static double findY(double* p1, double* p2)
{
double a = p1[0];
double B = p2[1];
double D = p2[3];
double x = findX(p1, p2);
return -(a*x+D)/B;
}
bool findX(int u) {
for (int v = 0; v < nx; v++) {
if (v != delX && !used[v] && g[v][u]) {//notice it's g[v][u]
used[v] = 1;
if (mx[v] == -1 || findX(mx[v]))
return 1;
}
}
return 0;
}
/// <summary>
/// Finds bounding-box of the data present in given image.
/// </summary>
/// <params name="imsSrc">
/// Source image for which bouding box has to be found.
/// </params>
/// <returns> Bounding box as CvRect. </returns>
CvRect OCR::findBB(IplImage* imgSrc)
{
CvRect aux;
int xmin, xmax, ymin, ymax;
xmin=xmax=ymin=ymax=0;
findX(imgSrc, &xmin, &xmax);
findY(imgSrc, &ymin, &ymax);
aux=cvRect(xmin, ymin, xmax-xmin, ymax-ymin);
return aux;
}
line intervalRange(line I, vector a, vector b, line e) {
point i1a = intersection(I.pt1, a, e);
point i1b = intersection(I.pt1, b, e);
point i2a = intersection(I.pt2, a, e);
point i2b = intersection(I.pt2, b, e);
double xmin = min(i1a.x, i1b.x, i2a.x, i2b.x);
double ymin = min(i1a.y, i1b.y, i2a.y, i2b.y);
if (i1a.x == INFINITY) {
i1a.x = -INFINITY;
i1a.y = -INFINITY;
}
if (i1b.x == INFINITY) {
i1b.x = -INFINITY;
i1b.y = -INFINITY;
}
if (i2a.x == INFINITY) {
i2a.x = -INFINITY;
i2a.y = -INFINITY;
}
if (i2b.x == INFINITY) {
i2b.x = -INFINITY;
i2b.y = -INFINITY;
}
double xmax = max(i1a.x, i1b.x, i2a.x, i2b.x);
double ymax = max(i1a.y, i1b.y, i2a.y, i2b.y);
line l;
if (xmin < xmax) {
l.pt1.x = xmin;
l.pt1.y = findY(xmin, e);
l.pt2.x = xmax;
l.pt2.y = findY(xmax, e);
return l;
}
l.pt1.x = findX(ymin, e);
l.pt1.y = ymin;
l.pt2.x = findX(ymax, e);
l.pt2.y = ymax;
return l;
}
void solve(Point p1, Point p2) {
if (p1.y == p2.y) return;
if (p1.y > p2.y) {
Point tmp = p1;
p1 = p2;
p2 = tmp;
}
for (int i = upperBound(p1.y); i <= lowerBound(p2.y); i++)
if (i > 0 && i < 100) {
double v = findX(p1,i,p2);
if (maxX[i] < v) maxX[i] = v;
if (minX[i] > v) minX[i] = v;
}
}
CvRect findBB(IplImage* imgSrc)
{
CvRect aux;
int xmin, xmax, ymin, ymax;
xmin=xmax=ymin=ymax=0;
findX(imgSrc, &xmin, &xmax);
findY(imgSrc, &ymin, &ymax);
aux=cvRect(xmin, ymin, xmax-xmin, ymax-ymin);
//printf("BB: %d,%d - %d,%d\n", aux.x, aux.y, aux.width, aux.height);
return aux;
}
QuantisedFunctionPtr QuantisedFunction::inverse() const
{
if(!isMonotonous(true)) return QuantisedFunctionPtr();
std::vector<real_t> values(__sampling,0);
real_t firsty = __values[0];
real_t lasty = __values[__sampling-1];
if (firsty > lasty) std::swap(firsty,lasty);
real_t x = __firstx;
real_t y = firsty ;
real_t extent = lasty - firsty;
real_t deltay = extent / (__sampling-1);
bool found;
for (uint_t i = 0; i < __sampling; ++i){
x = findX(y,found,x);
assert(found == true);
values[i] = x;
y += deltay;
}
return QuantisedFunctionPtr(new QuantisedFunction(values,firsty,lasty));
}
//X[i]=1 or Y[i]=1 means it's not a key vertex!!!
void solve() {
memset(X, 0, sizeof(X));
memset(Y, 0, sizeof(Y));
for (int i = 0; i < nx; i++) {
if (mx[i] == -1) {
X[i] = 1;
} else {
delY = mx[i];
memset(used, 0, sizeof(used));
if (findY(i)) Y[delY] = 1;
}
}
for (int j = 0; j < ny; j++) {
if (my[j] == -1) {
Y[j] = 1;
} else {
delX = my[j];
memset(used, 0, sizeof(used));
if (findX(j)) X[delX] = 1;
}
}
}
int findX(int a[], int left, int right, int x)
{
int mid=(left+right)/2;
if(a[mid]==x)
return mid;
if(left>right)
return -1;
if(a[left]<a[mid]) //left is in order
{
if(x>=a[left]&&x<a[mid]) //x in left half
return findX(a, left, mid-1, x);
else
return findX(a, mid+1, right, x);
}
else if(a[left]>a[mid]) //right is in order
{
if(x>a[mid]&&x<=a[right])
return findX(a, mid+1, right, x);
else
return findX(a, left, mid-1, x);
}else if(a[left]==a[mid])
{
if(a[mid]!=a[right]) // left half is all repeated, right half is different
return findX(a, mid+1, right, x);
else
{
int result=findX(a, left, mid-1, x);
if(result==-1)
return findX(a, mid+1, right, x);
else
return result;
}
}
return -1;
}
void main()
{
int a[N]={3, 0, 1, 2, 3, 3, 3};
printf("The index is %d\n", findX(a, 0, N-1, 3));
}
int main (int argc, char **argv)
{
Visual *vis;
Colormap cm;
Display *_display;
Imlib_Context context;
Imlib_Image image;
Pixmap pixmap;
Imlib_Color_Modifier modifier = NULL;
_display = XOpenDisplay (NULL);
int width, height, depth, i, alpha;
char str1[40];
char str2[40];
char str3[40];
char str4[40];
char str5[40];
int ck0;
int w, h;
w = 0;
h = 0;
char strA1[30] = "hwe";
char strA2[30] = "hwer";
const char jpg[15] = "jpg"; //1
const char png[15] = "png"; //2
char *A1;
char *A2;
strcpy(strA1, argv[argc-1]);
strcpy(strA2, strA1);
A1 = strstr(strA1, jpg);
A2 = strstr(strA2, png);
//check to be sure image format is written right or abort
checkForNull(A1, A2);
for (screen = 0; screen < ScreenCount (_display); screen++)
{
display = XOpenDisplay (NULL);
context = imlib_context_new ();
imlib_context_push (context);
imlib_context_set_display (display);
vis = DefaultVisual (display, screen);
cm = DefaultColormap (display, screen);
width = DisplayWidth (display, screen);
height = DisplayHeight (display, screen);
depth = DefaultDepth (display, screen);
pixmap =
XCreatePixmap (display, RootWindow (display, screen),
width, height, depth);
imlib_context_set_visual (vis);
imlib_context_set_colormap (cm);
imlib_context_set_drawable (pixmap);
imlib_context_set_color_range (imlib_create_color_range ());
image = imlib_create_image (width, height);
imlib_context_set_image (image);
printf("1\n");
imlib_context_set_color (0, 0, 0, 255);
imlib_image_fill_rectangle (0, 0, width, height);
imlib_context_set_dither (1);
imlib_context_set_blend (1);
printf("2\n");
alpha = 255;
for (i = 1; i < argc; i++)
{
if (modifier != NULL)
{
imlib_apply_color_modifier ();
imlib_free_color_modifier ();
}
modifier = imlib_create_color_modifier ();
imlib_context_set_color_modifier (modifier);
if (strcmp (argv[i], "-alpha") == 0)
{
if ((++i) >= argc)
{
fprintf (stderr, "Missing alpha\n");
continue;
}
if (sscanf (argv[i], "%i", &alpha) == 0)
{
fprintf (stderr, "Bad alpha (%s)\n", argv[i]);
continue;
}
}
else if (strcmp (argv[i], "-solid") == 0)
{
Color c;
if ((++i) >= argc)
{
fprintf (stderr, "Missing color\n");
continue;
}
if (parse_color (argv[i], &c, alpha) == 1)
{
fprintf (stderr, "Bad color (%s)\n", argv[i]);
continue;
}
imlib_context_set_color (c.r, c.g, c.b, c.a);
imlib_image_fill_rectangle (0, 0, width, height);
}
else if (strcmp (argv[i], "-clear") == 0)
{
imlib_free_color_range ();
imlib_context_set_color_range (imlib_create_color_range ());
}
else if (strcmp (argv[i], "-add") == 0)
{
Color c;
if ((++i) >= argc)
{
fprintf (stderr, "Missing color\n");
continue;
}
if (parse_color (argv[i], &c, alpha) == 1)
{
fprintf (stderr, "Bad color (%s)\n", argv[i - 1]);
continue;
}
imlib_context_set_color (c.r, c.g, c.b, c.a);
imlib_add_color_to_color_range (1);
}
else if (strcmp (argv[i], "-addd") == 0)
{
Color c;
int distance;
if ((++i) >= argc)
{
fprintf (stderr, "Missing color\n");
continue;
}
if ((++i) >= argc)
{
fprintf (stderr, "Missing distance\n");
continue;
}
if (parse_color (argv[i - 1], &c, alpha) == 1)
{
fprintf (stderr, "Bad color (%s)\n", argv[i - 1]);
continue;
}
if (sscanf (argv[i], "%i", &distance) == 1)
{
fprintf (stderr, "Bad distance (%s)\n", argv[i]);
continue;
}
imlib_context_set_color (c.r, c.g, c.b, c.a);
imlib_add_color_to_color_range (distance);
}
else if (strcmp (argv[i], "-gradient") == 0)
{
int angle;
if ((++i) >= argc)
{
fprintf (stderr, "Missing angle\n");
continue;
}
if (sscanf (argv[i], "%i", &angle) == 1)
{
fprintf (stderr, "Bad angle (%s)\n", argv[i]);
continue;
}
imlib_image_fill_color_range_rectangle (0, 0, width, height,
angle);
}
else if (strcmp (argv[i], "-fill") == 0)
{
if ((++i) >= argc)
{
fprintf (stderr, "Missing image\n");
continue;
}
if ( load_Mod_image(Fill, argv[i], width, height, alpha, image, ck0) == 1)
{
fprintf (stderr, "Bad image (%s)\n", argv[i]);
continue;
}
}
else if (strcmp (argv[i], "-dia") == 0)
{
if((++i) >= argc)
{
fprintf(stderr, "missing Dia, and Image\n");
continue;
}
strcpy (str1, argv[i]);
strcpy (str2, str1);
if ( findX(str1, &w, &h) == 1 )
{
fprintf(stderr, " Bad Format\n");
continue;
}
else if (findX(str2, &w, &h) == 0 && ((++i) >= argc))
{
fprintf(stderr, "Missing Image\n");
continue;
}
else
{
//if format is correct then assign a number for
//load_Mod_Image to check
ck0 = -2;
w = w;
h = h;
}
if( load_Mod_image(Dia, argv[i], w, h, alpha, image, ck0) == 1 )
{
fprintf(stderr, "Bad Image or Bad Image Dimensions \n");
}
}
else if (strcmp (argv[i], "-tile") == 0)
{
if ((++i) >= argc)
{
fprintf(stderr, "format 0 missing \n");
continue;
}
strcpy (str1, argv[i]);
strcpy (str2, str1);
strcpy (str3, str2);
strcpy (str4, str3);
strcpy (str5, str4);
if ( findX(str1, &w, &h) == 3 && ((++i) >= argc))
{
fprintf(stderr, "missing Image\n");
continue;
} //check to see if format is -tile 0
else if (findX(str2, &w, &h) == 3)
{
ck0 = 3;
if( load_Mod_image(Tile, argv[i], width, height, alpha, image, ck0) == 1 )
{
fprintf(stderr, "Bad Image or Bad Image Dimensions \n");
continue;
}
}
if (findX(str3, &w, &h) == 1)
{
fprintf(stderr, "bad format\n");
continue;
}
if (findX(str4, &w, &h) == 0 && ((++i) >= argc))
{
fprintf(stderr, "missing something again\n");
continue;
}
if (findX (str5, &w, &h) == 0 )
{
ck0 = 2;
w = w;
h = h;
}
if( load_Mod_image(Tile, argv[i], w, h, alpha, image, ck0) == 1 )
{
fprintf(stderr, "Bad Image or Bad Image Dimension\n");
}
}
else if (strcmp (argv[i], "-center") == 0)
{
if ((++i) >= argc)
{
fprintf (stderr, "Missing image\n");
continue;
}
if (load_Mod_image (Center, argv[i], width, height, alpha, image, ck0) == 1)
{
fprintf (stderr, "Bad image (%s)\n", argv[i]);
continue;
}
}
else if (strcmp (argv[i], "-tint") == 0)
{
Color c;
DATA8 r[256], g[256], b[256], a[256];
int j;
if ((++i) >= argc)
{
fprintf (stderr, "Missing color\n");
continue;
}
if (parse_color (argv[i], &c, 255) == 1)
{
fprintf (stderr, "Bad color\n");
continue;
}
imlib_get_color_modifier_tables (r, g, b, a);
for (j = 0; j < 256; j++)
{
r[j] = (DATA8) (((double) r[j] / 255.0) * (double) c.r);
g[j] = (DATA8) (((double) g[j] / 255.0) * (double) c.g);
b[j] = (DATA8) (((double) b[j] / 255.0) * (double) c.b);
}
imlib_set_color_modifier_tables (r, g, b, a);
}
else if (strcmp (argv[i], "-blur") == 0)
{
int intval;
if ((++i) >= argc)
{
fprintf (stderr, "Missing value\n");
continue;
}
if (sscanf (argv[i], "%i", &intval) == 1)
{
fprintf (stderr, "Bad value (%s)\n", argv[i]);
continue;
}
imlib_image_blur (intval);
}
else if (strcmp (argv[i], "-sharpen") == 0)
{
int intval;
if ((++i) >= argc)
{
fprintf (stderr, "Missing value\n");
continue;
}
if (sscanf (argv[i], "%i", &intval) == 1)
{
fprintf (stderr, "Bad value (%s)\n", argv[i]);
continue;
}
imlib_image_sharpen (intval);
}
else if (strcmp (argv[i], "-contrast") == 0)
{
double dblval;
if ((++i) >= argc)
{
fprintf (stderr, "Missing value\n");
continue;
}
if (sscanf (argv[i], "%lf", &dblval) == 1)
{
fprintf (stderr, "Bad value (%s)\n", argv[i]);
continue;
}
imlib_modify_color_modifier_contrast (dblval);
}
else if (strcmp (argv[i], "-brightness") == 0)
{
double dblval;
if ((++i) >= argc)
{
fprintf (stderr, "Missing value\n");
continue;
}
if (sscanf (argv[i], "%lf", &dblval) == 1)
{
fprintf (stderr, "Bad value (%s)\n", argv[i]);
continue;
}
imlib_modify_color_modifier_brightness (dblval);
}
else if (strcmp (argv[i], "-gamma") == 0)
{
double dblval;
if ((++i) >= argc)
{
fprintf (stderr, "Missing value\n");
continue;
}
if (sscanf (argv[i], "%lf", &dblval) == 1)
{
fprintf (stderr, "Bad value (%s)\n", argv[i]);
continue;
}
imlib_modify_color_modifier_gamma (dblval);
}
else if (strcmp (argv[i], "-flipv") == 0)
{
imlib_image_flip_vertical ();
}
else if (strcmp (argv[i], "-fliph") == 0)
{
imlib_image_flip_horizontal ();
}
else if (strcmp (argv[i], "-flipd") == 0)
{
imlib_image_flip_diagonal ();
}
else if (strcmp (argv[i], "-write") == 0)
{
if ((++i) >= argc)
{
fprintf (stderr, "Missing filename\n");
continue;
}
imlib_save_image (argv[i]);
}
else
{
usage (argv[0]);
imlib_free_image ();
imlib_free_color_range ();
if (modifier != NULL)
{
imlib_context_set_color_modifier (modifier);
imlib_free_color_modifier ();
modifier = NULL;
}
XFreePixmap (display, pixmap);
exit (1);
} // end else
} // end loop off of argc
if (modifier != NULL)
{
imlib_context_set_color_modifier (modifier);
imlib_apply_color_modifier ();
imlib_free_color_modifier ();
modifier = NULL;
}
imlib_render_image_on_drawable (0, 0);
imlib_free_image ();
imlib_free_color_range ();
if (setRootAtoms (pixmap) == 0)
fprintf (stderr, "Couldn't create atoms...\n");
XKillClient (display, AllTemporary);
XSetCloseDownMode (display, RetainTemporary);
XSetWindowBackgroundPixmap (display, RootWindow (display, screen),
pixmap);
XClearWindow (display, RootWindow (display, screen));
XFlush (display);
XSync (display, False);
imlib_context_pop ();
imlib_context_free (context);
} // end for loop off screen
// } // frist if statment at start of main
return 0;
}
/* project onto intersection of (alpha)z-L1-ball and 1-LInf-ball */
static void project(double* x, double* v, double z, int N)
{
int i;
// first, check in v \in C
double norm1=0; double normInf=0; double absvi;
for (i=0;i<N;i++){
absvi=fabs(v[i]); norm1+=absvi;
if (absvi>normInf) {normInf=absvi;}
}
if ((norm1<=z)&(normInf<=1)){
for (i=0;i<N;i++){x[i]=v[i];}
return;
}
/* now, if v \not\in C */
/* transform to the non-negative orthant */
int* signv = new int[N]; double sumx=0;
for (i=0;i<N;i++){
signv[i]=sign(v[i]); v[i]=v[i]*signv[i];
if (v[i]>1){x[i]=1;} else {x[i]=v[i];} /* this x for case theta=0 */
sumx+=x[i];
}
/* check if theta=0 */
if (sumx<=z){
for (i=0;i<N;i++){x[i]=x[i]*signv[i];}
delete[] signv;
return;
}
/* case theta > 0 */
/* construct vvb array & find its min(thetaL) and max(thetaR) */
/* only non-negative values included (dual feasibility: theta>=0) */
int counter=0;
for (i=0;i<N;i++){if(v[i]>=1){counter++;}}
int K=N+counter; /* the length of vvb array */
double* vvb = new double[K];
double thetaL=DBL_MAX; double thetaR=-DBL_MAX; /* requires <float.h> */
for (i=0;i<N;i++){
vvb[i]=v[i];
if(v[i]>thetaR){thetaR=v[i];} /* max(thetaR) is among v[i]'s */
}
counter=N; for (i=0;i<N;i++){
if(v[i]>=1){vvb[counter]=v[i]-1;counter++;}
if(v[i]-1<thetaL){thetaL=v[i]-1;} /* min(thetaL) is among (v[i]-1)'s */
}
/* vvbadd is an array of adresses of vvb[left]...vvb[right] */
int left=0; int right=K-1;
double** vvbadd = new double*[K];
for (i=0;i<K;i++) {vvbadd[i]=&vvb[i];}
/* vadd - addresses of v[leftv]...v[rightv] */
int leftv=0; int rightv=N-1;
double** vadd = new double*[K];
for (i=0;i<N;i++) {vadd[i]=&v[i];}
double S=0; for(i=0;i<N;i++) {S=S+v[i];}
double SL=0; double SR=0; int nL=0; int nR=0;
double SLTemp, SRTemp; int nLTemp, nRTemp;
int cardL, cardM, cardU;
double sumvM, thetaP, zP;
int *medInds = new int[2];
int medLInd, medRInd;
double theta = -1;
int iter = 0;
int il,ic,ir;
while (1>0){
median(vvbadd,left,right,medInds);
medLInd=medInds[0]; medRInd=medInds[1];
thetaP = *vvbadd[medLInd];
SLTemp=0; SRTemp=0; nLTemp=0; nRTemp=0;
il=leftv-1; ic=leftv; ir=rightv+1;
while (ic<ir){
if (*vadd[ic]<thetaP){il++; swap(vadd,ic,il); SLTemp=SLTemp+*vadd[il]; nLTemp++; ic++;}
else if (*vadd[ic]>thetaP+1){ir--; swap(vadd,ic,ir); SRTemp=SRTemp+*vadd[ir]; nRTemp++;}
else {ic++;}
}
cardU = nR+nRTemp; cardL = nL+nLTemp; cardM = N-cardU-cardL;
sumvM = S-SLTemp-SRTemp;
zP = cardU+sumvM-thetaP*cardM;
if (zP>z)
{SL=SL+SLTemp; S=S-SLTemp; nL=nL+nLTemp; thetaL=thetaP; left=medRInd; leftv=il+1;}
if (zP < z)
{SR=SR+SRTemp; S=S-SRTemp; nR=nR+nRTemp; thetaR=thetaP; right=medLInd; rightv=ir-1;}
if (zP == z){theta = thetaP; break;}
if (right-left<=1) {break;}
if ((right==medRInd)&(left==medLInd)){break;} /* median(thetaP) is not unique */
iter++;if (iter == 100){printf("PROJ MAXITER: %d (error)\n",iter); break;}
}
if (theta==-1) /* theta != to one of the vvb[i] */
{
double zL,zR;
double thetaL=*vvbadd[left]; double thetaR=*vvbadd[right];
double SLTempL=0; double SRTempL=0; int nLTempL=0; int nRTempL=0;
il=leftv-1; ic=leftv; ir=rightv+1;
while (ic<ir){
if (*vadd[ic]<=thetaL){il++; swap(vadd,ic,il); SLTempL=SLTempL+*vadd[il]; nLTempL++; ic++;}
else if (*vadd[ic]>=thetaL+1){ir--; swap(vadd,ic,ir); SRTempL=SRTempL+*vadd[ir]; nRTempL++;}
else {ic++;}
}
cardU = nR+nRTempL; cardL = nL+nLTempL; cardM = N-cardU-cardL;
sumvM = S-SLTempL-SRTempL;
zL = cardU+sumvM-thetaL*cardM;
double SLTempR=0; double SRTempR=0; int nLTempR=0; int nRTempR=0;
il=leftv-1; ic=leftv; ir=rightv+1;
while (ic<ir){
if (*vadd[ic]<=thetaR){il++; swap(vadd,ic,il); SLTempR=SLTempR+*vadd[il]; nLTempR++; ic++;}
else if (*vadd[ic]>=thetaR+1){ir--; swap(vadd,ic,ir); SRTempR=SRTempR+*vadd[ir]; nRTempR++;}
else {ic++;}
}
cardU = nR+nRTempR; cardL = nL+nLTempR; cardM = N-cardU-cardL;
sumvM = S-SLTempR-SRTempR;
zR = cardU+sumvM-thetaR*cardM;
if (z>zL){nR+=nRTempL+nRTempR; SR+=SRTempL+SRTempR; S-=(SRTempL+SRTempR);}
if (z<zR){nL+=nLTempL+nLTempR; SL+=SLTempL+SLTempR; S-=(SLTempL+SLTempR);}
if ((z>zR)&(z<zL)){nL+=nLTempL; SL+=SLTempL; nR+=nRTempR; SR+=SRTempR; S-=(SLTempL+SRTempR);}
theta=(nR+S-z)/(N-nR-nL); /* S is sumvM by construction */
}
findX(x,v,N,theta,signv);
delete[] vvbadd; delete[] vadd; delete[] medInds; delete[] vvb; delete[] signv;
}
void mdFindFrustum(
double* topLeftX,
double* bottomLeftX,
double* topLeftY,
double* bottomLeftY)
{
float proj[16];
float modl[16];
float clip[16];
float t;
/* Get the current PROJECTION matrix from OpenGL */
glGetFloatv( GL_PROJECTION_MATRIX, proj );
/* Get the current MODELVIEW matrix from OpenGL */
glGetFloatv( GL_MODELVIEW_MATRIX, modl );
/* Combine the two matrices (multiply projection by modelview) */
clip[ 0] = modl[ 0] * proj[ 0] + modl[ 1] * proj[ 4] + modl[ 2] * proj[ 8] + modl[ 3] * proj[12];
clip[ 1] = modl[ 0] * proj[ 1] + modl[ 1] * proj[ 5] + modl[ 2] * proj[ 9] + modl[ 3] * proj[13];
clip[ 2] = modl[ 0] * proj[ 2] + modl[ 1] * proj[ 6] + modl[ 2] * proj[10] + modl[ 3] * proj[14];
clip[ 3] = modl[ 0] * proj[ 3] + modl[ 1] * proj[ 7] + modl[ 2] * proj[11] + modl[ 3] * proj[15];
clip[ 4] = modl[ 4] * proj[ 0] + modl[ 5] * proj[ 4] + modl[ 6] * proj[ 8] + modl[ 7] * proj[12];
clip[ 5] = modl[ 4] * proj[ 1] + modl[ 5] * proj[ 5] + modl[ 6] * proj[ 9] + modl[ 7] * proj[13];
clip[ 6] = modl[ 4] * proj[ 2] + modl[ 5] * proj[ 6] + modl[ 6] * proj[10] + modl[ 7] * proj[14];
clip[ 7] = modl[ 4] * proj[ 3] + modl[ 5] * proj[ 7] + modl[ 6] * proj[11] + modl[ 7] * proj[15];
clip[ 8] = modl[ 8] * proj[ 0] + modl[ 9] * proj[ 4] + modl[10] * proj[ 8] + modl[11] * proj[12];
clip[ 9] = modl[ 8] * proj[ 1] + modl[ 9] * proj[ 5] + modl[10] * proj[ 9] + modl[11] * proj[13];
clip[10] = modl[ 8] * proj[ 2] + modl[ 9] * proj[ 6] + modl[10] * proj[10] + modl[11] * proj[14];
clip[11] = modl[ 8] * proj[ 3] + modl[ 9] * proj[ 7] + modl[10] * proj[11] + modl[11] * proj[15];
clip[12] = modl[12] * proj[ 0] + modl[13] * proj[ 4] + modl[14] * proj[ 8] + modl[15] * proj[12];
clip[13] = modl[12] * proj[ 1] + modl[13] * proj[ 5] + modl[14] * proj[ 9] + modl[15] * proj[13];
clip[14] = modl[12] * proj[ 2] + modl[13] * proj[ 6] + modl[14] * proj[10] + modl[15] * proj[14];
clip[15] = modl[12] * proj[ 3] + modl[13] * proj[ 7] + modl[14] * proj[11] + modl[15] * proj[15];
/* Extract the numbers for the RIGHT plane */
frustum[0][0] = clip[ 3] - clip[ 0];
frustum[0][1] = clip[ 7] - clip[ 4];
frustum[0][2] = clip[11] - clip[ 8];
frustum[0][3] = clip[15] - clip[12];
/* Normalize the result */
t = sqrt( frustum[0][0] * frustum[0][0] + frustum[0][1] * frustum[0][1] + frustum[0][2] * frustum[0][2] );
frustum[0][0] /= t;
frustum[0][1] /= t;
frustum[0][2] /= t;
frustum[0][3] /= t;
/* Extract the numbers for the LEFT plane */
frustum[1][0] = clip[ 3] + clip[ 0];
frustum[1][1] = clip[ 7] + clip[ 4];
frustum[1][2] = clip[11] + clip[ 8];
frustum[1][3] = clip[15] + clip[12];
/* Normalize the result */
t = sqrt( frustum[1][0] * frustum[1][0] + frustum[1][1] * frustum[1][1] + frustum[1][2] * frustum[1][2] );
frustum[1][0] /= t;
frustum[1][1] /= t;
frustum[1][2] /= t;
frustum[1][3] /= t;
/* Extract the BOTTOM plane */
frustum[2][0] = clip[ 3] + clip[ 1];
frustum[2][1] = clip[ 7] + clip[ 5];
frustum[2][2] = clip[11] + clip[ 9];
frustum[2][3] = clip[15] + clip[13];
/* Normalize the result */
t = sqrt( frustum[2][0] * frustum[2][0] + frustum[2][1] * frustum[2][1] + frustum[2][2] * frustum[2][2] );
frustum[2][0] /= t;
frustum[2][1] /= t;
frustum[2][2] /= t;
frustum[2][3] /= t;
/* Extract the TOP plane */
frustum[3][0] = clip[ 3] - clip[ 1];
frustum[3][1] = clip[ 7] - clip[ 5];
frustum[3][2] = clip[11] - clip[ 9];
frustum[3][3] = clip[15] - clip[13];
/* Normalize the result */
t = sqrt( frustum[3][0] * frustum[3][0] + frustum[3][1] * frustum[3][1] + frustum[3][2] * frustum[3][2] );
frustum[3][0] /= t;
frustum[3][1] /= t;
frustum[3][2] /= t;
frustum[3][3] /= t;
/* Extract the FAR plane */
frustum[4][0] = clip[ 3] - clip[ 2];
frustum[4][1] = clip[ 7] - clip[ 6];
frustum[4][2] = clip[11] - clip[10];
frustum[4][3] = clip[15] - clip[14];
/* Normalize the result */
t = sqrt( frustum[4][0] * frustum[4][0] + frustum[4][1] * frustum[4][1] + frustum[4][2] * frustum[4][2] );
frustum[4][0] /= t;
frustum[4][1] /= t;
frustum[4][2] /= t;
frustum[4][3] /= t;
/* Extract the NEAR plane */
frustum[5][0] = clip[ 3] + clip[ 2];
frustum[5][1] = clip[ 7] + clip[ 6];
frustum[5][2] = clip[11] + clip[10];
frustum[5][3] = clip[15] + clip[14];
/* Normalize the result */
t = sqrt( frustum[5][0] * frustum[5][0] + frustum[5][1] * frustum[5][1] + frustum[5][2] * frustum[5][2] );
frustum[5][0] /= t;
frustum[5][1] /= t;
frustum[5][2] /= t;
frustum[5][3] /= t;
//Top X and Y: intersect LEFT and TOP
*topLeftX = findX(frustum[1],frustum[3]);
*topLeftY = findY(frustum[1],frustum[3]);
//Bottom X and Y: intersect LEFT and BOTTOM
*bottomLeftX = findX(frustum[1],frustum[2]);
*bottomLeftY = findY(frustum[1],frustum[2]);
}