Esempio n. 1
0
void rot_omega (gleDouble axis[3])		/* input */
{
   gleDouble m[4][4];

   urot_omega (m, axis);
   MULTMATRIX(m);
}
Esempio n. 2
0
void rot_about_axis (gleDouble angle, 		/* input */
                     gleDouble axis[3])		/* input */
{
   gleDouble m[4][4];

   urot_about_axis (m, angle, axis);
   MULTMATRIX (m);
}
Esempio n. 3
0
void rot_axis (gleDouble omega, 		/* input */
               gleDouble axis[3])		/* input */
{
   gleDouble m[4][4];

   urot_axis (m, omega, axis);
   MULTMATRIX (m);

}
Esempio n. 4
0
static 
void rotz_cs (gleDouble cosine,		/* input */
              gleDouble sine) 		/* input */
{
   /* create and load matrix that represents rotation about the z-azis */
   gleDouble m[4][4];

   urotz_cs (m, cosine, sine);
   MULTMATRIX (m);
}
Esempio n. 5
0
void rot_prince (gleDouble theta,	/* input */
                 char axis) 		/* input */
{
   gleDouble m[4][4];
   /* 
    * generate rotation matrix for rotation around principal axis;
    * note that angle is measured in radians (divide by 180, multiply by
    * PI to convert from degrees).
    */

   urot_prince (m, theta, axis);
   MULTMATRIX (m);
}
Esempio n. 6
0
void
extrusion_round_or_cut_join (int ncp,	/* number of contour points */
                           gleDouble contour[][2],	/* 2D contour */
                           gleDouble cont_normal[][2],/* 2D normal vecs */
                           gleDouble up[3],	/* up vector for contour */
                           int npoints,		/* numpoints in poly-line */
                           gleDouble point_array[][3],	/* polyline */
                           float color_array[][3],	/* color of polyline */
                           gleDouble xform_array[][2][3])   /* 2D contour xforms */
{
   int i, j;
   int inext, inextnext;
   gleDouble m[4][4];
   gleDouble tube_len, seg_len;
   gleDouble diff[3];
   gleDouble bi_0[3], bi_1[3];		/* bisecting plane */
   gleDouble bisector_0[3], bisector_1[3];		/* bisecting plane */
   gleDouble cut_0[3], cut_1[3];	/* cutting planes */
   gleDouble lcut_0[3], lcut_1[3];	/* cutting planes */
   int valid_cut_0, valid_cut_1;	/* flag -- cut vector is valid */
   gleDouble end_point_0[3], end_point_1[3];
   gleDouble torsion_point_0[3], torsion_point_1[3];
   gleDouble isect_point[3];
   gleDouble origin[3], neg_z[3];
   gleDouble yup[3];		/* alternate up vector */
   gleDouble *front_cap, *back_cap;	/* arrays containing the end caps */
   gleDouble *front_loop, *back_loop; /* arrays containing the tube ends */
   double *front_norm, *back_norm; /* arrays containing normal vecs */
   double *norm_loop=0x0, *tmp; /* normal vectors, cast into 3d from 2d */
   int *front_is_trimmed, *back_is_trimmed;   /* T or F */
   float *front_color, *back_color;  /* pointers to segment colors */
   gleCapCallback cap_callback = 0x0 ;  /* function callback to draw cap */
   gleCapCallback tmp_cap_callback = 0x0;  /* function callback to draw cap */
   int join_style_is_cut;      /* TRUE if join style is cut */
   double dot;                  /* partial dot product */
   char *mem_anchor;
   int first_time = TRUE;
   gleDouble *cut_vec;

   /* create a local, block scope copy of of the join style.
    * this will alleviate wasted cycles and register write-backs */
   /* choose the right callback, depending on the choosen join style */
   if (__TUBE_CUT_JOIN) {
      join_style_is_cut = TRUE;
      cap_callback =  draw_cut_style_cap_callback;
   } else {
      join_style_is_cut = FALSE;
      cap_callback =  draw_round_style_cap_callback;
   }

   /* By definition, the contour passed in has its up vector pointing in
    * the y direction */
   if (up == NULL) {
      yup[0] = 0.0;
      yup[1] = 1.0;
      yup[2] = 0.0;
   } else {
      VEC_COPY (yup, up);
   }

   /* ========== "up" vector sanity check ========== */
   (void) up_sanity_check (yup, npoints, point_array);

   /* the origin is at the origin */
   origin [0] = 0.0;
   origin [1] = 0.0;
   origin [2] = 0.0;

   /* and neg_z is at neg z */
   neg_z[0] = 0.0;
   neg_z[1] = 0.0;
   neg_z[2] = 1.0;

   /* malloc the data areas that we'll need to store the end-caps */
   mem_anchor = malloc (4 * 3*ncp*sizeof(gleDouble)
                      + 2 * 3*ncp*sizeof(double)
                      + 2 * 1*ncp*sizeof(int));
   front_norm = (double *) mem_anchor;
   back_norm = front_norm + 3*ncp;
   front_loop = (gleDouble *) (back_norm + 3*ncp);
   back_loop = front_loop + 3*ncp;
   front_cap = back_loop + 3*ncp;
   back_cap  = front_cap + 3*ncp;
   front_is_trimmed = (int *) (back_cap + 3*ncp);
   back_is_trimmed = front_is_trimmed + ncp;

   /* ======================================= */

   /* |-|-|-|-|-|-|-|-| SET UP FOR FIRST SEGMENT |-|-|-|-|-|-|-| */

   /* ignore all segments of zero length */
   i = 1;
   inext = i;
   FIND_NON_DEGENERATE_POINT (inext, npoints, seg_len, diff, point_array);
   tube_len = seg_len;	/* store for later use */

   /* may as well get the normals set up now */
   if (cont_normal != NULL) {
      if (xform_array == NULL) {
         norm_loop = front_norm;
         back_norm = norm_loop;
         for (j=0; j<ncp; j++) {
            norm_loop[3*j] = cont_normal[j][0];
            norm_loop[3*j+1] = cont_normal[j][1];
            norm_loop[3*j+2] = 0.0;
         }
      } else {
         for (j=0; j<ncp; j++) {
            NORM_XFORM_2X2 ( (&front_norm[3*j]),
                              xform_array[inext-1],
                              cont_normal [j]);
            front_norm[3*j+2] = 0.0;
            back_norm[3*j+2] = 0.0;
         }
      }
   } else {
      front_norm = back_norm = norm_loop = NULL;
   }

   /* get the bisecting plane */
   bisecting_plane (bi_0, point_array[i-1],
                          point_array[i],
                          point_array[inext]);

   /* compute cutting plane */
   CUTTING_PLANE (valid_cut_0, cut_0, point_array[i-1],
                         point_array[i],
                         point_array[inext]);

   /* reflect the up vector in the bisecting plane */
   VEC_REFLECT (yup, yup, bi_0);

   /* |-|-|-|-|-|-|-|-| START LOOP OVER SEGMENTS |-|-|-|-|-|-|-| */

   /* draw tubing, not doing the first segment */
   while (inext<npoints-1) {

      inextnext = inext;
      /* ignore all segments of zero length */
      FIND_NON_DEGENERATE_POINT (inextnext, npoints,
                                 seg_len, diff, point_array);

      /* get the far bisecting plane */
      bisecting_plane (bi_1, point_array[i],
                             point_array[inext],
                             point_array[inextnext]);


      /* compute cutting plane */
      CUTTING_PLANE (valid_cut_1, cut_1, point_array[i],
                            point_array[inext],
                            point_array[inextnext]);

      /* rotate so that z-axis points down v2-v1 axis,
       * and so that origen is at v1 */
      uviewpoint (m, point_array[i], point_array[inext], yup);
      PUSHMATRIX ();
      MULTMATRIX (m);

      /* rotate the cutting planes into the local coordinate system */
      MAT_DOT_VEC_3X3 (lcut_0, m, cut_0);
      MAT_DOT_VEC_3X3 (lcut_1, m, cut_1);

      /* rotate the bisecting planes into the local coordinate system */
      MAT_DOT_VEC_3X3 (bisector_0, m, bi_0);
      MAT_DOT_VEC_3X3 (bisector_1, m, bi_1);


      neg_z[2] = -tube_len;

      /* draw the tube */
      /* --------- START OF TMESH GENERATION -------------- */
      for (j=0; j<ncp; j++) {

         /* set up the endpoints for segment clipping */
         if (xform_array == NULL) {
            VEC_COPY_2 (end_point_0, contour[j]);
            VEC_COPY_2 (end_point_1, contour[j]);
            VEC_COPY_2 (torsion_point_0, contour[j]);
            VEC_COPY_2 (torsion_point_1, contour[j]);
         } else {
            /* transform the contour points with the local xform */
            MAT_DOT_VEC_2X3 (end_point_0,
                             xform_array[inext-1], contour[j]);
            MAT_DOT_VEC_2X3 (torsion_point_0,
                             xform_array[inext], contour[j]);
            MAT_DOT_VEC_2X3 (end_point_1,
                             xform_array[inext], contour[j]);
            MAT_DOT_VEC_2X3 (torsion_point_1,
                             xform_array[inext-1], contour[j]);

            /* if there are normals and there are affine xforms,
             * then compute local coordinate system normals.
             * Set up the back normals. (The front normals we inherit
             * from previous pass through the loop).  */
            if (cont_normal != NULL) {
               /* do up the normal vectors with the inverse transpose */
               NORM_XFORM_2X2 ( (&back_norm[3*j]),
                                xform_array[inext],
                                cont_normal [j]);
            }
         }
         end_point_0 [2] = 0.0;
         torsion_point_0 [2] = 0.0;
         end_point_1 [2] = - tube_len;
         torsion_point_1 [2] = - tube_len;

         /* The two end-points define a line.  Intersect this line
          * against the clipping plane defined by the PREVIOUS
          * tube segment.  */

         /* if this and the last tube are co-linear, don't cut the angle
          * if you do, a divide by zero will result.  This and last tube
          * are co-linear when the cut vector is of zero length */
         if (valid_cut_0 && join_style_is_cut) {
             INNERSECT (isect_point,  /* isect point (returned) */
                       origin,		/* point on intersecting plane */
                       lcut_0,		/* normal vector to plane */
                       end_point_0,	/* point on line */
                       end_point_1);	/* another point on the line */

            /* determine whether the raw end of the extrusion would have
             * been cut, by checking to see if the raw and is on the
             * far end of the half-plane defined by the cut vector.
             * If the raw end is not "cut", then it is "trimmed".
             */
            if (lcut_0[2] < 0.0) { VEC_SCALE (lcut_0, -1.0, lcut_0); }
            dot = lcut_0[0] * end_point_0[0];
            dot += lcut_0[1] * end_point_0[1];

            VEC_COPY ((&front_loop[3*j]), isect_point);
         } else {
            /* actual value of dot not interseting; need
             * only be positive so that if test below failes */
            dot = 1.0;
            VEC_COPY ((&front_loop[3*j]), end_point_0);
         }

         INNERSECT (isect_point, 	/* intersection point (returned) */
                    origin,		/* point on intersecting plane */
                    bisector_0,		/* normal vector to plane */
                    end_point_0,	/* point on line */
                    torsion_point_1);	/* another point on the line */

         /* trim out interior of intersecting tube */
         /* ... but save the untrimmed version for drawing the endcaps */
         /* ... note that cap contains valid data ONLY when is_trimmed
          * is TRUE. */
         if ((dot <= 0.0) || (isect_point[2] < front_loop[3*j+2])) {
/*
         if ((dot <= 0.0) || (front_loop[3*j+2] > 0.0)) {
*/
            VEC_COPY ((&front_cap[3*j]), (&front_loop [3*j]));
            VEC_COPY ((&front_loop[3*j]), isect_point);
            front_is_trimmed[j] = TRUE;
         } else {
            front_is_trimmed[j] = FALSE;
         }

         /* if intersection is behind the end of the segment,
          * truncate to the end of the segment
          * Note that coding front_loop [3*j+2] = -tube_len;
          * doesn't work when twists are involved, */
         if (front_loop[3*j+2] < -tube_len) {
            VEC_COPY( (&front_loop[3*j]), end_point_1);
         }

         /* --------------------------------------------------- */
         /* The two end-points define a line.  We did one endpoint
          * above. Now do the other.Intersect this line
          * against the clipping plane defined by the NEXT
          * tube segment.  */

         /* if this and the last tube are co-linear, don't cut the angle
          * if you do, a divide by zero will result.  This and last tube
          * are co-linear when the cut vector is of zero length */
         if (valid_cut_1 && join_style_is_cut) {
            INNERSECT (isect_point,  /* isect point (returned) */
                       neg_z,		/* point on intersecting plane */
                       lcut_1,		/* normal vector to plane */
                       end_point_1,	/* point on line */
                       end_point_0);	/* another point on the line */

            if (lcut_1[2] > 0.0) { VEC_SCALE (lcut_1, -1.0, lcut_1); }
            dot = lcut_1[0] * end_point_1[0];
            dot += lcut_1[1] * end_point_1[1];


            VEC_COPY ((&back_loop[3*j]), isect_point);
         } else {
            /* actual value of dot not interseting; need
             * only be positive so that if test below failes */
            dot = 1.0;
            VEC_COPY ((&back_loop[3*j]), end_point_1);
         }

         INNERSECT (isect_point, 	/* intersection point (returned) */
                    neg_z,		/* point on intersecting plane */
                    bisector_1,		/* normal vector to plane */
                    torsion_point_0,	/* point on line */
                    end_point_1);	/* another point on the line */

         /* cut out interior of intersecting tube */
         /* ... but save the uncut version for drawing the endcaps */
         /* ... note that cap contains valid data ONLY when is
          *_trimmed is TRUE. */
/*
        if ((dot <= 0.0) || (back_loop[3*j+2] < -tube_len)) {
*/
        if ((dot <= 0.0) || (isect_point[2] > back_loop[3*j+2])) {
            VEC_COPY ((&back_cap[3*j]), (&back_loop [3*j]));
            VEC_COPY ((&back_loop[3*j]), isect_point);
            back_is_trimmed[j] = TRUE;
         } else {
            back_is_trimmed[j] = FALSE;
         }

         /* if intersection is behind the end of the segment,
          * truncate to the end of the segment
          * Note that coding back_loop [3*j+2] = 0.0;
          * doesn't work when twists are involved, */
         if (back_loop[3*j+2] > 0.0) {
            VEC_COPY( (&back_loop[3*j]), end_point_0);
         }
      }

      /* --------- END OF TMESH GENERATION -------------- */

      /* |||||||||||||||||| START SEGMENT DRAW |||||||||||||||||||| */
      /* There are six different cases we can have for presence and/or
       * absecnce of colors and normals, and for interpretation of
       * normals. The blechy set of nested if statements below
       * branch to each of the six cases */
      if (xform_array == NULL) {
         if (color_array == NULL) {
            if (cont_normal == NULL) {
               draw_segment_plain (ncp, (gleVector *) front_loop, (gleVector *) back_loop, inext, seg_len);
            } else
            if (__TUBE_DRAW_FACET_NORMALS) {
               draw_segment_facet_n (ncp, (gleVector *) front_loop, (gleVector *) back_loop, (gleVector *) norm_loop,
                                     inext, seg_len);
            } else {
               draw_segment_edge_n (ncp, (gleVector *) front_loop, (gleVector *) back_loop, (gleVector *) norm_loop,
                                    inext, seg_len);
            }
         } else {
            if (cont_normal == NULL) {
               draw_segment_color (ncp, (gleVector *) front_loop, (gleVector *) back_loop,
                                   color_array[inext-1],
                                   color_array[inext], inext, seg_len);
            } else
            if (__TUBE_DRAW_FACET_NORMALS) {
               draw_segment_c_and_facet_n (ncp,
                                   (gleVector *) front_loop, (gleVector *) back_loop, (gleVector *) norm_loop,
                                   color_array[inext-1],
                                   color_array[inext], inext, seg_len);
            } else {
               draw_segment_c_and_edge_n (ncp,
                                   (gleVector *) front_loop, (gleVector *) back_loop, (gleVector *) norm_loop,
                                   color_array[inext-1],
                                   color_array[inext], inext, seg_len);
             }
          }
      } else {
         if (color_array == NULL) {
            if (cont_normal == NULL) {
               draw_segment_plain (ncp, (gleVector *) front_loop, (gleVector *) back_loop, inext, seg_len);
            } else
            if (__TUBE_DRAW_FACET_NORMALS) {
               draw_binorm_segment_facet_n (ncp, (gleVector *) front_loop, (gleVector *) back_loop,
                                                 (gleVector *) front_norm, (gleVector *) back_norm,
                                                 inext, seg_len);
            } else {
               draw_binorm_segment_edge_n (ncp, (gleVector *) front_loop, (gleVector *) back_loop,
                                                (gleVector *) front_norm, (gleVector *) back_norm,
                                                inext, seg_len);
            }
         } else {
            if (cont_normal == NULL) {
               draw_segment_color (ncp, (gleVector *) front_loop, (gleVector *) back_loop,
                                   color_array[inext-1],
                                   color_array[inext], inext, seg_len);
            } else
            if (__TUBE_DRAW_FACET_NORMALS) {
               draw_binorm_segment_c_and_facet_n (ncp,
                                   (gleVector *) front_loop, (gleVector *) back_loop,
                                   (gleVector *) front_norm, (gleVector *) back_norm,
                                   color_array[inext-1],
                                   color_array[inext], inext, seg_len);
            } else {
               draw_binorm_segment_c_and_edge_n (ncp,
                                   (gleVector *) front_loop, (gleVector *) back_loop,
                                   (gleVector *) front_norm, (gleVector *) back_norm,
                                   color_array[inext-1],
                                   color_array[inext], inext, seg_len);
             }
          }
      }
      /* |||||||||||||||||| END SEGMENT DRAW |||||||||||||||||||| */

      /* v^v^v^v^v^v^v^v^v  BEGIN END CAPS v^v^v^v^v^v^v^v^v^v^v^v */

      /* if end caps are required, draw them. But don't draw any
       * but the very first and last caps */
      if (first_time) {
         first_time = FALSE;
         tmp_cap_callback = cap_callback;
         cap_callback = null_cap_callback;
         if (__TUBE_DRAW_CAP) {
            if (color_array != NULL) C3F (color_array[inext-1]);
            draw_angle_style_front_cap (ncp, bisector_0,
                                       (gleDouble (*)[3]) front_loop);
         }
      }
      /* v^v^v^v^v^v^v^v^v  END END CAPS v^v^v^v^v^v^v^v^v^v^v^v */

      /* $$$$$$$$$$$$$$$$ BEGIN -1, FILLET & JOIN DRAW $$$$$$$$$$$$$$$$$ */
      /*
       * Now, draw the fillet triangles, and the join-caps.
       */
      if (color_array != NULL) {
         front_color = color_array[inext-1];
         back_color = color_array[inext];
      } else {
         front_color = NULL;
         back_color = NULL;
      }

      if (cont_normal == NULL) {
         /* the flag valid-cut is true if the cut vector has a valid
          * value (i.e. if a degenerate case has not occured).
          */
         if (valid_cut_0) {
            cut_vec = lcut_0;
         } else {
            cut_vec = NULL;
         }
         draw_fillets_and_join_plain (ncp,
                                  (gleVector *) front_loop,
                                  (gleVector *) front_cap,
                                  front_is_trimmed,
                                  origin,
                                  bisector_0,
                                  front_color,
                                  back_color,
                                  cut_vec,
                                  TRUE,
                                  cap_callback);

         /* v^v^v^v^v^v^v^v^v  BEGIN END CAPS v^v^v^v^v^v^v^v^v^v^v^v */
         if (inext == npoints-2) {
            if (__TUBE_DRAW_CAP) {
               if (color_array != NULL) C3F (color_array[inext]);
               draw_angle_style_back_cap (ncp, bisector_1,
                                           (gleDouble (*)[3]) back_loop);
               cap_callback = null_cap_callback;
            }
         } else {
            /* restore ability to draw cap */
            cap_callback = tmp_cap_callback;
         }
         /* v^v^v^v^v^v^v^v^v  END END CAPS v^v^v^v^v^v^v^v^v^v^v^v */

         /* the flag valid-cut is true if the cut vector has a valid
          * value (i.e. if a degenerate case has not occured).
          */
         if (valid_cut_1) {
            cut_vec = lcut_1;
         } else {
            cut_vec = NULL;
         }
         draw_fillets_and_join_plain (ncp,
                                  (gleVector *) back_loop,
                                  (gleVector *) back_cap,
                                  back_is_trimmed,
                                  neg_z,
                                  bisector_1,
                                  back_color,
                                  front_color,
                                  cut_vec,
                                  FALSE,
                                  cap_callback);
      } else {

         /* the flag valid-cut is true if the cut vector has a valid
          * value (i.e. if a degenerate case has not occured).
          */
         if (valid_cut_0) {
            cut_vec = lcut_0;
         } else {
            cut_vec = NULL;
         }
         draw_fillets_and_join_n_norms (ncp,
                                  (gleVector *) front_loop,
                                  (gleVector *) front_cap,
                                  front_is_trimmed,
                                  origin,
                                  bisector_0,
                                  (gleVector *) front_norm,
                                  front_color,
                                  back_color,
                                  cut_vec,
                                  TRUE,
                                  cap_callback);

         /* v^v^v^v^v^v^v^v^v  BEGIN END CAPS v^v^v^v^v^v^v^v^v^v^v^v */
         if (inext == npoints-2) {
            if (__TUBE_DRAW_CAP) {
               if (color_array != NULL) C3F (color_array[inext]);
               draw_angle_style_back_cap (ncp, bisector_1,
                                         (gleDouble (*)[3]) back_loop);
               cap_callback = null_cap_callback;
            }
         } else {
            /* restore ability to draw cap */
            cap_callback = tmp_cap_callback;
         }
         /* v^v^v^v^v^v^v^v^v  END END CAPS v^v^v^v^v^v^v^v^v^v^v^v */

         /* the flag valid-cut is true if the cut vector has a valid
          * value (i.e. if a degenerate case has not occured).
          */
         if (valid_cut_1) {
            cut_vec = lcut_1;
         } else {
            cut_vec = NULL;
         }
         draw_fillets_and_join_n_norms (ncp,
                                  (gleVector *) back_loop,
                                  (gleVector *) back_cap,
                                  back_is_trimmed,
                                  neg_z,
                                  bisector_1,
                                  (gleVector *) back_norm,
                                  back_color,
                                  front_color,
                                  cut_vec,
                                  FALSE,
                                  cap_callback);
      }

      /* $$$$$$$$$$$$$$$$ END FILLET & JOIN DRAW $$$$$$$$$$$$$$$$$ */

      /* pop this matrix, do the next set */
      POPMATRIX ();

      /* slosh stuff over to next vertex */
      tmp = front_norm;
      front_norm = back_norm;
      back_norm = tmp;

      tube_len = seg_len;
      i = inext;
      inext = inextnext;
      VEC_COPY (bi_0, bi_1);
      VEC_COPY (cut_0, cut_1);
      valid_cut_0 = valid_cut_1;

      /* reflect the up vector in the bisecting plane */
      VEC_REFLECT (yup, yup, bi_0);
   }
   /* |-|-|-|-|-|-|-|-| END LOOP OVER SEGMENTS |-|-|-|-|-|-|-| */

   free (mem_anchor);

}
Esempio n. 7
0
void extrusion_angle_join (int ncp,		/* number of contour points */
                           gleDouble contour[][2],	/* 2D contour */
                           gleDouble cont_normal[][2], /* 2D normal vecs */
                           gleDouble up[3],	/* up vector for contour */
                           int npoints,		/* numpoints in poly-line */
                           gleDouble point_array[][3],	/* polyline */
                           float color_array[][3],	/* color of polyline */
                           gleDouble xform_array[][2][3])  /* 2D contour xforms */
{
   int i, j;
   int inext, inextnext;
   gleDouble m[4][4];
   gleDouble len;
   gleDouble len_seg;
   gleDouble diff[3];
   gleDouble bi_0[3], bi_1[3];		/* bisecting plane */
   gleDouble bisector_0[3], bisector_1[3];	/* bisecting plane */
   gleDouble end_point_0[3], end_point_1[3]; 
   gleDouble origin[3], neg_z[3];
   gleDouble yup[3];		/* alternate up vector */
   gleDouble *front_loop, *back_loop;   /* contours in 3D */
   char * mem_anchor;
   double *norm_loop; 
   double *front_norm, *back_norm, *tmp; /* contour normals in 3D */
   int first_time;

   /* By definition, the contour passed in has its up vector pointing in
    * the y direction */
   if (up == NULL) {
      yup[0] = 0.0;
      yup[1] = 1.0;
      yup[2] = 0.0;
   } else {
      VEC_COPY(yup, up);
   }

   /* ========== "up" vector sanity check ========== */
   (void) up_sanity_check (yup, npoints, point_array);

   /* the origin is at the origin */
   origin [0] = 0.0;
   origin [1] = 0.0;
   origin [2] = 0.0;

   /* and neg_z is at neg z */
   neg_z[0] = 0.0;
   neg_z[1] = 0.0;
   neg_z[2] = 1.0;

   /* ignore all segments of zero length */
   i = 1;
   inext = i;
   FIND_NON_DEGENERATE_POINT (inext, npoints, len, diff, point_array);
   len_seg = len;	/* store for later use */

   /* get the bisecting plane */
   bisecting_plane (bi_0, point_array[0], 
                          point_array[1], 
                          point_array[inext]);
   /* reflect the up vector in the bisecting plane */
   VEC_REFLECT (yup, yup, bi_0);

   /* malloc the storage we'll need for relaying changed contours to the
    * drawing routines. */
   mem_anchor =  malloc (2 * 3 * ncp * sizeof(double)
                      +  2 * 3 * ncp * sizeof(gleDouble));
   front_loop = (gleDouble *) mem_anchor;
   back_loop = front_loop + 3 * ncp;
   front_norm = (double *) (back_loop + 3 * ncp);
   back_norm = front_norm + 3 * ncp;
   norm_loop = front_norm;

   /* may as well get the normals set up now */
   if (cont_normal != NULL) {
      if (xform_array == NULL) {
         for (j=0; j<ncp; j++) {
            norm_loop[3*j] = cont_normal[j][0];
            norm_loop[3*j+1] = cont_normal[j][1];
            norm_loop[3*j+2] = 0.0;
         }
      } else {
         for (j=0; j<ncp; j++) {
            NORM_XFORM_2X2 ( (&front_norm[3*j]),
                              xform_array[inext-1],
                              cont_normal [j]);
            front_norm[3*j+2] = 0.0;
            back_norm[3*j+2] = 0.0;
         }
      }
   }

   first_time = TRUE;
   /* draw tubing, not doing the first segment */
   while (inext<npoints-1) {

      inextnext = inext;
      /* ignore all segments of zero length */
      FIND_NON_DEGENERATE_POINT (inextnext, npoints, len, diff, point_array);

      /* get the next bisecting plane */
      bisecting_plane (bi_1, point_array[i], 
                             point_array[inext], 
                             point_array[inextnext]);  

      /* rotate so that z-axis points down v2-v1 axis, 
       * and so that origen is at v1 */
      uviewpoint (m, point_array[i], point_array[inext], yup);
      PUSHMATRIX ();
      MULTMATRIX (m);

      /* rotate the bisecting planes into the local coordinate system */
      MAT_DOT_VEC_3X3 (bisector_0, m, bi_0);
      MAT_DOT_VEC_3X3 (bisector_1, m, bi_1);

      neg_z[2] = -len_seg;

      /* draw the tube */
      /* --------- START OF TMESH GENERATION -------------- */
      for (j=0; j<ncp; j++) {

         /* if there are normals, and there are either affine xforms, OR
          * path-edge normals need to be drawn, then compute local
          * coordinate system normals. 
          */
         if (cont_normal != NULL) {
          
            /* set up the back normals. (The front normals we inherit
             * from previous pass through the loop) */
            if (xform_array != NULL) {
               /* do up the normal vectors with the inverse transpose */
               NORM_XFORM_2X2 ( (&back_norm[3*j]),
                                 xform_array[inext],
                                 cont_normal [j]);
            }

            /* Note that if the xform array is NULL, then normals are
             * constant, and are set up outside of the loop.
             */

            /* 
             * if there are normal vectors, and the style calls for it, 
             * then we want to project the normal vectors into the
             * bisecting plane. (This style is needed to make toroids, etc. 
             * look good: Without this, segmentation artifacts show up
             * under lighting.
             */
            if (__TUBE_DRAW_PATH_EDGE_NORMALS) {
               /* Hmm, if no affine xforms, then we haven't yet set
                * back vector. So do it. */
               if (xform_array == NULL) {
                  back_norm[3*j] = cont_normal[j][0];
                  back_norm[3*j+1] = cont_normal[j][1];
               }
   
               /* now, start with a fresh normal (z component equal to
                * zero), project onto bisecting plane (by computing 
                * perpendicular componenet to bisect vector, and renormalize 
                * (since projected vector is not of unit length */ 
               front_norm[3*j+2] = 0.0;
               VEC_PERP ((&front_norm[3*j]), (&front_norm[3*j]), bisector_0);
               VEC_NORMALIZE ((&front_norm[3*j]));
    
               back_norm[3*j+2] = 0.0;
               VEC_PERP ((&back_norm[3*j]), (&back_norm[3*j]), bisector_1);
               VEC_NORMALIZE ((&back_norm[3*j]));
            } 
         } 

         /* Next, we want to define segements. We find the endpoints of
          * the segments by intersecting the contour with the bisecting
          * plane.  If there is no local affine transform, this is easy.
          *
          * If there is an affine tranform, then we want to remove the
          * torsional component, so that the intersection points won't
          * get twisted out of shape.  We do this by applying the
          * local affine transform to the entire coordinate system.
          */
         if (xform_array == NULL) {
            end_point_0 [0] = contour[j][0];
            end_point_0 [1] = contour[j][1];
   
            end_point_1 [0] = contour[j][0];
            end_point_1 [1] = contour[j][1];
         } else {
            /* transform the contour points with the local xform */
            MAT_DOT_VEC_2X3 (end_point_0,
                             xform_array[inext-1], contour[j]);
            MAT_DOT_VEC_2X3 (end_point_1,
                             xform_array[inext-1], contour[j]);
         }

         end_point_0 [2] = 0.0;
         end_point_1 [2] = - len_seg;

         /* The two end-points define a line.  Intersect this line
          * against the clipping plane defined by the PREVIOUS
          * tube segment.  */

         INNERSECT ((&front_loop[3*j]), /* intersection point (returned) */
                    origin,		/* point on intersecting plane */
                    bisector_0,		/* normal vector to plane */
                    end_point_0,	/* point on line */
                    end_point_1);	/* another point on the line */	

         /* The two end-points define a line.  Intersect this line
          * against the clipping plane defined by the NEXT
          * tube segment.  */

         /* if there's an affine coordinate change, be sure to use it */
         if (xform_array != NULL) {
            /* transform the contour points with the local xform */
            MAT_DOT_VEC_2X3 (end_point_0,
                             xform_array[inext], contour[j]);
            MAT_DOT_VEC_2X3 (end_point_1,
                             xform_array[inext], contour[j]);
         }

         INNERSECT ((&back_loop[3*j]),	/* intersection point (returned) */
                    neg_z,		/* point on intersecting plane */
                    bisector_1,		/* normal vector to plane */
                    end_point_0,	/* point on line */
                    end_point_1);	/* another point on the line */	

      }

      /* --------- END OF TMESH GENERATION -------------- */

      /* v^v^v^v^v^v^v^v^v  BEGIN END CAPS v^v^v^v^v^v^v^v^v^v^v^v */

      /* if end caps are required, draw them. But don't draw any 
       * but the very first and last caps */
      if (__TUBE_DRAW_CAP) {
         if (first_time) {
            if (color_array != NULL) C3F (color_array[inext-1]);
            first_time = FALSE;
            draw_angle_style_front_cap (ncp, bisector_0, (gleVector *) front_loop);
         }
         if (inext == npoints-2) {
            if (color_array != NULL) C3F (color_array[inext]);
            draw_angle_style_back_cap (ncp, bisector_1, (gleVector *) back_loop);
         }
      }
      /* v^v^v^v^v^v^v^v^v  END END CAPS v^v^v^v^v^v^v^v^v^v^v^v */

      /* |||||||||||||||||| START SEGMENT DRAW |||||||||||||||||||| */
      /* There are six different cases we can have for presence and/or
       * absecnce of colors and normals, and for interpretation of
       * normals. The blechy set of nested if statements below
       * branch to each of the six cases */
      if ((xform_array == NULL) && (!__TUBE_DRAW_PATH_EDGE_NORMALS)) {
         if (color_array == NULL) {
            if (cont_normal == NULL) {
               draw_segment_plain (ncp, (gleVector *) front_loop,
                                        (gleVector *) back_loop, inext, len_seg);
            } else
            if (__TUBE_DRAW_FACET_NORMALS) {
               draw_segment_facet_n (ncp, (gleVector *) front_loop,
                                          (gleVector *) back_loop, 
                                          (gleVector *) norm_loop, inext, len_seg);
            } else {
               draw_segment_edge_n (ncp, (gleVector *) front_loop, 
                                         (gleVector *) back_loop, 
                                         (gleVector *) norm_loop, inext, len_seg);
            }
         } else {
            if (cont_normal == NULL) {
               draw_segment_color (ncp, (gleVector *) front_loop, 
                                        (gleVector *) back_loop, 
                                   color_array[inext-1],
                                   color_array[inext], inext, len_seg);
            } else
            if (__TUBE_DRAW_FACET_NORMALS) {
               draw_segment_c_and_facet_n (ncp, 
                                   (gleVector *) front_loop, 
                                   (gleVector *) back_loop, 
                                   (gleVector *) norm_loop,
                                   color_array[inext-1],
                                   color_array[inext], inext, len_seg);
            } else {
               draw_segment_c_and_edge_n (ncp, 
                                   (gleVector *) front_loop, 
                                   (gleVector *) back_loop, 
                                   (gleVector *) norm_loop,
                                   color_array[inext-1],
                                   color_array[inext], inext, len_seg);
             }
          }
      } else {
         if (color_array == NULL) {
            if (cont_normal == NULL) {
               draw_segment_plain (ncp, (gleVector *) front_loop, 
                                        (gleVector *)  back_loop, inext, len_seg);
            } else 
            if (__TUBE_DRAW_FACET_NORMALS) {
               draw_binorm_segment_facet_n (ncp, (gleVector *) front_loop, 
                                                 (gleVector *) back_loop,
                                                 (gleVector *) front_norm, 
                                                 (gleVector *) back_norm,
                                                 inext, len_seg);
            } else {
               draw_binorm_segment_edge_n (ncp, (gleVector *) front_loop, 
                                                (gleVector *) back_loop,
                                                (gleVector *) front_norm,
                                                (gleVector *) back_norm,
                                                inext, len_seg);
            }
         } else {
            if (cont_normal == NULL) {
               draw_segment_color (ncp, (gleVector *) front_loop, 
                                        (gleVector *) back_loop, 
                                   color_array[inext-1],
                                   color_array[inext], inext, len_seg);
            } else
            if (__TUBE_DRAW_FACET_NORMALS) {
               draw_binorm_segment_c_and_facet_n (ncp, 
                                   (gleVector *) front_loop, 
                                   (gleVector *) back_loop, 
                                   (gleVector *) front_norm, 
                                   (gleVector *) back_norm, 
                                   color_array[inext-1],
                                   color_array[inext], inext, len_seg);
            } else {
               draw_binorm_segment_c_and_edge_n (ncp, 
                                   (gleVector *) front_loop, 
                                   (gleVector *) back_loop, 
                                   (gleVector *) front_norm, 
                                   (gleVector *) back_norm, 
                                   color_array[inext-1],
                                   color_array[inext], inext, len_seg);
             }
          }
      }
      /* |||||||||||||||||| END SEGMENT DRAW |||||||||||||||||||| */

      /* pop this matrix, do the next set */
      POPMATRIX ();

      /* bump everything to the next vertex */
      len_seg = len;
      i = inext;
      inext = inextnext;
      VEC_COPY (bi_0, bi_1);

      /* trade norm loops */
      tmp = front_norm;
      front_norm = back_norm;
      back_norm = tmp;

      /* reflect the up vector in the bisecting plane */
      VEC_REFLECT (yup, yup, bi_0);
   }

   /* be sure to free it all up */
   free (mem_anchor);

}