1f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 2f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org/* 3f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * Mesa 3-D graphics library 4f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * Version: 3.5 5f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * 6f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * Copyright (C) 1999-2001 Brian Paul All Rights Reserved. 7f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * 8f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * Permission is hereby granted, free of charge, to any person obtaining a 9f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * copy of this software and associated documentation files (the "Software"), 10f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * to deal in the Software without restriction, including without limitation 11f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * the rights to use, copy, modify, merge, publish, distribute, sublicense, 12f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * and/or sell copies of the Software, and to permit persons to whom the 13f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * Software is furnished to do so, subject to the following conditions: 14f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * 15f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * The above copyright notice and this permission notice shall be included 16f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * in all copies or substantial portions of the Software. 17f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * 18f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 19f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 20f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 21f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN 22f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN 23f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. 24f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org */ 25f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 26f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 27f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org/* 28f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * eval.c was written by 29f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * Bernd Barsuhn (bdbarsuh@cip.informatik.uni-erlangen.de) and 30f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * Volker Weiss (vrweiss@cip.informatik.uni-erlangen.de). 31f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * 32f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * My original implementation of evaluators was simplistic and didn't 33f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * compute surface normal vectors properly. Bernd and Volker applied 34f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * used more sophisticated methods to get better results. 35f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * 36f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * Thanks guys! 37f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org */ 38f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 39f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 40f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org#include "main/glheader.h" 41f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org#include "main/config.h" 42f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org#include "m_eval.h" 43f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 444ba6f50a5bc78554a4108750a342c2b5b6b99e73kbr@chromium.org/* 454ba6f50a5bc78554a4108750a342c2b5b6b99e73kbr@chromium.org * XXX: MSVC takes forever to compile this module for x86 unless we disable 464ba6f50a5bc78554a4108750a342c2b5b6b99e73kbr@chromium.org * optimizations. 474ba6f50a5bc78554a4108750a342c2b5b6b99e73kbr@chromium.org * 484ba6f50a5bc78554a4108750a342c2b5b6b99e73kbr@chromium.org */ 494ba6f50a5bc78554a4108750a342c2b5b6b99e73kbr@chromium.org#if defined(_MSC_VER) && defined(_M_IX86) 504ba6f50a5bc78554a4108750a342c2b5b6b99e73kbr@chromium.org# pragma optimize( "", off ) 514ba6f50a5bc78554a4108750a342c2b5b6b99e73kbr@chromium.org#endif 524ba6f50a5bc78554a4108750a342c2b5b6b99e73kbr@chromium.org 53f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.orgstatic GLfloat inv_tab[MAX_EVAL_ORDER]; 54f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 55f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 56f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 57f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org/* 58f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * Horner scheme for Bezier curves 59f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * 60f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * Bezier curves can be computed via a Horner scheme. 61f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * Horner is numerically less stable than the de Casteljau 62f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * algorithm, but it is faster. For curves of degree n 63f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * the complexity of Horner is O(n) and de Casteljau is O(n^2). 64f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * Since stability is not important for displaying curve 65f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * points I decided to use the Horner scheme. 66f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * 67f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * A cubic Bezier curve with control points b0, b1, b2, b3 can be 68f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * written as 69f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * 70f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * (([3] [3] ) [3] ) [3] 71f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * c(t) = (([0]*s*b0 + [1]*t*b1)*s + [2]*t^2*b2)*s + [3]*t^2*b3 72f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * 73f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * [n] 74f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * where s=1-t and the binomial coefficients [i]. These can 75f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * be computed iteratively using the identity: 76f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * 77f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * [n] [n ] [n] 78f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * [i] = (n-i+1)/i * [i-1] and [0] = 1 79f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org */ 80f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 81f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 82f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.orgvoid 83f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org_math_horner_bezier_curve(const GLfloat * cp, GLfloat * out, GLfloat t, 84f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLuint dim, GLuint order) 85f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org{ 86f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLfloat s, powert, bincoeff; 87f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLuint i, k; 88f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 89f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org if (order >= 2) { 90f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org bincoeff = (GLfloat) (order - 1); 91f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org s = 1.0F - t; 92f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 93f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (k = 0; k < dim; k++) 94f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org out[k] = s * cp[k] + bincoeff * t * cp[dim + k]; 95f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 96f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (i = 2, cp += 2 * dim, powert = t * t; i < order; 97f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org i++, powert *= t, cp += dim) { 98f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org bincoeff *= (GLfloat) (order - i); 99f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org bincoeff *= inv_tab[i]; 100f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 101f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (k = 0; k < dim; k++) 102f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org out[k] = s * out[k] + bincoeff * powert * cp[k]; 103f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 104f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 105f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org else { /* order=1 -> constant curve */ 106f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 107f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (k = 0; k < dim; k++) 108f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org out[k] = cp[k]; 109f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 110f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org} 111f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 112f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org/* 113f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * Tensor product Bezier surfaces 114f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * 115f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * Again the Horner scheme is used to compute a point on a 116f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * TP Bezier surface. First a control polygon for a curve 117f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * on the surface in one parameter direction is computed, 118f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * then the point on the curve for the other parameter 119f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * direction is evaluated. 120f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * 121f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * To store the curve control polygon additional storage 122f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * for max(uorder,vorder) points is needed in the 123f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * control net cn. 124f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org */ 125f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 126f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.orgvoid 127f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org_math_horner_bezier_surf(GLfloat * cn, GLfloat * out, GLfloat u, GLfloat v, 128f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLuint dim, GLuint uorder, GLuint vorder) 129f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org{ 130f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLfloat *cp = cn + uorder * vorder * dim; 131f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLuint i, uinc = vorder * dim; 132f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 133f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org if (vorder > uorder) { 134f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org if (uorder >= 2) { 135f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLfloat s, poweru, bincoeff; 136f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLuint j, k; 137f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 138f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* Compute the control polygon for the surface-curve in u-direction */ 139f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (j = 0; j < vorder; j++) { 140f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLfloat *ucp = &cn[j * dim]; 141f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 142f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* Each control point is the point for parameter u on a */ 143f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* curve defined by the control polygons in u-direction */ 144f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org bincoeff = (GLfloat) (uorder - 1); 145f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org s = 1.0F - u; 146f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 147f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (k = 0; k < dim; k++) 148f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org cp[j * dim + k] = s * ucp[k] + bincoeff * u * ucp[uinc + k]; 149f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 150f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (i = 2, ucp += 2 * uinc, poweru = u * u; i < uorder; 151f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org i++, poweru *= u, ucp += uinc) { 152f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org bincoeff *= (GLfloat) (uorder - i); 153f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org bincoeff *= inv_tab[i]; 154f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 155f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (k = 0; k < dim; k++) 156f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org cp[j * dim + k] = 157f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org s * cp[j * dim + k] + bincoeff * poweru * ucp[k]; 158f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 159f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 160f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 161f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* Evaluate curve point in v */ 162f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org _math_horner_bezier_curve(cp, out, v, dim, vorder); 163f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 164f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org else /* uorder=1 -> cn defines a curve in v */ 165f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org _math_horner_bezier_curve(cn, out, v, dim, vorder); 166f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 167f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org else { /* vorder <= uorder */ 168f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 169f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org if (vorder > 1) { 170f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLuint i; 171f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 172f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* Compute the control polygon for the surface-curve in u-direction */ 173f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (i = 0; i < uorder; i++, cn += uinc) { 174f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* For constant i all cn[i][j] (j=0..vorder) are located */ 175f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* on consecutive memory locations, so we can use */ 176f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* horner_bezier_curve to compute the control points */ 177f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 178f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org _math_horner_bezier_curve(cn, &cp[i * dim], v, dim, vorder); 179f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 180f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 181f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* Evaluate curve point in u */ 182f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org _math_horner_bezier_curve(cp, out, u, dim, uorder); 183f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 184f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org else /* vorder=1 -> cn defines a curve in u */ 185f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org _math_horner_bezier_curve(cn, out, u, dim, uorder); 186f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 187f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org} 188f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 189f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org/* 190f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * The direct de Casteljau algorithm is used when a point on the 191f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * surface and the tangent directions spanning the tangent plane 192f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * should be computed (this is needed to compute normals to the 193f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * surface). In this case the de Casteljau algorithm approach is 194f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * nicer because a point and the partial derivatives can be computed 195f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * at the same time. To get the correct tangent length du and dv 196f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * must be multiplied with the (u2-u1)/uorder-1 and (v2-v1)/vorder-1. 197f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * Since only the directions are needed, this scaling step is omitted. 198f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * 199f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * De Casteljau needs additional storage for uorder*vorder 200f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * values in the control net cn. 201f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org */ 202f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 203f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.orgvoid 204f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org_math_de_casteljau_surf(GLfloat * cn, GLfloat * out, GLfloat * du, 205f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLfloat * dv, GLfloat u, GLfloat v, GLuint dim, 206f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLuint uorder, GLuint vorder) 207f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org{ 208f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLfloat *dcn = cn + uorder * vorder * dim; 209f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLfloat us = 1.0F - u, vs = 1.0F - v; 210f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLuint h, i, j, k; 211f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLuint minorder = uorder < vorder ? uorder : vorder; 212f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLuint uinc = vorder * dim; 213f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLuint dcuinc = vorder; 214f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 215f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* Each component is evaluated separately to save buffer space */ 216f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* This does not drasticaly decrease the performance of the */ 217f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* algorithm. If additional storage for (uorder-1)*(vorder-1) */ 218f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* points would be available, the components could be accessed */ 219f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* in the innermost loop which could lead to less cache misses. */ 220f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 221f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org#define CN(I,J,K) cn[(I)*uinc+(J)*dim+(K)] 222f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org#define DCN(I, J) dcn[(I)*dcuinc+(J)] 223f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org if (minorder < 3) { 224f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org if (uorder == vorder) { 225f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (k = 0; k < dim; k++) { 226f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* Derivative direction in u */ 227f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org du[k] = vs * (CN(1, 0, k) - CN(0, 0, k)) + 228f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org v * (CN(1, 1, k) - CN(0, 1, k)); 229f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 230f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* Derivative direction in v */ 231f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org dv[k] = us * (CN(0, 1, k) - CN(0, 0, k)) + 232f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org u * (CN(1, 1, k) - CN(1, 0, k)); 233f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 234f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* bilinear de Casteljau step */ 235f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org out[k] = us * (vs * CN(0, 0, k) + v * CN(0, 1, k)) + 236f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org u * (vs * CN(1, 0, k) + v * CN(1, 1, k)); 237f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 238f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 239f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org else if (minorder == uorder) { 240f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (k = 0; k < dim; k++) { 241f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* bilinear de Casteljau step */ 242f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(1, 0) = CN(1, 0, k) - CN(0, 0, k); 243f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(0, 0) = us * CN(0, 0, k) + u * CN(1, 0, k); 244f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 245f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (j = 0; j < vorder - 1; j++) { 246f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* for the derivative in u */ 247f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(1, j + 1) = CN(1, j + 1, k) - CN(0, j + 1, k); 248f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(1, j) = vs * DCN(1, j) + v * DCN(1, j + 1); 249f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 250f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* for the `point' */ 251f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(0, j + 1) = us * CN(0, j + 1, k) + u * CN(1, j + 1, k); 252f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(0, j) = vs * DCN(0, j) + v * DCN(0, j + 1); 253f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 254f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 255f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* remaining linear de Casteljau steps until the second last step */ 256f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (h = minorder; h < vorder - 1; h++) 257f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (j = 0; j < vorder - h; j++) { 258f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* for the derivative in u */ 259f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(1, j) = vs * DCN(1, j) + v * DCN(1, j + 1); 260f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 261f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* for the `point' */ 262f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(0, j) = vs * DCN(0, j) + v * DCN(0, j + 1); 263f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 264f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 265f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* derivative direction in v */ 266f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org dv[k] = DCN(0, 1) - DCN(0, 0); 267f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 268f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* derivative direction in u */ 269f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org du[k] = vs * DCN(1, 0) + v * DCN(1, 1); 270f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 271f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* last linear de Casteljau step */ 272f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org out[k] = vs * DCN(0, 0) + v * DCN(0, 1); 273f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 274f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 275f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org else { /* minorder == vorder */ 276f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 277f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (k = 0; k < dim; k++) { 278f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* bilinear de Casteljau step */ 279f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(0, 1) = CN(0, 1, k) - CN(0, 0, k); 280f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(0, 0) = vs * CN(0, 0, k) + v * CN(0, 1, k); 281f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (i = 0; i < uorder - 1; i++) { 282f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* for the derivative in v */ 283f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i + 1, 1) = CN(i + 1, 1, k) - CN(i + 1, 0, k); 284f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, 1) = us * DCN(i, 1) + u * DCN(i + 1, 1); 285f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 286f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* for the `point' */ 287f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i + 1, 0) = vs * CN(i + 1, 0, k) + v * CN(i + 1, 1, k); 288f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, 0) = us * DCN(i, 0) + u * DCN(i + 1, 0); 289f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 290f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 291f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* remaining linear de Casteljau steps until the second last step */ 292f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (h = minorder; h < uorder - 1; h++) 293f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (i = 0; i < uorder - h; i++) { 294f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* for the derivative in v */ 295f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, 1) = us * DCN(i, 1) + u * DCN(i + 1, 1); 296f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 297f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* for the `point' */ 298f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, 0) = us * DCN(i, 0) + u * DCN(i + 1, 0); 299f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 300f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 301f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* derivative direction in u */ 302f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org du[k] = DCN(1, 0) - DCN(0, 0); 303f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 304f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* derivative direction in v */ 305f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org dv[k] = us * DCN(0, 1) + u * DCN(1, 1); 306f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 307f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* last linear de Casteljau step */ 308f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org out[k] = us * DCN(0, 0) + u * DCN(1, 0); 309f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 310f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 311f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 312f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org else if (uorder == vorder) { 313f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (k = 0; k < dim; k++) { 314f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* first bilinear de Casteljau step */ 315f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (i = 0; i < uorder - 1; i++) { 316f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, 0) = us * CN(i, 0, k) + u * CN(i + 1, 0, k); 317f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (j = 0; j < vorder - 1; j++) { 318f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, j + 1) = us * CN(i, j + 1, k) + u * CN(i + 1, j + 1, k); 319f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, j) = vs * DCN(i, j) + v * DCN(i, j + 1); 320f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 321f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 322f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 323f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* remaining bilinear de Casteljau steps until the second last step */ 324f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (h = 2; h < minorder - 1; h++) 325f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (i = 0; i < uorder - h; i++) { 326f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, 0) = us * DCN(i, 0) + u * DCN(i + 1, 0); 327f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (j = 0; j < vorder - h; j++) { 328f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, j + 1) = us * DCN(i, j + 1) + u * DCN(i + 1, j + 1); 329f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, j) = vs * DCN(i, j) + v * DCN(i, j + 1); 330f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 331f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 332f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 333f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* derivative direction in u */ 334f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org du[k] = vs * (DCN(1, 0) - DCN(0, 0)) + v * (DCN(1, 1) - DCN(0, 1)); 335f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 336f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* derivative direction in v */ 337f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org dv[k] = us * (DCN(0, 1) - DCN(0, 0)) + u * (DCN(1, 1) - DCN(1, 0)); 338f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 339f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* last bilinear de Casteljau step */ 340f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org out[k] = us * (vs * DCN(0, 0) + v * DCN(0, 1)) + 341f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org u * (vs * DCN(1, 0) + v * DCN(1, 1)); 342f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 343f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 344f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org else if (minorder == uorder) { 345f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (k = 0; k < dim; k++) { 346f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* first bilinear de Casteljau step */ 347f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (i = 0; i < uorder - 1; i++) { 348f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, 0) = us * CN(i, 0, k) + u * CN(i + 1, 0, k); 349f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (j = 0; j < vorder - 1; j++) { 350f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, j + 1) = us * CN(i, j + 1, k) + u * CN(i + 1, j + 1, k); 351f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, j) = vs * DCN(i, j) + v * DCN(i, j + 1); 352f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 353f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 354f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 355f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* remaining bilinear de Casteljau steps until the second last step */ 356f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (h = 2; h < minorder - 1; h++) 357f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (i = 0; i < uorder - h; i++) { 358f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, 0) = us * DCN(i, 0) + u * DCN(i + 1, 0); 359f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (j = 0; j < vorder - h; j++) { 360f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, j + 1) = us * DCN(i, j + 1) + u * DCN(i + 1, j + 1); 361f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, j) = vs * DCN(i, j) + v * DCN(i, j + 1); 362f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 363f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 364f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 365f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* last bilinear de Casteljau step */ 366f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(2, 0) = DCN(1, 0) - DCN(0, 0); 367f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(0, 0) = us * DCN(0, 0) + u * DCN(1, 0); 368f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (j = 0; j < vorder - 1; j++) { 369f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* for the derivative in u */ 370f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(2, j + 1) = DCN(1, j + 1) - DCN(0, j + 1); 371f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(2, j) = vs * DCN(2, j) + v * DCN(2, j + 1); 372f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 373f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* for the `point' */ 374f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(0, j + 1) = us * DCN(0, j + 1) + u * DCN(1, j + 1); 375f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(0, j) = vs * DCN(0, j) + v * DCN(0, j + 1); 376f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 377f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 378f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* remaining linear de Casteljau steps until the second last step */ 379f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (h = minorder; h < vorder - 1; h++) 380f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (j = 0; j < vorder - h; j++) { 381f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* for the derivative in u */ 382f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(2, j) = vs * DCN(2, j) + v * DCN(2, j + 1); 383f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 384f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* for the `point' */ 385f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(0, j) = vs * DCN(0, j) + v * DCN(0, j + 1); 386f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 387f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 388f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* derivative direction in v */ 389f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org dv[k] = DCN(0, 1) - DCN(0, 0); 390f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 391f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* derivative direction in u */ 392f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org du[k] = vs * DCN(2, 0) + v * DCN(2, 1); 393f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 394f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* last linear de Casteljau step */ 395f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org out[k] = vs * DCN(0, 0) + v * DCN(0, 1); 396f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 397f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 398f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org else { /* minorder == vorder */ 399f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 400f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (k = 0; k < dim; k++) { 401f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* first bilinear de Casteljau step */ 402f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (i = 0; i < uorder - 1; i++) { 403f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, 0) = us * CN(i, 0, k) + u * CN(i + 1, 0, k); 404f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (j = 0; j < vorder - 1; j++) { 405f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, j + 1) = us * CN(i, j + 1, k) + u * CN(i + 1, j + 1, k); 406f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, j) = vs * DCN(i, j) + v * DCN(i, j + 1); 407f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 408f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 409f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 410f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* remaining bilinear de Casteljau steps until the second last step */ 411f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (h = 2; h < minorder - 1; h++) 412f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (i = 0; i < uorder - h; i++) { 413f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, 0) = us * DCN(i, 0) + u * DCN(i + 1, 0); 414f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (j = 0; j < vorder - h; j++) { 415f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, j + 1) = us * DCN(i, j + 1) + u * DCN(i + 1, j + 1); 416f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, j) = vs * DCN(i, j) + v * DCN(i, j + 1); 417f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 418f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 419f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 420f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* last bilinear de Casteljau step */ 421f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(0, 2) = DCN(0, 1) - DCN(0, 0); 422f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(0, 0) = vs * DCN(0, 0) + v * DCN(0, 1); 423f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (i = 0; i < uorder - 1; i++) { 424f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* for the derivative in v */ 425f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i + 1, 2) = DCN(i + 1, 1) - DCN(i + 1, 0); 426f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, 2) = us * DCN(i, 2) + u * DCN(i + 1, 2); 427f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 428f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* for the `point' */ 429f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i + 1, 0) = vs * DCN(i + 1, 0) + v * DCN(i + 1, 1); 430f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, 0) = us * DCN(i, 0) + u * DCN(i + 1, 0); 431f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 432f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 433f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* remaining linear de Casteljau steps until the second last step */ 434f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (h = minorder; h < uorder - 1; h++) 435f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (i = 0; i < uorder - h; i++) { 436f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* for the derivative in v */ 437f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, 2) = us * DCN(i, 2) + u * DCN(i + 1, 2); 438f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 439f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* for the `point' */ 440f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org DCN(i, 0) = us * DCN(i, 0) + u * DCN(i + 1, 0); 441f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 442f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 443f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* derivative direction in u */ 444f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org du[k] = DCN(1, 0) - DCN(0, 0); 445f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 446f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* derivative direction in v */ 447f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org dv[k] = us * DCN(0, 2) + u * DCN(1, 2); 448f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 449f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* last linear de Casteljau step */ 450f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org out[k] = us * DCN(0, 0) + u * DCN(1, 0); 451f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 452f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org } 453f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org#undef DCN 454f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org#undef CN 455f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org} 456f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 457f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 458f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org/* 459f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org * Do one-time initialization for evaluators. 460f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org */ 461f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.orgvoid 462f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org_math_init_eval(void) 463f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org{ 464f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org GLuint i; 465f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org 466f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org /* KW: precompute 1/x for useful x. 467f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org */ 468f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org for (i = 1; i < MAX_EVAL_ORDER; i++) 469f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org inv_tab[i] = 1.0F / i; 470f2ba7591b1407a7ee9209f842c50696914dc2dedkbr@chromium.org} 471