + s0*lineDir[0];
inter[1] = line[1] + s0*lineDir[1];
} else {
#if !defined(__CUDA_ARCH__)
inter[0] = NAN;
inter[1] = NAN;
#else
inter[0] = CUDART_NAN_F;
inter[1] = CUDART_NAN_F;
#endif
}
return;
}
// Lines are parallel
normalizeVec(originDiff);
float diffNDotPerpD1 = dotPerp(originDiff, segDir);
if (diffNDotPerpD1 <= 1e-14) {
#if !defined(__CUDA_ARCH__)
inter[0] = INFINITY;
inter[1] = INFINITY;
#else
inter[0] = CUDART_INF_F;
inter[1] = CUDART_INF_F;
#endif
return;
}
#if !defined(__CUDA_ARCH__)
inter[0] = NAN;
inter[1] = NAN;
#else
inter[0] = CUDART_NAN_F;
inter[1] = CUDART_NAN_F;
#endif
return;
}
__device__ __host__ void IntrLine2Line(float *line0, float *line1, float *inter ) {
// The intersection of two lines is a solution to P0+s0*D0 = P1+s1*D1.
// Rewrite this as s0*D0 - s1*D1 = P1 - P0 = Q. If D0.Dot(Perp(D1)) = 0,
// the lines are parallel. Additionally, if Q.Dot(Perp(D1)) = 0, the
// lines are the same. If D0.Dot(Perp(D1)) is not zero, then
// s0 = Q.Dot(Perp(D1))/D0.Dot(Perp(D1))
// produces the point of intersection. Also,
// s1 = Q.Dot(Perp(D0))/D0.Dot(Perp(D1))
float originDiff[2];
originDiff[0] = line1[0] - line0[0];
originDiff[1] = line1[1] - line0[1];
float lineDir0[2],lineDir1[2];
lineDir0[0] = line0[2];
lineDir0[1] = line0[3];
lineDir1[0] = line1[2];
lineDir1[1] = line1[3];
float D0DotPerpD1 = dotPerp(lineDir0, lineDir1);
if (D0DotPerpD1 > 1e-14) {
float invD0DotPerpD1 = 1.0/D0DotPerpD1;
// float diffDotPerpD0 = dotPerp(originDiff, lineDir0);
float diffDotPerpD1 = dotPerp(originDiff, lineDir1);
float s0 = diffDotPerpD1*invD0DotPerpD1;
// float s1 = diffDotPerpD0*invD0DotPerpD1;
inter[0] = line0[0] + s0*lineDir0[0];
inter[1] = line0[1] + s0*lineDir0[1];
return;
}
// Lines are parallel
normalizeVec(originDiff);
float diffNDotPerpD1 = dotPerp(originDiff, lineDir1);
if (diffNDotPerpD1 <= 1e-14) {
#if !defined(__CUDA_ARCH__)
inter[0] = INFINITY;
inter[1] = INFINITY;
#else
inter[0] = CUDART_INF_F;
inter[1] = CUDART_INF_F;
#endif
return;
}
#if !defined(__CUDA_ARCH__)
inter[0] = NAN;
inter[1] = NAN;
#else
inter[0] = CUDART_NAN_F;
inter[1] = CUDART_NAN_F;
#endif
return;
}
__device__ __host__ int isAnyNaN(float *t, int len) {
int test = 0;
for (int l=0; l<len; l++) {
test += isnan(t[l]);
}
return test > 0;
}
__device__ __host__ int isAnyInf(float *t, int len) {
int test = 0;
for (int l=0; l<len; l++) {
test += isinf(t[l]);
}
return test > 0;
}
__device__ __host__ void insertSortVectors(float ** list, int len, int vectorLen) {
// Loop over list
for (int index=0; index < len-1; index++) {
int indexOfSmallest = index;
// Look over rest for smallest
for (int scan=index+1; scan<len; scan++) {
int notLess = false;
// Compare elements
for (int t=0; t<vectorLen; t++)
if (list[indexOfSmallest][t]<list[scan][t])
break;
else if (list[indexOfSmallest][t]>list[scan][t]) {
notLess = true;
break;
}
// Swap
if (notLess) {// smallest is not actually the smallest
float *temp = list[scan];
list[scan] = list[indexOfSmallest];
list[indexOfSmallest] = temp;
indexOfSmallest = scan;
}
}
}
}
__host__ int selfitsComp ( const void * a, const void *b ) {
float xa,ya,xb,yb;
float **ap, **bp;
ap = (float **)a;
bp = (float **)b;
xa = (*ap)[0];
ya = (*ap)[1];
xb = (*bp)[0];
yb = (*bp)[1];
if (xa < xb)
return -1;
if (xa > xb)
return 1;
if (ya < yb)
return -1;
if (ya > yb)
return 1;
return 0;
}
__device__ __host__ int uniqueRowsCount(float **list, int len) {
//#if !defined(__CUDA_ARCH__)
// qsort(list, 4, sizeof(float*), selfitsComp);
//#else
insertSortVectors(list, len, 2);
//#endif
int count=1; // The first is unique
for (int l=0; l<len-1; l++) {
//#if !defined(__CUDA_ARCH__)
// if (selfitsComp(&list[l],&list[l+1]) != 0)
// count++;
//#else
int notEqual = false;
for (int t=0; t<2; t++)
if (list[l][t] != list[l+1][t]) { // if any element is not equal
notEqual = true;
break;
} // floating point equal for exact match only
if (notEqual)
count++;
//#endif
}
return count;
}
// Point Inclusion in Polygon Test
// Alogorithm from W. Randolph Franklin (WRF)
//
__device__ __host__ int pnpoly(int nvert, float *vertx, float *verty, float testx, float testy)
{
int i, j, c = 0;
for (i = 0, j = nvert-1; i < nvert; j = i++) {
if ( ((verty[i]>testy) != (verty[j]>testy)) &&
(testx < (vertx[j]-vertx[i]) * (testy-verty[i]) / (verty[j]-verty[i]) + vertx[i]) )
c = !c;
}
return c;
}
__device__ __host__ void pntsnpoly(float *intx, float *inty, float *xv, float *yv, int len, int *test, int tlen) {
for (int l=0; l<tlen; l++) {
test[l] = pnpoly(len,xv,yv,intx[l],inty[l]);
}
}
__device__ __host__ void centroidConformalCoords(float *xv,float *yv, float *intx, float *inty,
float **perpLines, int *inpolyTest, int len, FootPrint *newPoly, FootPrint*newTexcoords) {
// Compute texture coords for geometric coords and remove duplicates
float lineEdgeTol = .0001;
float tempVec[4];
float aInt[2];
float bInt[2];
int ii = 1;
for (int i=0; i<4; i++) {
if (inpolyTest[i]) {
newPoly->x[newPoly->numPoints] = intx[i];
newPoly->y[newPoly->numPoints] = inty[i];
newPoly->numPoints++;
ii +=2; // skip
} else {
//
// perp lines do not intersect inside quadrilateral so check
// intersections with a quadrilateral edge between neighbors
// Check intersect of two consecutive perp lines to shared edge
// next edge intersection
// left
tempVec[0] = xv[i%4];
tempVec[1] = yv[i%4];
tempVec[2] = xv[(i+1)%4];
tempVec[3] = yv[(i+1)%4];
intersectLineEdgeTol(perpLines[i%4], tempVec, aInt, lineEdgeTol);
if (isAnyNaN(aInt,2)) { // over shot the edge try the next one
tempVec[0] = xv[(i+1)%4];
tempVec[1] = yv[(i+1)%4];
tempVec[2] = xv[(i+2)%4];
tempVec[3] = yv[(i+2)%4];
intersectLineEdgeTol(perpLines[i%4], tempVec, aInt, lineEdgeTol);
}
// right, looking backwards
tempVec[0] = xv[i%4];
tempVec[1] = yv[i%4];
tempVec[2] = xv[(i+1)%4];
tempVec[3] = yv[(i+1)%4];
intersectLineEdgeTol(perpLines[(i+1)%4], tempVec, bInt, lineEdgeTol);
if (isAnyNaN(bInt, 2)) {
tempVec[0] = xv[(i+4-1)%4];
tempVec[1] = yv[(i+4-1)%4];
tempVec[2] = xv[i%4];
tempVec[3] = yv[i%4];
intersectLineEdgeTol(perpLines[(i+1)%4], tempVec, bInt, lineEdgeTol);
}
// detect and remove redundant points
int dupprevbIntaInt = 0; // new a same as prev b
int dupfirstaIntbInt = 0; // new b same as first a (cycle)
// check for and remove duplicates
if (newPoly->numPoints>0) {
dupprevbIntaInt = aInt[0]==newPoly->x[newPoly->numPoints-1] && aInt[1]==newPoly->y[newPoly->numPoints-1];
dupfirstaIntbInt = bInt[0]==newPoly->x[0] && bInt[1]==newPoly->y[0];
}
if (!dupprevbIntaInt) {
// no duplicate of new a so append to poly
newPoly->x[newPoly->numPoints] = aInt[0];
newPoly->y[newPoly->numPoints] = aInt[1];
newPoly->numPoints++;
}
if (!dupfirstaIntbInt) {
newPoly->x[newPoly->numPoints] = bInt[0];
newPoly->y[newPoly->numPoints] = bInt[1];
newPoly->numPoints++;
}
ii = ii + 2;
}
}
if (isAnyNaN(&newPoly->x[0], newPoly->numPoints) ||
isAnyNaN(&newPoly->y[0], newPoly->numPoints)) {
#if !defined(__CUDA_ARCH__)
printf("Mis-clip. Possible calculation problem\n");
#endif
newPoly->numPoints = 0;
newTexcoords->numPoints = 0;
return;
}
float testVerts[8][2];
float *testPtrs[8];
// Copy clipped points to buffer for unique tests
for (int g=0; g<newPoly->numPoints; g++) {
testVerts[g][0] = newPoly->x[g];
testVerts[g][1] = newPoly->y[g];
testPtrs[g]=&testVerts[g][0];// Used for qsort
}
if (uniqueRowsCount(&testPtrs[0], newPoly->numPoints)<4) {
#if !defined(__CUDA_ARCH__)
printf("Overclipped\n");
#endif
newPoly->numPoints = 0;
newTexcoords->numPoints = 0;
return;
}
// With polys we can find the centroid and define texture mapping
float Cr = 0.0, Cc = 0.0;
for (int g=0; g<newPoly->numPoints; g++) {
Cr += newPoly->y[g];
Cc += newPoly->x[g];
}
Cr *= 1.0/(float)(newPoly->numPoints);
Cc *= 1.0/(float)(newPoly->numPoints);
// Should not be needed
if (isnan(Cc) || isnan(Cr)) {
#if !defined(__CUDA_ARCH__)
printf("Can't find a centroid\n");
#endif
newPoly->numPoints = 0;
newTexcoords->numPoints = 0;
return;
}
for (int i=0; i<newPoly->numPoints; i++) {
float angle = fmod(atan2(newPoly->y[i]-Cr, newPoly->x[i]-Cc) + 2*M_PI,2*M_PI);
newTexcoords->x[i] = 0.5 + .5*cos(angle);
newTexcoords->y[i] = 0.5 + 0.5*sin(angle);
}
newTexcoords->numPoints = newPoly->numPoints;
}
}
// puts texRef into Cuda's reference name space
// texture<float,3,cudaReadModeElementType> texRefFilter;
// texture<unsigned char,3,cudaReadModeNormalizedFloat> texRefFilter;
texture<unsigned char,3,cudaReadModeNormalizedFloat> texRefFilter;
texture<unsigned short,2,cudaReadModeElementType> texRefIx;
texture<unsigned short,2,cudaReadModeElementType> texRefIy;
__device__ static void CopyBack(cudaArray *boxFilter_Src, int *d_sensorX, int *d_sensorY, int *d_plane,
clippedGeom *d_resultsGeom, int *d_resultsGeomLen, int maxSensors) {
int i = blockDim.x*blockIdx.x + threadIdx.x;
if (i>=maxSensors) {
++d_resultsGeomLen[0];
return;
}
i = threadIdx.x;
d_resultsGeom[i].x[0] = (float)d_sensorX[i];
d_resultsGeom[i].y[0] = (float)d_sensorY[i];
d_resultsGeomLen[i]=1;
++d_resultsGeomLen[1];
}
__device__ __host__ float magIntVec(int x, int y ) {
return sqrtf((float)x*x + (float)y*y);
}
__device__ int midRangeFilterReponse(int col, int row, int pOffSet, int numExposures ) {
int found = 0;
float imgtest = 0.0;
int expIndex = 0;
int j;
for (j=0; j<numExposures; j++) {
imgtest = tex3D(texRefFilter, (float)col, (float)row, (float) (pOffSet+j));
if (imgtest < 0.9 && imgtest > 0.3) {
expIndex = j;
found = 1;
}
}
if (!found) return numExposures - 1;
return expIndex;
}
__global__ void computeTriClipGPU(
int filterFrame, int numExposures,int spatialImgWidth, int spatialImgHeight, int *d_sensorX, int *d_sensorY, int *d_plane,
clippedGeom *d_resultsGeom, clippedGeom *d_resultsTex, int *d_resultsGeomLen, int numSensors, experimentData *debug) {
float dudx, dudy, dvdx, dvdy;
float ndudx, ndudy, ndvdx, ndvdy;
float magdx, magdy;
int sIndex = blockDim.x*blockIdx.x + threadIdx.x;
if (sIndex >= numSensors) return;
int pIndex = d_plane[sIndex];
int x = d_sensorX[sIndex]-1; // Matlab shift to C indexing
int y = d_sensorY[sIndex]-1;
dudx = (float)tex2D(texRefIx, (float)(x+1), (float)y) - (float)tex2D(texRefIx, (float)(x-1), (float)y);
dudy = (float)tex2D(texRefIx, (float)x, (float)(y+1)) - (float)tex2D(texRefIx, (float)x, (float)(y-1));
dvdx = (float)tex2D(texRefIy, (float)(x+1), (float)y) - (float)tex2D(texRefIy, (float)(x-1), (float)y);
dvdy = (float)tex2D(texRefIy, (float)x, (float)(y+1)) - (float)tex2D(texRefIy, (float)x, (float)(y-1));
magdx = magIntVec(dudx, dvdx);
magdy = magIntVec(dudy, dvdy);
ndudx = dudx/magdx;
ndvdx = dvdx/magdx;
ndudy = dudy/magdy;
ndvdy = dvdy/magdy;
// may be parallelized in CUDA
int n1r,n1c,n2r,n2c,n3r,n3c,n4c,n4r; // sensor neighborhood coordinates
int Cr, Cc; // sensor coordinates
int n5r,n5c,n6r,n6c,n7r,n7c,n8r,n8c; // corner sensors
float centroid_r,centroid_c;
Cc = x;
Cr = y;
// sensor neighborhood coordinates
n1r = Cr-1;
n1c = Cc;
n2r = Cr;
n2c = Cc-1;
n3r = Cr+1;
n3c = Cc;
n4r = Cr;
n4c = Cc+1;
// corner sensors
n5r = n1r;
n5c = n2c;
n6r = n3r;
n6c = n2c;
n7r = n3r;
n7c = n4c;
n8r = n1r;
n8c = n4c;
// Find the best linear response pixel
int Iexp = midRangeFilterReponse(Cc, Cr, pIndex*numExposures, numExposures);
// Sample image at linear exposure
float rIi1,rIi2,rIi3,rIi4,rIi5,rIi6,rIi7,rIi8,rIic;
int expIndex = pIndex*numExposures + Iexp;
rIi1 = tex3D(texRefFilter, (float)n1c, (float)n1r, (float)expIndex);
rIi2 = tex3D(texRefFilter, (float)n2c, (float)n2r, (float)expIndex);
rIi3 = tex3D(texRefFilter, (float)n3c, (float)n3r, (float)expIndex);
rIi4 = tex3D(texRefFilter, (float)n4c, (float)n4r, (float)expIndex);
rIi5 = tex3D(texRefFilter, (float)n5c, (float)n5r, (float)expIndex);
rIi6 = tex3D(texRefFilter, (float)n6c, (float)n6r, (float)expIndex);
rIi7 = tex3D(texRefFilter, (float)n7c, (float)n7r, (float)expIndex);
rIi8 = tex3D(texRefFilter, (float)n8c, (float)n8r, (float)expIndex);
rIic = tex3D(texRefFilter, (float)Cc, (float)Cr, (float)expIndex);
// Clipping computations
float Rtotal, areaL, kIinv, uneighbors[4], vneighbors[4];
Rtotal = rIi1 + rIi2 + rIic + rIi3 + rIi4;
Rtotal = Rtotal + rIi5 + rIi6 + rIi7 + rIi8;
uneighbors[0] = tex2D(texRefIx, (float)n1c, (float)n1r);//Ix[i1];
vneighbors[0] = tex2D(texRefIy, (float)n1c, (float)n1r);//Iy[i1];
uneighbors[1] = tex2D(texRefIx, (float)n2c, (float)n2r);//Ix[i2];
vneighbors[1] = tex2D(texRefIy, (float)n2c, (float)n2r);//Iy[i2];
uneighbors[2] = tex2D(texRefIx, (float)n3c, (float)n3r);//Ix[i3];
vneighbors[2] = tex2D(texRefIy, (float)n3c, (float)n3r);//Iy[i3];
uneighbors[3] = tex2D(texRefIx, (float)n4c, (float)n4r);//Ix[i4];
vneighbors[3] = tex2D(texRefIy, (float)n4c, (float)n4r);//Iy[i4];
float point1[2], point2[2], point3[2], point4[2];
point1[0] = uneighbors[0];
point1[1] = vneighbors[0];
point2[0] = uneighbors[1];
point2[1] = vneighbors[1];
point3[0] = uneighbors[2];
point3[1] = vneighbors[2];
point4[0] = uneighbors[3];
point4[1] = vneighbors[3];
// Warning, we assume the spatial image has the same dimensions as the filter response images
centroid_c = 0.25*(point1[0] + point2[0] + point3[0] + point4[0]);
centroid_r = 0.25*(point1[1] + point2[1] + point3[1] + point4[1]);
float tempF = polygonArea(uneighbors, vneighbors, 4);
areaL = fabs(tempF);
kIinv = areaL/Rtotal;
float diagvec1[4], diagvec2[4], diagvec3[4], diagvec4[4];
diagvec1[0] = point1[0];
diagvec1[1] = point1[1];
diagvec1[2] = ndudy;
diagvec1[3] = ndvdy;
diagvec2[0] = point2[0];
diagvec2[1] = point2[1];
diagvec2[2] = ndudx;
diagvec2[3] = ndvdx;
diagvec3[0] = point3[0];
diagvec3[1] = point3[1];
diagvec3[2] = -ndudy;
diagvec3[3] = -ndvdy;
diagvec4[0] = point4[0];
diagvec4[1] = point4[1];
diagvec4[2] = -ndudx;
diagvec4[3] = -ndvdx;
float projLeft1[2],projRight1[2],projDist1,projLeft2[2],projRight2[2],projDist2;
float projLeft3[2],projRight3[2],projDist3,projLeft4[2],projRight4[2],projDist4;
// Centroid based hclip
// Make a line for the base of a triangle,
// perpendicular to diagonal vector (vertex to centroid) or
// reference triangle altitiude
projPointOnLine(point4, diagvec1, projLeft1);
projPointOnLine(point2, diagvec1, projRight1);
float tempVecA[2], tempVecB[2];
tempVecA[0] = point1[0] - projLeft1[0]; tempVecA[1] = point1[1] - projLeft1[1];
tempVecB[0] = point1[0] - projRight1[0]; tempVecB[1] = point1[1] - projRight1[1];
projDist1 = fminf(vectorNorm(tempVecA), vectorNorm(tempVecB));
projPointOnLine(point1, diagvec2, projLeft2);
projPointOnLine(point3, diagvec2, projRight2);
tempVecA[0] = point2[0] - projLeft2[0]; tempVecA[1] = point2[1] - projLeft2[1];
tempVecB[0] = point2[0] - projRight2[0]; tempVecB[1] = point2[1] - projRight2[1];
projDist2 = fminf(vectorNorm(tempVecA), vectorNorm(tempVecB));
projPointOnLine(point2, diagvec3, projLeft3);
projPointOnLine(point4, diagvec3, projRight3);
tempVecA[0] = point3[0] - projLeft3[0]; tempVecA[1] = point3[1] - projLeft3[1];
tempVecB[0] = point3[0] - projRight3[0]; tempVecB[1] = point3[1] - projRight3[1];
projDist3 = fminf(vectorNorm(tempVecA), vectorNorm(tempVecB));
projPointOnLine(point3, diagvec4, projLeft4);
projPointOnLine(point1, diagvec4, projRight4);
tempVecA[0] = point4[0] - projLeft4[0]; tempVecA[1] = point4[1] - projLeft4[1];
tempVecB[0] = point4[0] - projRight4[0]; tempVecB[1] = point4[1] - projRight4[1];
projDist4 = fminf(vectorNorm(tempVecA), vectorNorm(tempVecB));
// projDist is the altitude length and
// convex_pln is the perpendicular base line equation of the
// reference triangle
//
float convex_pln_1[4], convex_pln_2[4], convex_pln_3[4], convex_pln_4[4];
convex_pln_1[0] = point1[0]+projDist1*ndudy;
convex_pln_1[1] = point1[1]+projDist1*ndvdy;
convex_pln_1[2] = -ndvdy;
convex_pln_1[3] = ndudy;
convex_pln_2[0] = point2[0]+projDist2*ndudx;
convex_pln_2[1] = point2[1]+projDist2*ndvdx;
convex_pln_2[2] = -ndvdx;
convex_pln_2[3] = ndudx;
convex_pln_3[0] = point3[0]-projDist3*ndudy;
convex_pln_3[1] = point3[1]-projDist3*ndvdy;
convex_pln_3[2] = -ndvdy;
convex_pln_3[3] = ndudy;
convex_pln_4[0] = point4[0]-projDist4*ndudx;
convex_pln_4[1] = point4[1]-projDist4*ndvdx;
convex_pln_4[2] = -ndvdx;
convex_pln_4[3] = ndudx;
// Compute intersections between base line and edges
// about a vertex of the quadrilateral
// a Nan may result if outside edge end points
float lineEdgeTol = .0001;
float intLeft1[2], intRight1[2], intLeft2[2], intRight2[2], intLeft3[2], intRight3[2], intLeft4[2], intRight4[2];
float edge41[4], edge12[4], edge23[4], edge34[4];
edge41[0] = point4[0]; edge41[1] = point4[1]; edge41[2] = point1[0]; edge41[3] = point1[1];
edge12[0] = point1[0]; edge12[1] = point1[1]; edge12[2] = point2[0]; edge12[3] = point2[1];
edge23[0] = point2[0]; edge23[1] = point2[1]; edge23[2] = point3[0]; edge23[3] = point3[1];
edge34[0] = point3[0]; edge34[1] = point3[1]; edge34[2] = point4[0]; edge34[3] = point4[1];
intersectLineEdgeTol(convex_pln_1, edge41, intLeft1, lineEdgeTol);
intersectLineEdgeTol(convex_pln_1, edge12, intRight1, lineEdgeTol);
intersectLineEdgeTol(convex_pln_2, edge12, intLeft2, lineEdgeTol);
intersectLineEdgeTol(convex_pln_2, edge23, intRight2, lineEdgeTol);
intersectLineEdgeTol(convex_pln_3, edge23, intLeft3, lineEdgeTol);
intersectLineEdgeTol(convex_pln_3, edge34, intRight3, lineEdgeTol);
intersectLineEdgeTol(convex_pln_4, edge34, intLeft4, lineEdgeTol);
intersectLineEdgeTol(convex_pln_4, edge41, intRight4, lineEdgeTol);
// Compute length of base edge-to-edge intersections
float base1, base2, base3, base4;
base1 = distancePoints(intLeft1, intRight1);
base2 = distancePoints(intLeft2, intRight2);
base3 = distancePoints(intLeft3, intRight3);
base4 = distancePoints(intLeft4, intRight4);
// Area of a triangle is .5*base*height
// height is magnitude of vertex-centroid vector
float A1, A2, A3, A4;
A1 = .5*base1*projDist1;
A2 = .5*base2*projDist2;
A3 = .5*base3*projDist3;
A4 = .5*base4*projDist4;
float hclip1, hclip2, hclip3, hclip4;
hclip1 = sqrtf(rIi1*kIinv*projDist1*projDist1/A1);
hclip2 = sqrtf(rIi2*kIinv*projDist2*projDist2/A2);
hclip3 = sqrtf(rIi3*kIinv*projDist3*projDist3/A3);
hclip4 = sqrtf(rIi4*kIinv*projDist4*projDist4/A4);
// Debug
debug[sIndex].hclip[0] = hclip1;
debug[sIndex].hclip[1] = hclip2;
debug[sIndex].hclip[2] = hclip3;