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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.

 */

#define _M_EVAL_H

 * 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

 */

_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.

 */

_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.

 */

_math_de_casteljau_surf(GLfloat *cn, GLfloat *out, GLfloat *du, GLfloat *dv,

			GLfloat u, GLfloat v, GLuint dim,

			GLuint uorder, GLuint vorder);