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-
-/*
- * 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;
-}
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