-// this code written by Forest Hale, on 2003-08-23, and placed into public domain
-// this code deals with quadratic splines (minimum of 3 points), the same kind used in Quake3 maps.
+/*
+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
-// LordHavoc's 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 spline (minimum of 4 control points, cubic spline).
+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);
+}
+*/
+
+#include <math.h>
#include "curves.h"
-void QuadraticSplineSubdivideFloat(int inpoints, int components, const float *in, int instride, float *out, int outstride)
+// 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 s;
- // the input (control points) is read as a stream of points, and buffered
- // by the cpprev, cpcurr, and cpnext variables (to allow subdivision in
- // overlapping memory buffers, even subdivision in-place with pre-spaced
- // control points in the buffer)
- // the output (resulting curve) is written as a stream of points
- // this subdivision is meant to be repeated until the desired flatness
- // level is reached
- if (components == 1 && instride == (int)sizeof(float) && outstride == instride)
+ int k, l, x, y, component, outputwidth = (patchwidth-1)*tesselationwidth+1;
+ float px, py, *v, a, b, c, *cp[3][3], temp[3][64];
+ // 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)
{
- // simple case, single component and no special stride
- float cpprev0 = 0, cpcurr0 = 0, cpnext0;
- cpnext0 = *in++;
- for (s = 0;s < inpoints - 1;s++)
+ for (l = 0;l < patchwidth-1;l += 2)
{
- cpprev0 = cpcurr0;
- cpcurr0 = cpnext0;
- if (s < inpoints - 1)
- cpnext0 = *in++;
- if (s > 0)
- {
- // 50% flattened control point
- // cp1 = average(cp1, average(cp0, cp2));
- *out++ = (cpcurr0 + (cpprev0 + cpnext0) * 0.5f) * 0.5f;
- }
- else
+ // 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 <= tesselationheight*2;y++)
{
- // copy the control point directly
- *out++ = cpcurr0;
+ // 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);
+ // 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 * tesselationheight + y) * outputwidth + l * tesselationwidth) * outputstride);
+ // for each column of the row...
+ for (x = 0;x <= (tesselationwidth*2);x++)
+ {
+ // calculate point based on the row control points
+ px = (float)x / (float)(tesselationwidth*2);
+ // 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);
+ }
}
- // midpoint
- // mid = average(cp0, cp1);
- *out++ = (cpcurr0 + cpnext0) * 0.5f;
}
- // copy the final control point
- *out++ = cpnext0;
}
- else
+#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++)
{
- // multiple components or stride is used (complex case)
- int c;
- float cpprev[4], cpcurr[4], cpnext[4];
- // check if there are too many components for the buffers
- if (components > 1)
+ for (x = 0;x < (patchwidth-1)*tesselationwidth+1;x++)
{
- // more components can be handled, but slowly, by calling self multiple times...
- for (c = 0;c < components;c++, in++, out++)
- QuadraticSplineSubdivideFloat(inpoints, 1, in, instride, out, outstride);
- return;
+ printf("(");
+ for (component = 0;component < numcomponents;component++)
+ printf("%f ", outputvertices[(y*((patchwidth-1)*tesselationwidth+1)+x)*numcomponents+component]);
+ printf(") ");
}
- for (c = 0;c < components;c++)
- cpnext[c] = in[c];
- (unsigned char *)in += instride;
- for (s = 0;s < inpoints - 1;s++)
+ printf("\n");
+ }
+ printf("}\n");
+#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;
+ const float *patch;
+ float deviation, squareddeviation, bestsquareddeviation;
+ bestsquareddeviation = 0;
+ for (y = 0;y < patchheight;y++)
+ {
+ for (x = 0;x < patchwidth-1;x += 2)
{
- for (c = 0;c < components;c++)
- cpprev[c] = cpcurr[c];
- for (c = 0;c < components;c++)
- cpcurr[c] = cpnext[c];
- for (c = 0;c < components;c++)
- cpnext[c] = in[c];
- (unsigned char *)in += instride;
- // the end points are copied as-is
- if (s > 0)
- {
- // 50% flattened control point
- // cp1 = average(cp1, average(cp0, cp2));
- for (c = 0;c < components;c++)
- out[c] = (cpcurr[c] + (cpprev[c] + cpnext[c]) * 0.5f) * 0.5f;
- }
- else
+ squareddeviation = 0;
+ for (c = 0, patch = in + ((y * patchwidth) + x) * components;c < components;c++, patch++)
{
- // copy the control point directly
- for (c = 0;c < components;c++)
- out[c] = cpcurr[c];
+ deviation = patch[components] * 0.5f - patch[0] * 0.25f - patch[2*components] * 0.25f;
+ squareddeviation += deviation*deviation;
}
- (unsigned char *)out += outstride;
- // midpoint
- // mid = average(cp0, cp1);
- for (c = 0;c < components;c++)
- out[c] = (cpcurr[c] + cpnext[c]) * 0.5f;
- (unsigned char *)out += outstride;
+ if (bestsquareddeviation < squareddeviation)
+ bestsquareddeviation = squareddeviation;
}
- // copy the final control point
- for (c = 0;c < components;c++)
- out[c] = cpnext[c];
- //(unsigned char *)out += outstride;
}
+ return (int)floor(log(sqrt(bestsquareddeviation) / tolerance) / log(2)) + 1;
}
-// note: out must have enough room!
-// (see finalwidth/finalheight calcs below)
-void QuadraticSplinePatchSubdivideFloatBuffer(int cpwidth, int cpheight, int xlevel, int ylevel, int components, const float *in, float *out)
+// 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 finalwidth, finalheight, xstep, ystep, x, y, c;
- float *o;
-
- // error out on various bogus conditions
- if (xlevel < 0 || ylevel < 0 || xlevel > 16 || ylevel > 16 || cpwidth < 3 || cpheight < 3)
- return;
-
- xstep = 1 << xlevel;
- ystep = 1 << ylevel;
- finalwidth = (cpwidth - 1) * xstep + 1;
- finalheight = (cpheight - 1) * ystep + 1;
-
- for (y = 0;y < finalheight;y++)
- for (x = 0;x < finalwidth;x++)
- for (c = 0, o = out + (y * finalwidth + x) * components;c < components;c++)
- o[c] = 0;
-
- if (xlevel == 1 && ylevel == 0)
- {
- for (y = 0;y < finalheight;y++)
- QuadraticSplineSubdivideFloat(cpwidth, components, in + y * cpwidth * components, sizeof(float) * components, out + y * finalwidth * components, sizeof(float) * components);
- return;
- }
- if (xlevel == 0 && ylevel == 1)
+ int c, x, y;
+ const float *patch;
+ float deviation, squareddeviation, bestsquareddeviation;
+ bestsquareddeviation = 0;
+ for (y = 0;y < patchheight-1;y += 2)
{
- for (x = 0;x < finalwidth;x++)
- QuadraticSplineSubdivideFloat(cpheight, components, in + x * components, sizeof(float) * cpwidth * components, out + x * components, sizeof(float) * finalwidth * components);
- return;
+ for (x = 0;x < patchwidth;x++)
+ {
+ squareddeviation = 0;
+ for (c = 0, patch = in + ((y * patchwidth) + x) * components;c < components;c++, patch++)
+ {
+ deviation = patch[patchwidth*components] * 0.5f - patch[0] * 0.25f - patch[2*patchwidth*components] * 0.25f;
+ squareddeviation += deviation*deviation;
+ }
+ if (bestsquareddeviation < squareddeviation)
+ bestsquareddeviation = squareddeviation;
+ }
}
+ return (int)floor(log(sqrt(bestsquareddeviation) / tolerance) / log(2)) + 1;
+}
- // copy control points into correct positions in destination buffer
- for (y = 0;y < finalheight;y += ystep)
- for (x = 0;x < finalwidth;x += xstep)
- for (c = 0, o = out + (y * finalwidth + x) * components;c < components;c++)
- o[c] = *in++;
-
- // subdivide in place in the destination buffer
- while (xstep > 1 || ystep > 1)
+// 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 (xstep > 1)
+ row0 = firstvertex + (y + 0) * width;
+ row1 = firstvertex + (y + 1) * width;
+ for (x = 0;x < width - 1;x++)
{
- xstep >>= 1;
- for (y = 0;y < finalheight;y += ystep)
- QuadraticSplineSubdivideFloat(cpwidth, components, out + y * finalwidth * components, sizeof(float) * xstep * 2 * components, out + y * finalwidth * components, sizeof(float) * xstep * components);
- cpwidth = (cpwidth - 1) * 2 + 1;
- }
- if (ystep > 1)
- {
- ystep >>= 1;
- for (x = 0;x < finalwidth;x += xstep)
- QuadraticSplineSubdivideFloat(cpheight, components, out + x * components, sizeof(float) * ystep * 2 * finalwidth * components, out + x * components, sizeof(float) * ystep * finalwidth * components);
- cpheight = (cpheight - 1) * 2 + 1;
+ *elements++ = row0;
+ *elements++ = row1;
+ *elements++ = row0 + 1;
+ *elements++ = row1;
+ *elements++ = row1 + 1;
+ *elements++ = row0 + 1;
+ row0++;
+ row1++;
}
}
}
-
projects / xonotic / darkplaces.git / blobdiff