| |
| /* |
| * 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. |
| */ |
| |
| #ifndef _M_EVAL_H |
| #define _M_EVAL_H |
| |
| #include "main/glheader.h" |
| |
| void _math_init_eval( void ); |
| |
| |
| /* |
| * 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); |
| |
| |
| /* |
| * 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); |
| |
| |
| /* |
| * 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); |
| |
| |
| #endif |
