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reactos/dll/opengl/mesa/math/m_eval.c

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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 <precomp.h>
#include <main/config.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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