0,0 → 1,103 |
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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. |
*/ |
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#ifndef _M_EVAL_H |
#define _M_EVAL_H |
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#include "main/glheader.h" |
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void _math_init_eval( void ); |
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/* |
* 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 |
*/ |
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void |
_math_horner_bezier_curve(const GLfloat *cp, GLfloat *out, GLfloat t, |
GLuint dim, GLuint order); |
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/* |
* 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. |
*/ |
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void |
_math_horner_bezier_surf(GLfloat *cn, GLfloat *out, GLfloat u, GLfloat v, |
GLuint dim, GLuint uorder, GLuint vorder); |
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/* |
* 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. |
*/ |
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void |
_math_de_casteljau_surf(GLfloat *cn, GLfloat *out, GLfloat *du, GLfloat *dv, |
GLfloat u, GLfloat v, GLuint dim, |
GLuint uorder, GLuint vorder); |
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#endif |