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/* $Id: m_eval.c,v 1.1 2003-02-28 11:48:05 pj Exp $ */

/*

 * 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 "glheader.h"

#include "config.h"

#include "m_eval.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;

}