File: curves.c

package info (click to toggle)
darkplaces 0~20180412~beta1-2
  • links: PTS, VCS
  • area: main
  • in suites: buster
  • size: 18,200 kB
  • sloc: ansic: 176,886; makefile: 485; pascal: 455; perl: 372; objc: 245; sh: 102
file content (440 lines) | stat: -rw-r--r-- 14,440 bytes parent folder | download | duplicates (2)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440

/*
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
	// mimicking 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++;
			}
		}
	}
}