index de4e89c..cf7569d 100644 (file)
--- a/curves.c
+++ b/curves.c
@@ -35,19 +35,40 @@ double bsplinesample(int dimensions, double t, double *param)
double o = 0;
for (i = 0;i < dimensions + 1;i++)
o += param[i] * factorial(dimensions)/(factorial(i)*factorial(dimensions-i)) * pow(t, i) * pow(1 - t, dimensions - i);
+       return o;
}
*/

+#include "quakedef.h"
+#include "mathlib.h"
+
#include <math.h>
#include "curves.h"

+// Calculate number of resulting vertex rows/columns by given patch size and tesselation factor
+// tess=0 means that we reduce detalization of base 3x3 patches by removing middle row and column of vertices
+// "DimForTess" is "DIMension FOR TESSelation factor"
+// NB: tess=0 actually means that tess must be 0.5, but obviously it can't because it is of int type. (so "a*tess"-like code is replaced by "a/2" if tess=0)
+int Q3PatchDimForTess(int size, int tess)
+{
+       if (tess > 0)
+               return (size - 1) * tess + 1;
+       else if (tess == 0)
+               return (size - 1) / 2 + 1;
+       else
+               return 0; // Maybe warn about wrong tess here?
+}
+
// usage:
// to expand a 5x5 patch to 21x21 vertices (4x4 tesselation), one might use this call:
// Q3PatchSubdivideFloat(3, sizeof(float), outvertices, 5, 5, sizeof(float), patchvertices, 4, 4);
void Q3PatchTesselateFloat(int numcomponents, int outputstride, float *outputvertices, int patchwidth, int patchheight, int inputstride, float *patchvertices, int tesselationwidth, int tesselationheight)
{
-       int k, l, x, y, component, outputwidth = (patchwidth-1)*tesselationwidth+1;
+       int k, l, x, y, component, outputwidth = Q3PatchDimForTess(patchwidth, tesselationwidth);
float px, py, *v, a, b, c, *cp, temp;
+       int xmax = max(1, 2*tesselationwidth);
+       int ymax = max(1, 2*tesselationheight);
+
// iterate over the individual 3x3 quadratic spline surfaces one at a time
// expanding them to fill the output array (with some overlap to ensure
// the edges are filled)
@@ -60,11 +81,11 @@ void Q3PatchTesselateFloat(int numcomponents, int outputstride, float *outputver
for (x = 0;x < 3;x++)
cp[y][x] = (float *)((unsigned char *)patchvertices + ((k+y)*patchwidth+(l+x)) * inputstride);
// for each row...
-                       for (y = 0;y <= tesselationheight*2;y++)
+                       for (y = 0;y <= ymax;y++)
{
// calculate control points for this row by collapsing the 3
// rows of control points to one row using py
-                               py = (float)y / (float)(tesselationheight*2);
+                               py = (float)y / (float)ymax;
// calculate quadratic spline weights for py
a = ((1.0f - py) * (1.0f - py));
b = ((1.0f - py) * (2.0f * py));
@@ -76,12 +97,12 @@ void Q3PatchTesselateFloat(int numcomponents, int outputstride, float *outputver
temp[component] = cp[component] * a + cp[component] * b + cp[component] * c;
}
// fetch a pointer to the beginning of the output vertex row
-                               v = (float *)((unsigned char *)outputvertices + ((k * tesselationheight + y) * outputwidth + l * tesselationwidth) * outputstride);
+                               v = (float *)((unsigned char *)outputvertices + ((k * ymax / 2 + y) * outputwidth + l * xmax / 2) * outputstride);
// for each column of the row...
-                               for (x = 0;x <= (tesselationwidth*2);x++)
+                               for (x = 0;x <= xmax;x++)
{
// calculate point based on the row control points
-                                       px = (float)x / (float)(tesselationwidth*2);
+                                       px = (float)x / (float)xmax;
// calculate quadratic spline weights for px
// (could be precalculated)
a = ((1.0f - px) * (1.0f - px));
@@ -115,75 +136,304 @@ void Q3PatchTesselateFloat(int numcomponents, int outputstride, float *outputver
#endif
}

+static int Q3PatchTesselation(float largestsquared3xcurvearea, float tolerance)
+{
+       float f;
+       // f is actually a squared 2x curve area... so the formula had to be adjusted to give roughly the same subdivisions
+       f = pow(largestsquared3xcurvearea / 64.0f, 0.25f) / tolerance;
+       //if(f < 0.25) // VERY flat patches
+       if(f < 0.0001) // TOTALLY flat patches
+               return 0;
+       else if(f < 2)
+               return 1;
+       else
+               return (int) floor(log(f) / log(2.0f)) + 1;
+               // this is always at least 2
+               // maps [0.25..0.5[ to -1 (actually, 1 is returned)
+               // maps [0.5..1[ to 0 (actually, 1 is returned)
+               // maps [1..2[ to 1
+               // maps [2..4[ to 2
+               // maps [4..8[ to 4
+}
+
+static float Squared3xCurveArea(const float *a, const float *control, const float *b, int components)
+{
+#if 0
+       // mimicing the old behaviour with the new code...
+
+       float deviation;
+       float quartercurvearea = 0;
+       int c;
+       for (c = 0;c < components;c++)
+       {
+               deviation = control[c] * 0.5f - a[c] * 0.25f - b[c] * 0.25f;
+               quartercurvearea += deviation*deviation;
+       }
+
+       // But as the new code now works on the squared 2x curve area, let's scale the value
+       return quartercurvearea * quartercurvearea * 64.0;
+
+#else
+       // ideally, we'd like the area between the spline a->control->b and the line a->b.
+       // but as this is hard to calculate, let's calculate an upper bound of it:
+       // the area of the triangle a->control->b->a.
+       //
+       // one can prove that the area of a quadratic spline = 2/3 * the area of
+       // the triangle of its control points!
+       // to do it, first prove it for the spline through (0,0), (1,1), (2,0)
+       // (which is a parabola) and then note that moving the control point
+       // left/right is just shearing and keeps the area of both the spline and
+       // the triangle invariant.
+       //
+       // why are we going for the spline area anyway?
+       // we know that:
+       //
+       //   the area between the spline and the line a->b is a measure of the
+       //   error of approximation of the spline by the line.
+       //
+       //   also, on circle-like or parabola-like curves, you easily get that the
+       //   double amount of line approximation segments reduces the error to its quarter
+       //   (also, easy to prove for splines by doing it for one specific one, and using
+       //   affine transforms to get all other splines)
+       //
+       // so...
+       //
+       // let's calculate the area! but we have to avoid the cross product, as
+       // components is not necessarily 3
+       //
+       // the area of a triangle spanned by vectors a and b is
+       //
+       // 0.5 * |a| |b| sin gamma
+       //
+       // now, cos gamma is
+       //
+       // a.b / (|a| |b|)
+       //
+       // so the area is
+       //
+       // 0.5 * sqrt(|a|^2 |b|^2 - (a.b)^2)
+       int c;
+       float aa = 0, bb = 0, ab = 0;
+       for (c = 0;c < components;c++)
+       {
+               float xa = a[c] - control[c];
+               float xb = b[c] - control[c];
+               aa += xa * xa;
+               ab += xa * xb;
+               bb += xb * xb;
+       }
+       // area is 0.5 * sqrt(aa*bb - ab*ab)
+       // 2x TRIANGLE area is sqrt(aa*bb - ab*ab)
+       // 3x CURVE area is sqrt(aa*bb - ab*ab)
+       return aa * bb - ab * ab;
+#endif
+}
+
// returns how much tesselation of each segment is needed to remain under tolerance
int Q3PatchTesselationOnX(int patchwidth, int patchheight, int components, const float *in, float tolerance)
{
-       int c, x, y;
+       int x, y;
const float *patch;
-       float deviation, squareddeviation, bestsquareddeviation;
-       bestsquareddeviation = 0;
+       float squared3xcurvearea, largestsquared3xcurvearea;
+       largestsquared3xcurvearea = 0;
for (y = 0;y < patchheight;y++)
{
for (x = 0;x < patchwidth-1;x += 2)
{
-                       squareddeviation = 0;
-                       for (c = 0, patch = in + ((y * patchwidth) + x) * components;c < components;c++, patch++)
-                       {
-                               deviation = patch[components] * 0.5f - patch * 0.25f - patch[2*components] * 0.25f;
-                               squareddeviation += deviation*deviation;
-                       }
-                       if (bestsquareddeviation < squareddeviation)
-                               bestsquareddeviation = squareddeviation;
+                       patch = in + ((y * patchwidth) + x) * components;
+                       squared3xcurvearea = Squared3xCurveArea(&patch, &patch[components], &patch[2*components], components);
+                       if (largestsquared3xcurvearea < squared3xcurvearea)
+                               largestsquared3xcurvearea = squared3xcurvearea;
}
}
-       return (int)floor(log(sqrt(bestsquareddeviation) / tolerance) / log(2)) + 1;
+       return Q3PatchTesselation(largestsquared3xcurvearea, tolerance);
}

// returns how much tesselation of each segment is needed to remain under tolerance
int Q3PatchTesselationOnY(int patchwidth, int patchheight, int components, const float *in, float tolerance)
{
-       int c, x, y;
+       int x, y;
const float *patch;
-       float deviation, squareddeviation, bestsquareddeviation;
-       bestsquareddeviation = 0;
+       float squared3xcurvearea, largestsquared3xcurvearea;
+       largestsquared3xcurvearea = 0;
for (y = 0;y < patchheight-1;y += 2)
{
for (x = 0;x < patchwidth;x++)
{
-                       squareddeviation = 0;
-                       for (c = 0, patch = in + ((y * patchwidth) + x) * components;c < components;c++, patch++)
+                       patch = in + ((y * patchwidth) + x) * components;
+                       squared3xcurvearea = Squared3xCurveArea(&patch, &patch[patchwidth*components], &patch[2*patchwidth*components], components);
+                       if (largestsquared3xcurvearea < squared3xcurvearea)
+                               largestsquared3xcurvearea = squared3xcurvearea;
+               }
+       }
+       return Q3PatchTesselation(largestsquared3xcurvearea, tolerance);
+}
+
+// Find an equal vertex in array. Check only vertices with odd X and Y
+static int FindEqualOddVertexInArray(int numcomponents, float *vertex, float *vertices, int width, int height)
+{
+       int x, y, j;
+       for (y=0; y<height; y+=2)
+       {
+               for (x=0; x<width; x+=2)
+               {
+                       qboolean found = true;
+                       for (j=0; j<numcomponents; j++)
+                               if (fabs(*(vertex+j) - *(vertices+j)) > 0.05)
+                               // div0: this is notably smaller than the smallest radiant grid
+                               // but large enough so we don't need to get scared of roundoff
+                               // errors
+                               {
+                                       found = false;
+                                       break;
+                               }
+                       if(found)
+                               return y*width+x;
+                       vertices += numcomponents*2;
+               }
+               vertices += numcomponents*(width-1);
+       }
+       return -1;
+}
+
+#define SIDE_INVALID -1
+#define SIDE_X 0
+#define SIDE_Y 1
+
+static int GetSide(int p1, int p2, int width, int height, int *pointdist)
+{
+       int x1 = p1 % width, y1 = p1 / width;
+       int x2 = p2 % width, y2 = p2 / width;
+       if (p1 < 0 || p2 < 0)
+               return SIDE_INVALID;
+       if (x1 == x2)
+       {
+               if (y1 != y2)
+               {
+                       *pointdist = abs(y2 - y1);
+                       return SIDE_Y;
+               }
+               else
+                       return SIDE_INVALID;
+       }
+       else if (y1 == y2)
+       {
+               *pointdist = abs(x2 - x1);
+               return SIDE_X;
+       }
+       else
+               return SIDE_INVALID;
+}
+
+// Increase tesselation of one of two touching patches to make a seamless connection between them
+// Returns 0 in case if patches were not modified, otherwise 1
+int Q3PatchAdjustTesselation(int numcomponents, patchinfo_t *patch1, float *patchvertices1, patchinfo_t *patch2, float *patchvertices2)
+{
+       // what we are doing here is:
+       //   we take for each corner of one patch
+       //   and check if the other patch contains that corner
+       //   once we have a pair of such matches
+
+       struct {int id1,id2;} commonverts;
+       int i, j, k, side1, side2, *tess1, *tess2;
+       int dist1 = 0, dist2 = 0;
+       qboolean modified = false;
+
+       // Potential paired vertices (corners of the first patch)
+       commonverts.id1 = 0;
+       commonverts.id1 = patch1->xsize-1;
+       commonverts.id1 = patch1->xsize*(patch1->ysize-1);
+       commonverts.id1 = patch1->xsize*patch1->ysize-1;
+       for (i=0;i<4;++i)
+               commonverts[i].id2 = FindEqualOddVertexInArray(numcomponents, patchvertices1+numcomponents*commonverts[i].id1, patchvertices2, patch2->xsize, patch2->ysize);
+
+       // Corners of the second patch
+       commonverts.id2 = 0;
+       commonverts.id2 = patch2->xsize-1;
+       commonverts.id2 = patch2->xsize*(patch2->ysize-1);
+       commonverts.id2 = patch2->xsize*patch2->ysize-1;
+       for (i=4;i<8;++i)
+               commonverts[i].id1 = FindEqualOddVertexInArray(numcomponents, patchvertices2+numcomponents*commonverts[i].id2, patchvertices1, patch1->xsize, patch1->ysize);
+
+       for (i=0;i<8;++i)
+               for (j=i+1;j<8;++j)
+               {
+                       side1 = GetSide(commonverts[i].id1,commonverts[j].id1,patch1->xsize,patch1->ysize,&dist1);
+                       side2 = GetSide(commonverts[i].id2,commonverts[j].id2,patch2->xsize,patch2->ysize,&dist2);
+
+                       if (side1 == SIDE_INVALID || side2 == SIDE_INVALID)
+                               continue;
+
+                       if(dist1 != dist2)
+                       {
+                               // no patch welding if the resolutions mismatch
+                               continue;
+                       }
+
+                       // Update every lod level
+                       for (k=0;k<PATCH_LODS_NUM;++k)
{
-                               deviation = patch[patchwidth*components] * 0.5f - patch * 0.25f - patch[2*patchwidth*components] * 0.25f;
-                               squareddeviation += deviation*deviation;
+                               tess1 = side1 == SIDE_X ? &patch1->lods[k].xtess : &patch1->lods[k].ytess;
+                               tess2 = side2 == SIDE_X ? &patch2->lods[k].xtess : &patch2->lods[k].ytess;
+                               if (*tess1 != *tess2)
+                               {
+                                       if (*tess1 < *tess2)
+                                               *tess1 = *tess2;
+                                       else
+                                               *tess2 = *tess1;
+                                       modified = true;
+                               }
}
-                       if (bestsquareddeviation < squareddeviation)
-                               bestsquareddeviation = squareddeviation;
}
-       }
-       return (int)floor(log(sqrt(bestsquareddeviation) / tolerance) / log(2)) + 1;
+
+       return modified;
}

+#undef SIDE_INVALID
+#undef SIDE_X
+#undef SIDE_Y
+
// calculates elements for a grid of vertices
// (such as those produced by Q3PatchTesselate)
// (note: width and height are the actual vertex size, this produces
-//  (width-1)*(height-1)*2 triangles, 3 elements each)
-void Q3PatchTriangleElements(int *elements, int width, int height)
+// (width-1)*(height-1)*2 triangles, 3 elements each)
+void Q3PatchTriangleElements(int *elements, int width, int height, int firstvertex)
{
int x, y, row0, row1;
for (y = 0;y < height - 1;y++)
{
-               row0 = (y + 0) * width;
-               row1 = (y + 1) * width;
-               for (x = 0;x < width - 1;x++)
+               if(y % 2)
+               {
+                       // swap the triangle order in odd rows as optimization for collision stride
+                       row0 = firstvertex + (y + 0) * width + width - 2;
+                       row1 = firstvertex + (y + 1) * width + width - 2;
+                       for (x = 0;x < width - 1;x++)
+                       {
+                               *elements++ = row1;
+                               *elements++ = row1 + 1;
+                               *elements++ = row0 + 1;
+                               *elements++ = row0;
+                               *elements++ = row1;
+                               *elements++ = row0 + 1;
+                               row0--;
+                               row1--;
+                       }
+               }
+               else
{
-                       *elements++ = row0;
-                       *elements++ = row1;
-                       *elements++ = row0 + 1;
-                       *elements++ = row1;
-                       *elements++ = row1 + 1;
-                       *elements++ = row0 + 1;
-                       row0++;
-                       row1++;
+                       row0 = firstvertex + (y + 0) * width;
+                       row1 = firstvertex + (y + 1) * width;
+                       for (x = 0;x < width - 1;x++)
+                       {
+                               *elements++ = row0;
+                               *elements++ = row1;
+                               *elements++ = row0 + 1;
+                               *elements++ = row1;
+                               *elements++ = row1 + 1;
+                               *elements++ = row0 + 1;
+                               row0++;
+                               row1++;
+                       }
}
}
}