From f4092abdf94af6a99aff944d6264bc1284e8bdd4 Mon Sep 17 00:00:00 2001 From: Reinhard Tartler Date: Mon, 10 Oct 2011 17:43:39 +0200 Subject: Imported nx-X11-3.1.0-1.tar.gz Summary: Imported nx-X11-3.1.0-1.tar.gz Keywords: Imported nx-X11-3.1.0-1.tar.gz into Git repository --- nx-X11/extras/Mesa/src/mesa/math/m_eval.c | 461 ++++++++++++++++++++++++++++++ 1 file changed, 461 insertions(+) create mode 100644 nx-X11/extras/Mesa/src/mesa/math/m_eval.c (limited to 'nx-X11/extras/Mesa/src/mesa/math/m_eval.c') diff --git a/nx-X11/extras/Mesa/src/mesa/math/m_eval.c b/nx-X11/extras/Mesa/src/mesa/math/m_eval.c new file mode 100644 index 000000000..42ffd4133 --- /dev/null +++ b/nx-X11/extras/Mesa/src/mesa/math/m_eval.c @@ -0,0 +1,461 @@ + +/* + * Mesa 3-D graphics library + * Version: 3.5 + * + * Copyright (C) 1999-2001 Brian Paul All Rights Reserved. + * + * Permission is hereby granted, free of charge, to any person obtaining a + * copy of this software and associated documentation files (the "Software"), + * to deal in the Software without restriction, including without limitation + * the rights to use, copy, modify, merge, publish, distribute, sublicense, + * and/or sell copies of the Software, and to permit persons to whom the + * Software is furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included + * in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS + * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL + * BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN + * AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN + * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + */ + + +/* + * eval.c was written by + * Bernd Barsuhn (bdbarsuh@cip.informatik.uni-erlangen.de) and + * Volker Weiss (vrweiss@cip.informatik.uni-erlangen.de). + * + * My original implementation of evaluators was simplistic and didn't + * compute surface normal vectors properly. Bernd and Volker applied + * used more sophisticated methods to get better results. + * + * Thanks guys! + */ + + +#include "glheader.h" +#include "config.h" +#include "m_eval.h" + +static GLfloat inv_tab[MAX_EVAL_ORDER]; + + + +/* + * Horner scheme for Bezier curves + * + * Bezier curves can be computed via a Horner scheme. + * Horner is numerically less stable than the de Casteljau + * algorithm, but it is faster. For curves of degree n + * the complexity of Horner is O(n) and de Casteljau is O(n^2). + * Since stability is not important for displaying curve + * points I decided to use the Horner scheme. + * + * A cubic Bezier curve with control points b0, b1, b2, b3 can be + * written as + * + * (([3] [3] ) [3] ) [3] + * c(t) = (([0]*s*b0 + [1]*t*b1)*s + [2]*t^2*b2)*s + [3]*t^2*b3 + * + * [n] + * where s=1-t and the binomial coefficients [i]. These can + * be computed iteratively using the identity: + * + * [n] [n ] [n] + * [i] = (n-i+1)/i * [i-1] and [0] = 1 + */ + + +void +_math_horner_bezier_curve(const GLfloat * cp, GLfloat * out, GLfloat t, + GLuint dim, GLuint order) +{ + GLfloat s, powert, bincoeff; + GLuint i, k; + + if (order >= 2) { + bincoeff = (GLfloat) (order - 1); + s = 1.0F - t; + + for (k = 0; k < dim; k++) + out[k] = s * cp[k] + bincoeff * t * cp[dim + k]; + + for (i = 2, cp += 2 * dim, powert = t * t; i < order; + i++, powert *= t, cp += dim) { + bincoeff *= (GLfloat) (order - i); + bincoeff *= inv_tab[i]; + + for (k = 0; k < dim; k++) + out[k] = s * out[k] + bincoeff * powert * cp[k]; + } + } + else { /* order=1 -> constant curve */ + + for (k = 0; k < dim; k++) + out[k] = cp[k]; + } +} + +/* + * Tensor product Bezier surfaces + * + * Again the Horner scheme is used to compute a point on a + * TP Bezier surface. First a control polygon for a curve + * on the surface in one parameter direction is computed, + * then the point on the curve for the other parameter + * direction is evaluated. + * + * To store the curve control polygon additional storage + * for max(uorder,vorder) points is needed in the + * control net cn. + */ + +void +_math_horner_bezier_surf(GLfloat * cn, GLfloat * out, GLfloat u, GLfloat v, + GLuint dim, GLuint uorder, GLuint vorder) +{ + GLfloat *cp = cn + uorder * vorder * dim; + GLuint i, uinc = vorder * dim; + + if (vorder > uorder) { + if (uorder >= 2) { + GLfloat s, poweru, bincoeff; + GLuint j, k; + + /* Compute the control polygon for the surface-curve in u-direction */ + for (j = 0; j < vorder; j++) { + GLfloat *ucp = &cn[j * dim]; + + /* Each control point is the point for parameter u on a */ + /* curve defined by the control polygons in u-direction */ + bincoeff = (GLfloat) (uorder - 1); + s = 1.0F - u; + + for (k = 0; k < dim; k++) + cp[j * dim + k] = s * ucp[k] + bincoeff * u * ucp[uinc + k]; + + for (i = 2, ucp += 2 * uinc, poweru = u * u; i < uorder; + i++, poweru *= u, ucp += uinc) { + bincoeff *= (GLfloat) (uorder - i); + bincoeff *= inv_tab[i]; + + for (k = 0; k < dim; k++) + cp[j * dim + k] = + s * cp[j * dim + k] + bincoeff * poweru * ucp[k]; + } + } + + /* Evaluate curve point in v */ + _math_horner_bezier_curve(cp, out, v, dim, vorder); + } + else /* uorder=1 -> cn defines a curve in v */ + _math_horner_bezier_curve(cn, out, v, dim, vorder); + } + else { /* vorder <= uorder */ + + if (vorder > 1) { + GLuint i; + + /* Compute the control polygon for the surface-curve in u-direction */ + for (i = 0; i < uorder; i++, cn += uinc) { + /* For constant i all cn[i][j] (j=0..vorder) are located */ + /* on consecutive memory locations, so we can use */ + /* horner_bezier_curve to compute the control points */ + + _math_horner_bezier_curve(cn, &cp[i * dim], v, dim, vorder); + } + + /* Evaluate curve point in u */ + _math_horner_bezier_curve(cp, out, u, dim, uorder); + } + else /* vorder=1 -> cn defines a curve in u */ + _math_horner_bezier_curve(cn, out, u, dim, uorder); + } +} + +/* + * The direct de Casteljau algorithm is used when a point on the + * surface and the tangent directions spanning the tangent plane + * should be computed (this is needed to compute normals to the + * surface). In this case the de Casteljau algorithm approach is + * nicer because a point and the partial derivatives can be computed + * at the same time. To get the correct tangent length du and dv + * must be multiplied with the (u2-u1)/uorder-1 and (v2-v1)/vorder-1. + * Since only the directions are needed, this scaling step is omitted. + * + * De Casteljau needs additional storage for uorder*vorder + * values in the control net cn. + */ + +void +_math_de_casteljau_surf(GLfloat * cn, GLfloat * out, GLfloat * du, + GLfloat * dv, GLfloat u, GLfloat v, GLuint dim, + GLuint uorder, GLuint vorder) +{ + GLfloat *dcn = cn + uorder * vorder * dim; + GLfloat us = 1.0F - u, vs = 1.0F - v; + GLuint h, i, j, k; + GLuint minorder = uorder < vorder ? uorder : vorder; + GLuint uinc = vorder * dim; + GLuint dcuinc = vorder; + + /* Each component is evaluated separately to save buffer space */ + /* This does not drasticaly decrease the performance of the */ + /* algorithm. If additional storage for (uorder-1)*(vorder-1) */ + /* points would be available, the components could be accessed */ + /* in the innermost loop which could lead to less cache misses. */ + +#define CN(I,J,K) cn[(I)*uinc+(J)*dim+(K)] +#define DCN(I, J) dcn[(I)*dcuinc+(J)] + if (minorder < 3) { + if (uorder == vorder) { + for (k = 0; k < dim; k++) { + /* Derivative direction in u */ + du[k] = vs * (CN(1, 0, k) - CN(0, 0, k)) + + v * (CN(1, 1, k) - CN(0, 1, k)); + + /* Derivative direction in v */ + dv[k] = us * (CN(0, 1, k) - CN(0, 0, k)) + + u * (CN(1, 1, k) - CN(1, 0, k)); + + /* bilinear de Casteljau step */ + out[k] = us * (vs * CN(0, 0, k) + v * CN(0, 1, k)) + + u * (vs * CN(1, 0, k) + v * CN(1, 1, k)); + } + } + else if (minorder == uorder) { + for (k = 0; k < dim; k++) { + /* bilinear de Casteljau step */ + DCN(1, 0) = CN(1, 0, k) - CN(0, 0, k); + DCN(0, 0) = us * CN(0, 0, k) + u * CN(1, 0, k); + + for (j = 0; j < vorder - 1; j++) { + /* for the derivative in u */ + DCN(1, j + 1) = CN(1, j + 1, k) - CN(0, j + 1, k); + DCN(1, j) = vs * DCN(1, j) + v * DCN(1, j + 1); + + /* for the `point' */ + DCN(0, j + 1) = us * CN(0, j + 1, k) + u * CN(1, j + 1, k); + DCN(0, j) = vs * DCN(0, j) + v * DCN(0, j + 1); + } + + /* remaining linear de Casteljau steps until the second last step */ + for (h = minorder; h < vorder - 1; h++) + for (j = 0; j < vorder - h; j++) { + /* for the derivative in u */ + DCN(1, j) = vs * DCN(1, j) + v * DCN(1, j + 1); + + /* for the `point' */ + DCN(0, j) = vs * DCN(0, j) + v * DCN(0, j + 1); + } + + /* derivative direction in v */ + dv[k] = DCN(0, 1) - DCN(0, 0); + + /* derivative direction in u */ + du[k] = vs * DCN(1, 0) + v * DCN(1, 1); + + /* last linear de Casteljau step */ + out[k] = vs * DCN(0, 0) + v * DCN(0, 1); + } + } + else { /* minorder == vorder */ + + for (k = 0; k < dim; k++) { + /* bilinear de Casteljau step */ + DCN(0, 1) = CN(0, 1, k) - CN(0, 0, k); + DCN(0, 0) = vs * CN(0, 0, k) + v * CN(0, 1, k); + for (i = 0; i < uorder - 1; i++) { + /* for the derivative in v */ + DCN(i + 1, 1) = CN(i + 1, 1, k) - CN(i + 1, 0, k); + DCN(i, 1) = us * DCN(i, 1) + u * DCN(i + 1, 1); + + /* for the `point' */ + DCN(i + 1, 0) = vs * CN(i + 1, 0, k) + v * CN(i + 1, 1, k); + DCN(i, 0) = us * DCN(i, 0) + u * DCN(i + 1, 0); + } + + /* remaining linear de Casteljau steps until the second last step */ + for (h = minorder; h < uorder - 1; h++) + for (i = 0; i < uorder - h; i++) { + /* for the derivative in v */ + DCN(i, 1) = us * DCN(i, 1) + u * DCN(i + 1, 1); + + /* for the `point' */ + DCN(i, 0) = us * DCN(i, 0) + u * DCN(i + 1, 0); + } + + /* derivative direction in u */ + du[k] = DCN(1, 0) - DCN(0, 0); + + /* derivative direction in v */ + dv[k] = us * DCN(0, 1) + u * DCN(1, 1); + + /* last linear de Casteljau step */ + out[k] = us * DCN(0, 0) + u * DCN(1, 0); + } + } + } + else if (uorder == vorder) { + for (k = 0; k < dim; k++) { + /* first bilinear de Casteljau step */ + for (i = 0; i < uorder - 1; i++) { + DCN(i, 0) = us * CN(i, 0, k) + u * CN(i + 1, 0, k); + for (j = 0; j < vorder - 1; j++) { + DCN(i, j + 1) = us * CN(i, j + 1, k) + u * CN(i + 1, j + 1, k); + DCN(i, j) = vs * DCN(i, j) + v * DCN(i, j + 1); + } + } + + /* remaining bilinear de Casteljau steps until the second last step */ + for (h = 2; h < minorder - 1; h++) + for (i = 0; i < uorder - h; i++) { + DCN(i, 0) = us * DCN(i, 0) + u * DCN(i + 1, 0); + for (j = 0; j < vorder - h; j++) { + DCN(i, j + 1) = us * DCN(i, j + 1) + u * DCN(i + 1, j + 1); + DCN(i, j) = vs * DCN(i, j) + v * DCN(i, j + 1); + } + } + + /* derivative direction in u */ + du[k] = vs * (DCN(1, 0) - DCN(0, 0)) + v * (DCN(1, 1) - DCN(0, 1)); + + /* derivative direction in v */ + dv[k] = us * (DCN(0, 1) - DCN(0, 0)) + u * (DCN(1, 1) - DCN(1, 0)); + + /* last bilinear de Casteljau step */ + out[k] = us * (vs * DCN(0, 0) + v * DCN(0, 1)) + + u * (vs * DCN(1, 0) + v * DCN(1, 1)); + } + } + else if (minorder == uorder) { + for (k = 0; k < dim; k++) { + /* first bilinear de Casteljau step */ + for (i = 0; i < uorder - 1; i++) { + DCN(i, 0) = us * CN(i, 0, k) + u * CN(i + 1, 0, k); + for (j = 0; j < vorder - 1; j++) { + DCN(i, j + 1) = us * CN(i, j + 1, k) + u * CN(i + 1, j + 1, k); + DCN(i, j) = vs * DCN(i, j) + v * DCN(i, j + 1); + } + } + + /* remaining bilinear de Casteljau steps until the second last step */ + for (h = 2; h < minorder - 1; h++) + for (i = 0; i < uorder - h; i++) { + DCN(i, 0) = us * DCN(i, 0) + u * DCN(i + 1, 0); + for (j = 0; j < vorder - h; j++) { + DCN(i, j + 1) = us * DCN(i, j + 1) + u * DCN(i + 1, j + 1); + DCN(i, j) = vs * DCN(i, j) + v * DCN(i, j + 1); + } + } + + /* last bilinear de Casteljau step */ + DCN(2, 0) = DCN(1, 0) - DCN(0, 0); + DCN(0, 0) = us * DCN(0, 0) + u * DCN(1, 0); + for (j = 0; j < vorder - 1; j++) { + /* for the derivative in u */ + DCN(2, j + 1) = DCN(1, j + 1) - DCN(0, j + 1); + DCN(2, j) = vs * DCN(2, j) + v * DCN(2, j + 1); + + /* for the `point' */ + DCN(0, j + 1) = us * DCN(0, j + 1) + u * DCN(1, j + 1); + DCN(0, j) = vs * DCN(0, j) + v * DCN(0, j + 1); + } + + /* remaining linear de Casteljau steps until the second last step */ + for (h = minorder; h < vorder - 1; h++) + for (j = 0; j < vorder - h; j++) { + /* for the derivative in u */ + DCN(2, j) = vs * DCN(2, j) + v * DCN(2, j + 1); + + /* for the `point' */ + DCN(0, j) = vs * DCN(0, j) + v * DCN(0, j + 1); + } + + /* derivative direction in v */ + dv[k] = DCN(0, 1) - DCN(0, 0); + + /* derivative direction in u */ + du[k] = vs * DCN(2, 0) + v * DCN(2, 1); + + /* last linear de Casteljau step */ + out[k] = vs * DCN(0, 0) + v * DCN(0, 1); + } + } + else { /* minorder == vorder */ + + for (k = 0; k < dim; k++) { + /* first bilinear de Casteljau step */ + for (i = 0; i < uorder - 1; i++) { + DCN(i, 0) = us * CN(i, 0, k) + u * CN(i + 1, 0, k); + for (j = 0; j < vorder - 1; j++) { + DCN(i, j + 1) = us * CN(i, j + 1, k) + u * CN(i + 1, j + 1, k); + DCN(i, j) = vs * DCN(i, j) + v * DCN(i, j + 1); + } + } + + /* remaining bilinear de Casteljau steps until the second last step */ + for (h = 2; h < minorder - 1; h++) + for (i = 0; i < uorder - h; i++) { + DCN(i, 0) = us * DCN(i, 0) + u * DCN(i + 1, 0); + for (j = 0; j < vorder - h; j++) { + DCN(i, j + 1) = us * DCN(i, j + 1) + u * DCN(i + 1, j + 1); + DCN(i, j) = vs * DCN(i, j) + v * DCN(i, j + 1); + } + } + + /* last bilinear de Casteljau step */ + DCN(0, 2) = DCN(0, 1) - DCN(0, 0); + DCN(0, 0) = vs * DCN(0, 0) + v * DCN(0, 1); + for (i = 0; i < uorder - 1; i++) { + /* for the derivative in v */ + DCN(i + 1, 2) = DCN(i + 1, 1) - DCN(i + 1, 0); + DCN(i, 2) = us * DCN(i, 2) + u * DCN(i + 1, 2); + + /* for the `point' */ + DCN(i + 1, 0) = vs * DCN(i + 1, 0) + v * DCN(i + 1, 1); + DCN(i, 0) = us * DCN(i, 0) + u * DCN(i + 1, 0); + } + + /* remaining linear de Casteljau steps until the second last step */ + for (h = minorder; h < uorder - 1; h++) + for (i = 0; i < uorder - h; i++) { + /* for the derivative in v */ + DCN(i, 2) = us * DCN(i, 2) + u * DCN(i + 1, 2); + + /* for the `point' */ + DCN(i, 0) = us * DCN(i, 0) + u * DCN(i + 1, 0); + } + + /* derivative direction in u */ + du[k] = DCN(1, 0) - DCN(0, 0); + + /* derivative direction in v */ + dv[k] = us * DCN(0, 2) + u * DCN(1, 2); + + /* last linear de Casteljau step */ + out[k] = us * DCN(0, 0) + u * DCN(1, 0); + } + } +#undef DCN +#undef CN +} + + +/* + * Do one-time initialization for evaluators. + */ +void +_math_init_eval(void) +{ + GLuint i; + + /* KW: precompute 1/x for useful x. + */ + for (i = 1; i < MAX_EVAL_ORDER; i++) + inv_tab[i] = 1.0F / i; +} -- cgit v1.2.3