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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.
- */
-
-#ifndef _M_EVAL_H
-#define _M_EVAL_H
-
-#include "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