mirror of
https://github.com/DrBeef/QuakeQuest.git
synced 2024-11-24 13:01:51 +00:00
440 lines
14 KiB
C
440 lines
14 KiB
C
|
|
/*
|
|
this code written by Forest Hale, on 2004-10-17, and placed into public domain
|
|
this implements Quadratic BSpline surfaces as seen in Quake3 by id Software
|
|
|
|
a small rant on misuse of the name 'bezier': many people seem to think that
|
|
bezier is a generic term for splines, but it is not, it is a term for a
|
|
specific type of bspline (4 control points, cubic bspline), bsplines are the
|
|
generalization of the bezier spline to support dimensions other than cubic.
|
|
|
|
example equations for 1-5 control point bsplines being sampled as t=0...1
|
|
1: flat (0th dimension)
|
|
o = a
|
|
2: linear (1st dimension)
|
|
o = a * (1 - t) + b * t
|
|
3: quadratic bspline (2nd dimension)
|
|
o = a * (1 - t) * (1 - t) + 2 * b * (1 - t) * t + c * t * t
|
|
4: cubic (bezier) bspline (3rd dimension)
|
|
o = a * (1 - t) * (1 - t) * (1 - t) + 3 * b * (1 - t) * (1 - t) * t + 3 * c * (1 - t) * t * t + d * t * t * t
|
|
5: quartic bspline (4th dimension)
|
|
o = a * (1 - t) * (1 - t) * (1 - t) * (1 - t) + 4 * b * (1 - t) * (1 - t) * (1 - t) * t + 6 * c * (1 - t) * (1 - t) * t * t + 4 * d * (1 - t) * t * t * t + e * t * t * t * t
|
|
|
|
arbitrary dimension bspline
|
|
double factorial(int n)
|
|
{
|
|
int i;
|
|
double f;
|
|
f = 1;
|
|
for (i = 1;i < n;i++)
|
|
f = f * i;
|
|
return f;
|
|
}
|
|
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[3]), outvertices, 5, 5, sizeof(float[3]), 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 = Q3PatchDimForTess(patchwidth, tesselationwidth);
|
|
float px, py, *v, a, b, c, *cp[3][3], temp[3][64];
|
|
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)
|
|
for (k = 0;k < patchheight-1;k += 2)
|
|
{
|
|
for (l = 0;l < patchwidth-1;l += 2)
|
|
{
|
|
// set up control point pointers for quicker lookup later
|
|
for (y = 0;y < 3;y++)
|
|
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 <= 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)ymax;
|
|
// calculate quadratic spline weights for py
|
|
a = ((1.0f - py) * (1.0f - py));
|
|
b = ((1.0f - py) * (2.0f * py));
|
|
c = (( py) * ( py));
|
|
for (component = 0;component < numcomponents;component++)
|
|
{
|
|
temp[0][component] = cp[0][0][component] * a + cp[1][0][component] * b + cp[2][0][component] * c;
|
|
temp[1][component] = cp[0][1][component] * a + cp[1][1][component] * b + cp[2][1][component] * c;
|
|
temp[2][component] = cp[0][2][component] * a + cp[1][2][component] * b + cp[2][2][component] * c;
|
|
}
|
|
// fetch a pointer to the beginning of the output vertex row
|
|
v = (float *)((unsigned char *)outputvertices + ((k * ymax / 2 + y) * outputwidth + l * xmax / 2) * outputstride);
|
|
// for each column of the row...
|
|
for (x = 0;x <= xmax;x++)
|
|
{
|
|
// calculate point based on the row control points
|
|
px = (float)x / (float)xmax;
|
|
// calculate quadratic spline weights for px
|
|
// (could be precalculated)
|
|
a = ((1.0f - px) * (1.0f - px));
|
|
b = ((1.0f - px) * (2.0f * px));
|
|
c = (( px) * ( px));
|
|
for (component = 0;component < numcomponents;component++)
|
|
v[component] = temp[0][component] * a + temp[1][component] * b + temp[2][component] * c;
|
|
// advance to next output vertex using outputstride
|
|
// (the next vertex may not be directly following this
|
|
// one, as this may be part of a larger structure)
|
|
v = (float *)((unsigned char *)v + outputstride);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
#if 0
|
|
// enable this if you want results printed out
|
|
printf("vertices[%i][%i] =\n{\n", (patchheight-1)*tesselationheight+1, (patchwidth-1)*tesselationwidth+1);
|
|
for (y = 0;y < (patchheight-1)*tesselationheight+1;y++)
|
|
{
|
|
for (x = 0;x < (patchwidth-1)*tesselationwidth+1;x++)
|
|
{
|
|
printf("(");
|
|
for (component = 0;component < numcomponents;component++)
|
|
printf("%f ", outputvertices[(y*((patchwidth-1)*tesselationwidth+1)+x)*numcomponents+component]);
|
|
printf(") ");
|
|
}
|
|
printf("\n");
|
|
}
|
|
printf("}\n");
|
|
#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 x, y;
|
|
const float *patch;
|
|
float squared3xcurvearea, largestsquared3xcurvearea;
|
|
largestsquared3xcurvearea = 0;
|
|
for (y = 0;y < patchheight;y++)
|
|
{
|
|
for (x = 0;x < patchwidth-1;x += 2)
|
|
{
|
|
patch = in + ((y * patchwidth) + x) * components;
|
|
squared3xcurvearea = Squared3xCurveArea(&patch[0], &patch[components], &patch[2*components], components);
|
|
if (largestsquared3xcurvearea < squared3xcurvearea)
|
|
largestsquared3xcurvearea = squared3xcurvearea;
|
|
}
|
|
}
|
|
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 x, y;
|
|
const float *patch;
|
|
float squared3xcurvearea, largestsquared3xcurvearea;
|
|
largestsquared3xcurvearea = 0;
|
|
for (y = 0;y < patchheight-1;y += 2)
|
|
{
|
|
for (x = 0;x < patchwidth;x++)
|
|
{
|
|
patch = in + ((y * patchwidth) + x) * components;
|
|
squared3xcurvearea = Squared3xCurveArea(&patch[0], &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[8];
|
|
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[0].id1 = 0;
|
|
commonverts[1].id1 = patch1->xsize-1;
|
|
commonverts[2].id1 = patch1->xsize*(patch1->ysize-1);
|
|
commonverts[3].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[4].id2 = 0;
|
|
commonverts[5].id2 = patch2->xsize-1;
|
|
commonverts[6].id2 = patch2->xsize*(patch2->ysize-1);
|
|
commonverts[7].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)
|
|
{
|
|
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;
|
|
}
|
|
}
|
|
}
|
|
|
|
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, int firstvertex)
|
|
{
|
|
int x, y, row0, row1;
|
|
for (y = 0;y < height - 1;y++)
|
|
{
|
|
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
|
|
{
|
|
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++;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|