diff options
Diffstat (limited to 'nx-X11/extras/Mesa/src/mesa/math/m_eval.c')
-rw-r--r-- | nx-X11/extras/Mesa/src/mesa/math/m_eval.c | 461 |
1 files changed, 0 insertions, 461 deletions
diff --git a/nx-X11/extras/Mesa/src/mesa/math/m_eval.c b/nx-X11/extras/Mesa/src/mesa/math/m_eval.c deleted file mode 100644 index 42ffd4133..000000000 --- a/nx-X11/extras/Mesa/src/mesa/math/m_eval.c +++ /dev/null @@ -1,461 +0,0 @@ - -/* - * 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; -} |