src/glu/mesa/nurbscrv.c - third_party/mesa - Git at Google


 /*
  * Mesa 3-D graphics library
  * Version:  3.3
  * Copyright (C) 1995-2000  Brian Paul
  *
  * This library is free software; you can redistribute it and/or
  * modify it under the terms of the GNU Library General Public
  * License as published by the Free Software Foundation; either
  * version 2 of the License, or (at your option) any later version.
  *
  * This library is distributed in the hope that it will be useful,
  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  * Library General Public License for more details.
  *
  * You should have received a copy of the GNU Library General Public
  * License along with this library; if not, write to the Free
  * Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
  */


 /*
  * NURBS implementation written by Bogdan Sikorski (bogdan@cira.it)
  * See README2 for more info.
  */


 #ifdef PC_HEADER
 #include "all.h"
 #else
 #include <math.h>
 #include <stdlib.h>
 #include "gluP.h"
 #include "nurbs.h"
 #endif


 static int
 get_curve_dim(GLenum type)
 {
    switch (type) {
    case GL_MAP1_VERTEX_3:
       return 3;
    case GL_MAP1_VERTEX_4:
       return 4;
    case GL_MAP1_INDEX:
       return 1;
    case GL_MAP1_COLOR_4:
       return 4;
    case GL_MAP1_NORMAL:
       return 3;
    case GL_MAP1_TEXTURE_COORD_1:
       return 1;
    case GL_MAP1_TEXTURE_COORD_2:
       return 2;
    case GL_MAP1_TEXTURE_COORD_3:
       return 3;
    case GL_MAP1_TEXTURE_COORD_4:
       return 4;
    default:
       abort();			/* TODO: is this OK? */
    }
    return 0;			/*never get here */
 }

 static GLenum
 test_nurbs_curve(GLUnurbsObj * nobj, curve_attribs * attribs)
 {
    GLenum err;
    GLint tmp_int;

    if (attribs->order < 0) {
       call_user_error(nobj, GLU_INVALID_VALUE);
       return GLU_ERROR;
    }
    glGetIntegerv(GL_MAX_EVAL_ORDER, &tmp_int);
    if (attribs->order > tmp_int || attribs->order < 2) {
       call_user_error(nobj, GLU_NURBS_ERROR1);
       return GLU_ERROR;
    }
    if (attribs->knot_count < attribs->order + 2) {
       call_user_error(nobj, GLU_NURBS_ERROR2);
       return GLU_ERROR;
    }
    if (attribs->stride < 0) {
       call_user_error(nobj, GLU_NURBS_ERROR34);
       return GLU_ERROR;
    }
    if (attribs->knot == NULL || attribs->ctrlarray == NULL) {
       call_user_error(nobj, GLU_NURBS_ERROR36);
       return GLU_ERROR;
    }
    if ((err = test_knot(attribs->knot_count, attribs->knot, attribs->order))
        != GLU_NO_ERROR) {
       call_user_error(nobj, err);
       return GLU_ERROR;
    }
    return GLU_NO_ERROR;
 }

 static GLenum
 test_nurbs_curves(GLUnurbsObj * nobj)
 {
    /* test the geometric data */
    if (test_nurbs_curve(nobj, &(nobj->curve.geom)) != GLU_NO_ERROR)
       return GLU_ERROR;
    /* now test the attributive data */
    /* color */
    if (nobj->curve.color.type != GLU_INVALID_ENUM)
       if (test_nurbs_curve(nobj, &(nobj->curve.color)) != GLU_NO_ERROR)
 	 return GLU_ERROR;
    /* normal */
    if (nobj->curve.normal.type != GLU_INVALID_ENUM)
       if (test_nurbs_curve(nobj, &(nobj->curve.normal)) != GLU_NO_ERROR)
 	 return GLU_ERROR;
    /* texture */
    if (nobj->curve.texture.type != GLU_INVALID_ENUM)
       if (test_nurbs_curve(nobj, &(nobj->curve.texture)) != GLU_NO_ERROR)
 	 return GLU_ERROR;
    return GLU_NO_ERROR;
 }

 /* prepare the knot information structures */
 static GLenum
 fill_knot_structures(GLUnurbsObj * nobj, knot_str_type * geom_knot,
 		     knot_str_type * color_knot, knot_str_type * normal_knot,
 		     knot_str_type * texture_knot)
 {
    GLint order;
    GLfloat *knot;
    GLint nknots;
    GLint t_min, t_max;

    geom_knot->unified_knot = NULL;
    knot = geom_knot->knot = nobj->curve.geom.knot;
    nknots = geom_knot->nknots = nobj->curve.geom.knot_count;
    order = geom_knot->order = nobj->curve.geom.order;
    geom_knot->delta_nknots = 0;
    t_min = geom_knot->t_min = order - 1;
    t_max = geom_knot->t_max = nknots - order;
    if (fabs(knot[t_min] - knot[t_max]) < EPSILON) {
       call_user_error(nobj, GLU_NURBS_ERROR3);
       return GLU_ERROR;
    }
    if (fabs(knot[0] - knot[t_min]) < EPSILON) {
       /* knot open at beggining */
       geom_knot->open_at_begin = GL_TRUE;
    }
    else
       geom_knot->open_at_begin = GL_FALSE;
    if (fabs(knot[t_max] - knot[nknots - 1]) < EPSILON) {
       /* knot open at end */
       geom_knot->open_at_end = GL_TRUE;
    }
    else
       geom_knot->open_at_end = GL_FALSE;
    if (nobj->curve.color.type != GLU_INVALID_ENUM) {
       color_knot->unified_knot = (GLfloat *) 1;
       knot = color_knot->knot = nobj->curve.color.knot;
       nknots = color_knot->nknots = nobj->curve.color.knot_count;
       order = color_knot->order = nobj->curve.color.order;
       color_knot->delta_nknots = 0;
       t_min = color_knot->t_min = order - 1;
       t_max = color_knot->t_max = nknots - order;
       if (fabs(knot[t_min] - knot[t_max]) < EPSILON) {
 	 call_user_error(nobj, GLU_NURBS_ERROR3);
 	 return GLU_ERROR;
       }
       if (fabs(knot[0] - knot[t_min]) < EPSILON) {
 	 /* knot open at beggining */
 	 color_knot->open_at_begin = GL_TRUE;
       }
       else
 	 color_knot->open_at_begin = GL_FALSE;
       if (fabs(knot[t_max] - knot[nknots - 1]) < EPSILON) {
 	 /* knot open at end */
 	 color_knot->open_at_end = GL_TRUE;
       }
       else
 	 color_knot->open_at_end = GL_FALSE;
    }
    else
       color_knot->unified_knot = NULL;
    if (nobj->curve.normal.type != GLU_INVALID_ENUM) {
       normal_knot->unified_knot = (GLfloat *) 1;
       knot = normal_knot->knot = nobj->curve.normal.knot;
       nknots = normal_knot->nknots = nobj->curve.normal.knot_count;
       order = normal_knot->order = nobj->curve.normal.order;
       normal_knot->delta_nknots = 0;
       t_min = normal_knot->t_min = order - 1;
       t_max = normal_knot->t_max = nknots - order;
       if (fabs(knot[t_min] - knot[t_max]) < EPSILON) {
 	 call_user_error(nobj, GLU_NURBS_ERROR3);
 	 return GLU_ERROR;
       }
       if (fabs(knot[0] - knot[t_min]) < EPSILON) {
 	 /* knot open at beggining */
 	 normal_knot->open_at_begin = GL_TRUE;
       }
       else
 	 normal_knot->open_at_begin = GL_FALSE;
       if (fabs(knot[t_max] - knot[nknots - 1]) < EPSILON) {
 	 /* knot open at end */
 	 normal_knot->open_at_end = GL_TRUE;
       }
       else
 	 normal_knot->open_at_end = GL_FALSE;
    }
    else
       normal_knot->unified_knot = NULL;
    if (nobj->curve.texture.type != GLU_INVALID_ENUM) {
       texture_knot->unified_knot = (GLfloat *) 1;
       knot = texture_knot->knot = nobj->curve.texture.knot;
       nknots = texture_knot->nknots = nobj->curve.texture.knot_count;
       order = texture_knot->order = nobj->curve.texture.order;
       texture_knot->delta_nknots = 0;
       t_min = texture_knot->t_min = order - 1;
       t_max = texture_knot->t_max = nknots - order;
       if (fabs(knot[t_min] - knot[t_max]) < EPSILON) {
 	 call_user_error(nobj, GLU_NURBS_ERROR3);
 	 return GLU_ERROR;
       }
       if (fabs(knot[0] - knot[t_min]) < EPSILON) {
 	 /* knot open at beggining */
 	 texture_knot->open_at_begin = GL_TRUE;
       }
       else
 	 texture_knot->open_at_begin = GL_FALSE;
       if (fabs(knot[t_max] - knot[nknots - 1]) < EPSILON) {
 	 /* knot open at end */
 	 texture_knot->open_at_end = GL_TRUE;
       }
       else
 	 texture_knot->open_at_end = GL_FALSE;
    }
    else
       texture_knot->unified_knot = NULL;
    return GLU_NO_ERROR;
 }

 /* covert the NURBS curve into a series of adjacent Bezier curves */
 static GLenum
 convert_curve(knot_str_type * the_knot, curve_attribs * attrib,
 	      GLfloat ** new_ctrl, GLint * ncontrol)
 {
    GLenum err;

    if ((err = explode_knot(the_knot)) != GLU_NO_ERROR) {
       if (the_knot->unified_knot) {
 	 free(the_knot->unified_knot);
 	 the_knot->unified_knot = NULL;
       }
       return err;
    }
    if (the_knot->unified_knot) {
       free(the_knot->unified_knot);
       the_knot->unified_knot = NULL;
    }
    if ((err = calc_alphas(the_knot)) != GLU_NO_ERROR) {
       free(the_knot->new_knot);
       return err;
    }
    free(the_knot->new_knot);
    if ((err = calc_new_ctrl_pts(attrib->ctrlarray, attrib->stride, the_knot,
 				attrib->dim, new_ctrl, ncontrol))
        != GLU_NO_ERROR) {
       free(the_knot->alpha);
       return err;
    }
    free(the_knot->alpha);
    return GLU_NO_ERROR;
 }

 /* covert curves - geometry and possible attribute ones into equivalent */
 /* sequence of adjacent Bezier curves */
 static GLenum
 convert_curves(GLUnurbsObj * nobj, GLfloat ** new_geom_ctrl,
 	       GLint * ncontrol, GLfloat ** new_color_ctrl,
 	       GLfloat ** new_normal_ctrl, GLfloat ** new_texture_ctrl)
 {
    knot_str_type geom_knot, color_knot, normal_knot, texture_knot;
    GLint junk;
    GLenum err;

    *new_color_ctrl = *new_normal_ctrl = *new_texture_ctrl = NULL;

    if (fill_knot_structures(nobj, &geom_knot, &color_knot, &normal_knot,
 			    &texture_knot) != GLU_NO_ERROR)
       return GLU_ERROR;

    /* unify knots - all knots should have the same number of working */
    /* ranges */
    if (
        (err =
 	select_knot_working_range(nobj, &geom_knot, &color_knot, &normal_knot,
 				  &texture_knot)) != GLU_NO_ERROR) {
       return err;
    }
    /* convert the geometry curve */
    nobj->curve.geom.dim = get_curve_dim(nobj->curve.geom.type);
    if ((err = convert_curve(&geom_knot, &(nobj->curve.geom), new_geom_ctrl,
 			    ncontrol)) != GLU_NO_ERROR) {
       free_unified_knots(&geom_knot, &color_knot, &normal_knot,
 			 &texture_knot);
       call_user_error(nobj, err);
       return err;
    }
    /* if additional attributive curves are given convert them as well */
    if (color_knot.unified_knot) {
       nobj->curve.color.dim = get_curve_dim(nobj->curve.color.type);
       if ((err = convert_curve(&color_knot, &(nobj->curve.color),
 			       new_color_ctrl, &junk)) != GLU_NO_ERROR) {
 	 free_unified_knots(&geom_knot, &color_knot, &normal_knot,
 			    &texture_knot);
 	 free(*new_geom_ctrl);
 	 call_user_error(nobj, err);
 	 return err;
       }
    }
    if (normal_knot.unified_knot) {
       nobj->curve.normal.dim = get_curve_dim(nobj->curve.normal.type);
       if ((err = convert_curve(&normal_knot, &(nobj->curve.normal),
 			       new_normal_ctrl, &junk)) != GLU_NO_ERROR) {
 	 free_unified_knots(&geom_knot, &color_knot, &normal_knot,
 			    &texture_knot);
 	 free(*new_geom_ctrl);
 	 if (*new_color_ctrl)
 	    free(*new_color_ctrl);
 	 call_user_error(nobj, err);
 	 return err;
       }
    }
    if (texture_knot.unified_knot) {
       nobj->curve.texture.dim = get_curve_dim(nobj->curve.texture.type);
       if ((err = convert_curve(&texture_knot, &(nobj->curve.texture),
 			       new_texture_ctrl, &junk)) != GLU_NO_ERROR) {
 	 free_unified_knots(&geom_knot, &color_knot, &normal_knot,
 			    &texture_knot);
 	 free(*new_geom_ctrl);
 	 if (*new_color_ctrl)
 	    free(*new_color_ctrl);
 	 if (*new_normal_ctrl)
 	    free(*new_normal_ctrl);
 	 call_user_error(nobj, err);
 	 return err;
       }
    }
    return GLU_NO_ERROR;
 }

 /* main NURBS curve procedure */
 void
 do_nurbs_curve(GLUnurbsObj * nobj)
 {
    GLint geom_order, color_order = 0, normal_order = 0, texture_order = 0;
    GLenum geom_type;
    GLint n_ctrl;
    GLfloat *new_geom_ctrl, *new_color_ctrl, *new_normal_ctrl,
       *new_texture_ctrl;
    GLfloat *geom_ctrl = 0, *color_ctrl = 0, *normal_ctrl = 0, *texture_ctrl = 0;
    GLint *factors;
    GLint i, j;
    GLint geom_dim, color_dim = 0, normal_dim = 0, texture_dim = 0;

    /* test the user supplied data */
    if (test_nurbs_curves(nobj) != GLU_NO_ERROR)
       return;

    if (convert_curves(nobj, &new_geom_ctrl, &n_ctrl, &new_color_ctrl,
 		      &new_normal_ctrl, &new_texture_ctrl) != GLU_NO_ERROR)
       return;

    geom_order = nobj->curve.geom.order;
    geom_type = nobj->curve.geom.type;
    geom_dim = nobj->curve.geom.dim;

    if (glu_do_sampling_crv(nobj, new_geom_ctrl, n_ctrl, geom_order, geom_dim,
 			   &factors) != GLU_NO_ERROR) {
       free(new_geom_ctrl);
       if (new_color_ctrl)
 	 free(new_color_ctrl);
       if (new_normal_ctrl)
 	 free(new_normal_ctrl);
       if (new_texture_ctrl)
 	 free(new_texture_ctrl);
       return;
    }
    glEnable(geom_type);
    if (new_color_ctrl) {
       glEnable(nobj->curve.color.type);
       color_dim = nobj->curve.color.dim;
       color_ctrl = new_color_ctrl;
       color_order = nobj->curve.color.order;
    }
    if (new_normal_ctrl) {
       glEnable(nobj->curve.normal.type);
       normal_dim = nobj->curve.normal.dim;
       normal_ctrl = new_normal_ctrl;
       normal_order = nobj->curve.normal.order;
    }
    if (new_texture_ctrl) {
       glEnable(nobj->curve.texture.type);
       texture_dim = nobj->curve.texture.dim;
       texture_ctrl = new_texture_ctrl;
       texture_order = nobj->curve.texture.order;
    }
    for (i = 0, j = 0, geom_ctrl = new_geom_ctrl;
 	i < n_ctrl; i += geom_order, j++, geom_ctrl += geom_order * geom_dim) {
       if (fine_culling_test_2D
 	  (nobj, geom_ctrl, geom_order, geom_dim, geom_dim)) {
 	 color_ctrl += color_order * color_dim;
 	 normal_ctrl += normal_order * normal_dim;
 	 texture_ctrl += texture_order * texture_dim;
 	 continue;
       }
       glMap1f(geom_type, 0.0, 1.0, geom_dim, geom_order, geom_ctrl);
       if (new_color_ctrl) {
 	 glMap1f(nobj->curve.color.type, 0.0, 1.0, color_dim,
 		 color_order, color_ctrl);
 	 color_ctrl += color_order * color_dim;
       }
       if (new_normal_ctrl) {
 	 glMap1f(nobj->curve.normal.type, 0.0, 1.0, normal_dim,
 		 normal_order, normal_ctrl);
 	 normal_ctrl += normal_order * normal_dim;
       }
       if (new_texture_ctrl) {
 	 glMap1f(nobj->curve.texture.type, 0.0, 1.0, texture_dim,
 		 texture_order, texture_ctrl);
 	 texture_ctrl += texture_order * texture_dim;
       }
       glMapGrid1f(factors[j], 0.0, 1.0);
       glEvalMesh1(GL_LINE, 0, factors[j]);
    }
    free(new_geom_ctrl);
    free(factors);
    if (new_color_ctrl)
       free(new_color_ctrl);
    if (new_normal_ctrl)
       free(new_normal_ctrl);
    if (new_texture_ctrl)
       free(new_texture_ctrl);
 }

	/*
	* Mesa 3-D graphics library
	* Version: 3.3
	* Copyright (C) 1995-2000 Brian Paul
	*
	* This library is free software; you can redistribute it and/or
	* modify it under the terms of the GNU Library General Public
	* License as published by the Free Software Foundation; either
	* version 2 of the License, or (at your option) any later version.
	*
	* This library is distributed in the hope that it will be useful,
	* but WITHOUT ANY WARRANTY; without even the implied warranty of
	* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
	* Library General Public License for more details.
	*
	* You should have received a copy of the GNU Library General Public
	* License along with this library; if not, write to the Free
	* Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
	*/


	/*
	* NURBS implementation written by Bogdan Sikorski (bogdan@cira.it)
	* See README2 for more info.
	*/


	#ifdef PC_HEADER
	#include "all.h"
	#else
	#include <math.h>
	#include <stdlib.h>
	#include "gluP.h"
	#include "nurbs.h"
	#endif


	static int
	get_curve_dim(GLenum type)
	{
	switch (type) {
	case GL_MAP1_VERTEX_3:
	return 3;
	case GL_MAP1_VERTEX_4:
	return 4;
	case GL_MAP1_INDEX:
	return 1;
	case GL_MAP1_COLOR_4:
	return 4;
	case GL_MAP1_NORMAL:
	return 3;
	case GL_MAP1_TEXTURE_COORD_1:
	return 1;
	case GL_MAP1_TEXTURE_COORD_2:
	return 2;
	case GL_MAP1_TEXTURE_COORD_3:
	return 3;
	case GL_MAP1_TEXTURE_COORD_4:
	return 4;
	default:
	abort(); /* TODO: is this OK? */
	}
	return 0; /never get here /
	}

	static GLenum
	test_nurbs_curve(GLUnurbsObj * nobj, curve_attribs * attribs)
	{
	GLenum err;
	GLint tmp_int;

	if (attribs->order < 0) {
	call_user_error(nobj, GLU_INVALID_VALUE);
	return GLU_ERROR;
	}
	glGetIntegerv(GL_MAX_EVAL_ORDER, &tmp_int);
	if (attribs->order > tmp_int \|\| attribs->order < 2) {
	call_user_error(nobj, GLU_NURBS_ERROR1);
	return GLU_ERROR;
	}
	if (attribs->knot_count < attribs->order + 2) {
	call_user_error(nobj, GLU_NURBS_ERROR2);
	return GLU_ERROR;
	}
	if (attribs->stride < 0) {
	call_user_error(nobj, GLU_NURBS_ERROR34);
	return GLU_ERROR;
	}
	if (attribs->knot == NULL \|\| attribs->ctrlarray == NULL) {
	call_user_error(nobj, GLU_NURBS_ERROR36);
	return GLU_ERROR;
	}
	if ((err = test_knot(attribs->knot_count, attribs->knot, attribs->order))
	!= GLU_NO_ERROR) {
	call_user_error(nobj, err);
	return GLU_ERROR;
	}
	return GLU_NO_ERROR;
	}

	static GLenum
	test_nurbs_curves(GLUnurbsObj * nobj)
	{
	/* test the geometric data */
	if (test_nurbs_curve(nobj, &(nobj->curve.geom)) != GLU_NO_ERROR)
	return GLU_ERROR;
	/* now test the attributive data */
	/* color */
	if (nobj->curve.color.type != GLU_INVALID_ENUM)
	if (test_nurbs_curve(nobj, &(nobj->curve.color)) != GLU_NO_ERROR)
	return GLU_ERROR;
	/* normal */
	if (nobj->curve.normal.type != GLU_INVALID_ENUM)
	if (test_nurbs_curve(nobj, &(nobj->curve.normal)) != GLU_NO_ERROR)
	return GLU_ERROR;
	/* texture */
	if (nobj->curve.texture.type != GLU_INVALID_ENUM)
	if (test_nurbs_curve(nobj, &(nobj->curve.texture)) != GLU_NO_ERROR)
	return GLU_ERROR;
	return GLU_NO_ERROR;
	}

	/* prepare the knot information structures */
	static GLenum
	fill_knot_structures(GLUnurbsObj * nobj, knot_str_type * geom_knot,
	knot_str_type * color_knot, knot_str_type * normal_knot,
	knot_str_type * texture_knot)
	{
	GLint order;
	GLfloat *knot;
	GLint nknots;
	GLint t_min, t_max;

	geom_knot->unified_knot = NULL;
	knot = geom_knot->knot = nobj->curve.geom.knot;
	nknots = geom_knot->nknots = nobj->curve.geom.knot_count;
	order = geom_knot->order = nobj->curve.geom.order;
	geom_knot->delta_nknots = 0;
	t_min = geom_knot->t_min = order - 1;
	t_max = geom_knot->t_max = nknots - order;
	if (fabs(knot[t_min] - knot[t_max]) < EPSILON) {
	call_user_error(nobj, GLU_NURBS_ERROR3);
	return GLU_ERROR;
	}
	if (fabs(knot[0] - knot[t_min]) < EPSILON) {
	/* knot open at beggining */
	geom_knot->open_at_begin = GL_TRUE;
	}
	else
	geom_knot->open_at_begin = GL_FALSE;
	if (fabs(knot[t_max] - knot[nknots - 1]) < EPSILON) {
	/* knot open at end */
	geom_knot->open_at_end = GL_TRUE;
	}
	else
	geom_knot->open_at_end = GL_FALSE;
	if (nobj->curve.color.type != GLU_INVALID_ENUM) {
	color_knot->unified_knot = (GLfloat *) 1;
	knot = color_knot->knot = nobj->curve.color.knot;
	nknots = color_knot->nknots = nobj->curve.color.knot_count;
	order = color_knot->order = nobj->curve.color.order;
	color_knot->delta_nknots = 0;
	t_min = color_knot->t_min = order - 1;
	t_max = color_knot->t_max = nknots - order;
	if (fabs(knot[t_min] - knot[t_max]) < EPSILON) {
	call_user_error(nobj, GLU_NURBS_ERROR3);
	return GLU_ERROR;
	}
	if (fabs(knot[0] - knot[t_min]) < EPSILON) {
	/* knot open at beggining */
	color_knot->open_at_begin = GL_TRUE;
	}
	else
	color_knot->open_at_begin = GL_FALSE;
	if (fabs(knot[t_max] - knot[nknots - 1]) < EPSILON) {
	/* knot open at end */
	color_knot->open_at_end = GL_TRUE;
	}
	else
	color_knot->open_at_end = GL_FALSE;
	}
	else
	color_knot->unified_knot = NULL;
	if (nobj->curve.normal.type != GLU_INVALID_ENUM) {
	normal_knot->unified_knot = (GLfloat *) 1;
	knot = normal_knot->knot = nobj->curve.normal.knot;
	nknots = normal_knot->nknots = nobj->curve.normal.knot_count;
	order = normal_knot->order = nobj->curve.normal.order;
	normal_knot->delta_nknots = 0;
	t_min = normal_knot->t_min = order - 1;
	t_max = normal_knot->t_max = nknots - order;
	if (fabs(knot[t_min] - knot[t_max]) < EPSILON) {
	call_user_error(nobj, GLU_NURBS_ERROR3);
	return GLU_ERROR;
	}
	if (fabs(knot[0] - knot[t_min]) < EPSILON) {
	/* knot open at beggining */
	normal_knot->open_at_begin = GL_TRUE;
	}
	else
	normal_knot->open_at_begin = GL_FALSE;
	if (fabs(knot[t_max] - knot[nknots - 1]) < EPSILON) {
	/* knot open at end */
	normal_knot->open_at_end = GL_TRUE;
	}
	else
	normal_knot->open_at_end = GL_FALSE;
	}
	else
	normal_knot->unified_knot = NULL;
	if (nobj->curve.texture.type != GLU_INVALID_ENUM) {
	texture_knot->unified_knot = (GLfloat *) 1;
	knot = texture_knot->knot = nobj->curve.texture.knot;
	nknots = texture_knot->nknots = nobj->curve.texture.knot_count;
	order = texture_knot->order = nobj->curve.texture.order;
	texture_knot->delta_nknots = 0;
	t_min = texture_knot->t_min = order - 1;
	t_max = texture_knot->t_max = nknots - order;
	if (fabs(knot[t_min] - knot[t_max]) < EPSILON) {
	call_user_error(nobj, GLU_NURBS_ERROR3);
	return GLU_ERROR;
	}
	if (fabs(knot[0] - knot[t_min]) < EPSILON) {
	/* knot open at beggining */
	texture_knot->open_at_begin = GL_TRUE;
	}
	else
	texture_knot->open_at_begin = GL_FALSE;
	if (fabs(knot[t_max] - knot[nknots - 1]) < EPSILON) {
	/* knot open at end */
	texture_knot->open_at_end = GL_TRUE;
	}
	else
	texture_knot->open_at_end = GL_FALSE;
	}
	else
	texture_knot->unified_knot = NULL;
	return GLU_NO_ERROR;
	}

	/* covert the NURBS curve into a series of adjacent Bezier curves */
	static GLenum
	convert_curve(knot_str_type * the_knot, curve_attribs * attrib,
	GLfloat ** new_ctrl, GLint * ncontrol)
	{
	GLenum err;

	if ((err = explode_knot(the_knot)) != GLU_NO_ERROR) {
	if (the_knot->unified_knot) {
	free(the_knot->unified_knot);
	the_knot->unified_knot = NULL;
	}
	return err;
	}
	if (the_knot->unified_knot) {
	free(the_knot->unified_knot);
	the_knot->unified_knot = NULL;
	}
	if ((err = calc_alphas(the_knot)) != GLU_NO_ERROR) {
	free(the_knot->new_knot);
	return err;
	}
	free(the_knot->new_knot);
	if ((err = calc_new_ctrl_pts(attrib->ctrlarray, attrib->stride, the_knot,
	attrib->dim, new_ctrl, ncontrol))
	!= GLU_NO_ERROR) {
	free(the_knot->alpha);
	return err;
	}
	free(the_knot->alpha);
	return GLU_NO_ERROR;
	}

	/* covert curves - geometry and possible attribute ones into equivalent */
	/* sequence of adjacent Bezier curves */
	static GLenum
	convert_curves(GLUnurbsObj * nobj, GLfloat ** new_geom_ctrl,
	GLint * ncontrol, GLfloat ** new_color_ctrl,
	GLfloat new_normal_ctrl, GLfloat new_texture_ctrl)
	{
	knot_str_type geom_knot, color_knot, normal_knot, texture_knot;
	GLint junk;
	GLenum err;

	new_color_ctrl = new_normal_ctrl = *new_texture_ctrl = NULL;

	if (fill_knot_structures(nobj, &geom_knot, &color_knot, &normal_knot,
	&texture_knot) != GLU_NO_ERROR)
	return GLU_ERROR;

	/* unify knots - all knots should have the same number of working */
	/* ranges */
	if (
	(err =
	select_knot_working_range(nobj, &geom_knot, &color_knot, &normal_knot,
	&texture_knot)) != GLU_NO_ERROR) {
	return err;
	}
	/* convert the geometry curve */
	nobj->curve.geom.dim = get_curve_dim(nobj->curve.geom.type);
	if ((err = convert_curve(&geom_knot, &(nobj->curve.geom), new_geom_ctrl,
	ncontrol)) != GLU_NO_ERROR) {
	free_unified_knots(&geom_knot, &color_knot, &normal_knot,
	&texture_knot);
	call_user_error(nobj, err);
	return err;
	}
	/* if additional attributive curves are given convert them as well */
	if (color_knot.unified_knot) {
	nobj->curve.color.dim = get_curve_dim(nobj->curve.color.type);
	if ((err = convert_curve(&color_knot, &(nobj->curve.color),
	new_color_ctrl, &junk)) != GLU_NO_ERROR) {
	free_unified_knots(&geom_knot, &color_knot, &normal_knot,
	&texture_knot);
	free(*new_geom_ctrl);
	call_user_error(nobj, err);
	return err;
	}
	}
	if (normal_knot.unified_knot) {
	nobj->curve.normal.dim = get_curve_dim(nobj->curve.normal.type);
	if ((err = convert_curve(&normal_knot, &(nobj->curve.normal),
	new_normal_ctrl, &junk)) != GLU_NO_ERROR) {
	free_unified_knots(&geom_knot, &color_knot, &normal_knot,
	&texture_knot);
	free(*new_geom_ctrl);
	if (*new_color_ctrl)
	free(*new_color_ctrl);
	call_user_error(nobj, err);
	return err;
	}
	}
	if (texture_knot.unified_knot) {
	nobj->curve.texture.dim = get_curve_dim(nobj->curve.texture.type);
	if ((err = convert_curve(&texture_knot, &(nobj->curve.texture),
	new_texture_ctrl, &junk)) != GLU_NO_ERROR) {
	free_unified_knots(&geom_knot, &color_knot, &normal_knot,
	&texture_knot);
	free(*new_geom_ctrl);
	if (*new_color_ctrl)
	free(*new_color_ctrl);
	if (*new_normal_ctrl)
	free(*new_normal_ctrl);
	call_user_error(nobj, err);
	return err;
	}
	}
	return GLU_NO_ERROR;
	}

	/* main NURBS curve procedure */
	void
	do_nurbs_curve(GLUnurbsObj * nobj)
	{
	GLint geom_order, color_order = 0, normal_order = 0, texture_order = 0;
	GLenum geom_type;
	GLint n_ctrl;
	GLfloat new_geom_ctrl, new_color_ctrl, *new_normal_ctrl,
	*new_texture_ctrl;
	GLfloat geom_ctrl = 0, color_ctrl = 0, normal_ctrl = 0, texture_ctrl = 0;
	GLint *factors;
	GLint i, j;
	GLint geom_dim, color_dim = 0, normal_dim = 0, texture_dim = 0;

	/* test the user supplied data */
	if (test_nurbs_curves(nobj) != GLU_NO_ERROR)
	return;

	if (convert_curves(nobj, &new_geom_ctrl, &n_ctrl, &new_color_ctrl,
	&new_normal_ctrl, &new_texture_ctrl) != GLU_NO_ERROR)
	return;

	geom_order = nobj->curve.geom.order;
	geom_type = nobj->curve.geom.type;
	geom_dim = nobj->curve.geom.dim;

	if (glu_do_sampling_crv(nobj, new_geom_ctrl, n_ctrl, geom_order, geom_dim,
	&factors) != GLU_NO_ERROR) {
	free(new_geom_ctrl);
	if (new_color_ctrl)
	free(new_color_ctrl);
	if (new_normal_ctrl)
	free(new_normal_ctrl);
	if (new_texture_ctrl)
	free(new_texture_ctrl);
	return;
	}
	glEnable(geom_type);
	if (new_color_ctrl) {
	glEnable(nobj->curve.color.type);
	color_dim = nobj->curve.color.dim;
	color_ctrl = new_color_ctrl;
	color_order = nobj->curve.color.order;
	}
	if (new_normal_ctrl) {
	glEnable(nobj->curve.normal.type);
	normal_dim = nobj->curve.normal.dim;
	normal_ctrl = new_normal_ctrl;
	normal_order = nobj->curve.normal.order;
	}
	if (new_texture_ctrl) {
	glEnable(nobj->curve.texture.type);
	texture_dim = nobj->curve.texture.dim;
	texture_ctrl = new_texture_ctrl;
	texture_order = nobj->curve.texture.order;
	}
	for (i = 0, j = 0, geom_ctrl = new_geom_ctrl;
	i < n_ctrl; i += geom_order, j++, geom_ctrl += geom_order * geom_dim) {
	if (fine_culling_test_2D
	(nobj, geom_ctrl, geom_order, geom_dim, geom_dim)) {
	color_ctrl += color_order * color_dim;
	normal_ctrl += normal_order * normal_dim;
	texture_ctrl += texture_order * texture_dim;
	continue;
	}
	glMap1f(geom_type, 0.0, 1.0, geom_dim, geom_order, geom_ctrl);
	if (new_color_ctrl) {
	glMap1f(nobj->curve.color.type, 0.0, 1.0, color_dim,
	color_order, color_ctrl);
	color_ctrl += color_order * color_dim;
	}
	if (new_normal_ctrl) {
	glMap1f(nobj->curve.normal.type, 0.0, 1.0, normal_dim,
	normal_order, normal_ctrl);
	normal_ctrl += normal_order * normal_dim;
	}
	if (new_texture_ctrl) {
	glMap1f(nobj->curve.texture.type, 0.0, 1.0, texture_dim,
	texture_order, texture_ctrl);
	texture_ctrl += texture_order * texture_dim;
	}
	glMapGrid1f(factors[j], 0.0, 1.0);
	glEvalMesh1(GL_LINE, 0, factors[j]);
	}
	free(new_geom_ctrl);
	free(factors);
	if (new_color_ctrl)
	free(new_color_ctrl);
	if (new_normal_ctrl)
	free(new_normal_ctrl);
	if (new_texture_ctrl)
	free(new_texture_ctrl);
	}