Initial incomplete GLU NURBS port under net.java.games.jogl.impl.nurbs

and a small README about the procedures being used during the port


git-svn-id: file:///usr/local/projects/SUN/JOGL/git-svn/svn-server-sync/jogl/trunk@180 232f8b59-042b-4e1e-8c03-345bb8c30851

1 files changed, 1781 insertions, 0 deletions

diff --git a/src/net/java/games/jogl/impl/nurbs/internals/Subdivider.java b/src/net/java/games/jogl/impl/nurbs/internals/Subdivider.java
new file mode 100755
index 000000000..155b6b7ac
--- /dev/null
+++ b/src/net/java/games/jogl/impl/nurbs/internals/Subdivider.java
@@ -0,0 +1,1781 @@
+/*
+** License Applicability. Except to the extent portions of this file are
+** made subject to an alternative license as permitted in the SGI Free
+** Software License B, Version 1.1 (the "License"), the contents of this
+** file are subject only to the provisions of the License. You may not use
+** this file except in compliance with the License. You may obtain a copy
+** of the License at Silicon Graphics, Inc., attn: Legal Services, 1600
+** Amphitheatre Parkway, Mountain View, CA 94043-1351, or at:
+**
+** http://oss.sgi.com/projects/FreeB
+**
+** Note that, as provided in the License, the Software is distributed on an
+** "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS
+** DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND
+** CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A
+** PARTICULAR PURPOSE, AND NON-INFRINGEMENT.
+**
+** Original Code. The Original Code is: OpenGL Sample Implementation,
+** Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
+** Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
+** Copyright in any portions created by third parties is as indicated
+** elsewhere herein. All Rights Reserved.
+**
+** Additional Notice Provisions: The application programming interfaces
+** established by SGI in conjunction with the Original Code are The
+** OpenGL(R) Graphics System: A Specification (Version 1.2.1), released
+** April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version
+** 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X
+** Window System(R) (Version 1.3), released October 19, 1998. This software
+** was created using the OpenGL(R) version 1.2.1 Sample Implementation
+** published by SGI, but has not been independently verified as being
+** compliant with the OpenGL(R) version 1.2.1 Specification.
+*/
+
+public class Subdivider {
+
+  /**
+   * Constructs a subdivider.
+   */
+  public Subdivider(RenderHints hints, Backend b) {
+    renderhints = hints;
+    arctessellator = new ArcTesselator();
+    backend = b;
+    slicer = new Slicer(b);
+  }
+
+  /**
+   * Resets all state after possible error condition.
+   */
+  public void clear() {
+    // FIXME: looks like nothing to do given that we have no object pools
+  }
+  public void beginTrims() {}
+  public void beginLoop() {
+    pjarc = 0;
+  }
+
+  /**
+   * Adds a bezier arc to a trim loop and to a bin.
+   */
+  public void addArc(float[] cpts, Quilt quilt, long _nuid) {
+    BezierArc bezierArc = new BezierArc();
+    Arc jarc = new Arc(Arc.SIDE_NONE, _nuid);
+    jarc.bezierArc = bezierArc;
+    bezierArc.order = quilt.qspec.order;
+    bezierArc.stride = quilt.qspec.stride;
+    bezierArc.mapdesc = quilt.mapdesc;
+    bezierArc.cpts = cpts;
+    initialbin.addarc( jarc );
+    pjarc = jarc.append( pjarc );
+  }
+
+  /**
+   * Adds a pwl arc to a trim loop and to a bin.
+   */
+  public void addArc(int npts, TrimVertex[] pts, long _nuid) {
+    Arc jarc = new Arc( Arc.SIDE_NONE, _nuid );
+    jarc.pwlArc = new PwlArc( npts, pts );        
+    initialbin.addarc( jarc  );
+    pjarc = jarc.append( pjarc );
+  }
+  public void endLoop() {}
+  public void endTrims() {}
+
+  public void beginQuilts() {
+    qlist = null;
+  }
+  public void addQuilt( Quilt quilt ) {
+    quilt.next = qlist;
+    qlist = quilt;
+  }
+  public void endQuilts() {}
+
+  /**
+   * Main curve rendering entry point
+   */
+  public void drawCurves() {
+    float[] from = new float[1];
+    float[] to   = new float[1];
+    Flist bpts = new Flist();
+    qlist.getRange( from, to, bpts );
+
+    renderhints.init( );
+
+    backend.bgncurv();
+    float[] pta = new float[0];
+    float[] ptb = new float[1];
+    for( int i=bpts.start; i<bpts.end-1; i++ ) {
+      pta[0] = bpts.pts[i];
+      ptb[0] = bpts.pts[i+1];
+
+      qlist.downloadAll( pta, ptb, backend );
+
+      Curvelist curvelist = new Curvelist( qlist, pta, ptb );
+      samplingSplit( curvelist, renderhints.maxsubdivisions );
+    }
+    backend.endcurv();
+  }
+  public void drawSurfaces(long nuid) {
+    renderhints.init( );
+
+    if (qlist == null) {
+      //initialbin could be nonempty due to some errors
+      freejarcs(initialbin);
+      return;
+    }
+
+    for( Quilt q = qlist; q != null; q = q.next ) {
+      if( q.isCulled( ) == Defines.CULL_TRIVIAL_REJECT ) {
+        freejarcs( initialbin );
+        return;
+      }
+    }
+
+
+    float[] from = new float[2];
+    float[] to   = new float[2];
+    qlist.getRange( from, to, spbrkpts, tpbrkpts );
+    //perform optimization only when the samplng method is 
+    //DOMAIN_DISTANCE and the display methdo is either 
+    //fill or outline_polygon.
+    bool optimize = (is_domain_distance_sampling && (renderhints.display_method != N_OUTLINE_PATCH));
+
+    if( ! initialbin.isnonempty() ) {
+      if(! optimize )
+        {  
+          makeBorderTrim( from, to );
+        }
+    } else {
+      float[] rate = new float[2];
+      qlist.findRates( spbrkpts, tpbrkpts, rate );
+
+      if( decompose( initialbin, Math.min(rate[0], rate[1]) ) ) 
+        throw new NurbsException( 31 );
+    }
+
+    backend.bgnsurf( renderhints.wiretris, renderhints.wirequads, nuid );
+
+    if( (!initialbin.isnonempty())  && optimize )
+      {
+        int i,j;
+        int num_u_steps;
+        int num_v_steps;
+        for(i=spbrkpts.start; i<spbrkpts.end-1; i++){
+          for(j=tpbrkpts.start; j<tpbrkpts.end-1; j++){
+            float[] pta = new float[2];
+            float[] ptb = new float[2];
+            pta[0] = spbrkpts.pts[i];
+            ptb[0] = spbrkpts.pts[i+1];
+            pta[1] = tpbrkpts.pts[j];
+            ptb[1] = tpbrkpts.pts[j+1];
+            qlist.downloadAll(pta, ptb, backend);
+     
+            num_u_steps = (int) (domain_distance_u_rate * (ptb[0]-pta[0]));
+            num_v_steps = (int) (domain_distance_v_rate * (ptb[1]-pta[1]));
+
+            if(num_u_steps <= 0) num_u_steps = 1;
+            if(num_v_steps <= 0) num_v_steps = 1;
+
+            backend.surfgrid(pta[0], ptb[0], num_u_steps, 
+                             ptb[1], pta[1], num_v_steps);
+            backend.surfmesh(0,0,num_u_steps,num_v_steps);
+
+            continue;
+          }
+        }
+      }
+    else
+      subdivideInS( initialbin );
+
+    backend.endsurf();
+  }
+
+  public int ccwTurn_sl(Arc j1, Arc j2 ) {
+    int v1i             = j1.pwlArc.npts-1;
+    int v1lasti         = 0;
+    int v2i             = 0;
+    int v2lasti         = j2.pwlArc.npts-1;
+    int v1nexti         = v1i-1;
+    int v2nexti         = v2i+1;
+    TrimVertex v1       = j1.pwlArc.pts[v1i];
+    TrimVertex v1last   = j1.pwlArc.pts[v1lasti];
+    TrimVertex v2       = j2.pwlArc.pts[v2i];
+    TrimVertex v2last   = j2.pwlArc.pts[v2lasti];
+    TrimVertex v1next   = j1.pwlArc.pts[v1nexti];
+    TrimVertex v2next   = j2.pwlArc.pts[v2nexti];
+    int sgn;
+
+    assert( v1 != v1last );
+    assert( v2 != v2last );
+
+    // the arcs lie on the line (0 == v1.param[0])
+    if( v1.param[0] == v1next.param[0] && v2.param[0] == v2next.param[0] )
+      return 0;
+
+    if( v2next.param[0] > v2.param[0] || v1next.param[0] > v1.param[0] ) 
+      throw new NurbsException(28);
+
+    if( v1.param[1] < v2.param[1] )
+      return 1;
+    else if( v1.param[1] > v2.param[1] )
+      return 0;
+
+    while( true ) {
+      if( v1next.param[0] > v2next.param[0] ) {
+        assert( v1.param[0] >= v1next.param[0] );
+        assert( v2.param[0] >= v1next.param[0] );
+        switch( bbox( v2next, v2, v1next, 1 ) ) {
+        case -1:
+          return 1;
+        case 0:
+          sgn = ccw( v1next, v2, v2next );
+          if( sgn != -1 ) 
+            return sgn;
+          else {
+            v1i = v1nexti--;
+            v1 = j1.pwlArc.pts[v1i];
+            v1next = j1.pwlArc.pts[v1nexti];
+            if( v1 == v1last ) {
+              return 0; // ill-conditioned, guess answer
+            }
+          }
+          break;
+        case 1:
+          return 0;
+        }
+      } else if( v1next.param[0] < v2next.param[0] ) {
+        assert( v1.param[0] >= v2next.param[0] );
+        assert( v2.param[0] >= v2next.param[0] );
+        switch( bbox( v1next, v1, v2next, 1 ) ) {
+        case -1:
+          return 0;
+        case 0:
+          sgn = ccw( v1next, v1, v2next );
+          if( sgn != -1 ) 
+            return sgn;
+          else {
+            v2i = v2nexti++;
+            v2 = j2.pwlArc.pts[v2i];
+            v2next = j2.pwlArc.pts[v2nexti];
+            if( v2 == v2last ) {
+              return 0; // ill-conditioned, guess answer
+            }
+          }
+          break;
+        case 1:
+          return 1;
+        }
+      } else {
+        if( v1next.param[1] < v2next.param[1] )
+          return 1;
+        else if( v1next.param[1] > v2next.param[1] )
+          return 0;
+        else {
+          v2i = v2nexti++;
+          v2 = j2.pwlArc.pts[v2i];
+          v2next = j2.pwlArc.pts[v2nexti];
+          if( v2 == v2last ) {
+            return 0; // ill-conditioned, guess answer
+          }
+        }
+      }
+    }
+  }
+
+  public int ccwTurn_sr(Arc j1, Arc j2 ) {
+    // dir = 1
+    int v1i             = j1.pwlArc.npts-1;
+    int v1lasti         = 0;
+    int v2i             = 0;
+    int v2lasti         = j2.pwlArc.npts-1;
+    int v1nexti         = v1i-1;
+    int v2nexti         = v2i+1;
+    TrimVertex v1       = j1.pwlArc.pts[v1i];
+    TrimVertex v1last   = j1.pwlArc.pts[v1lasti];
+    TrimVertex v2       = j2.pwlArc.pts[v2i];
+    TrimVertex v2last   = j2.pwlArc.pts[v2lasti];
+    TrimVertex v1next   = j1.pwlArc.pts[v1nexti];
+    TrimVertex v2next   = j2.pwlArc.pts[v2nexti];
+    int sgn;
+
+    assert( v1 != v1last );
+    assert( v2 != v2last );
+
+    // the arcs lie on the line (0 == v1.param[0])
+    if( v1.param[0] == v1next.param[0] && v2.param[0] == v2next.param[0] )
+      return 0;
+
+    if( v2next.param[0] < v2.param[0] || v1next.param[0] < v1.param[0] )
+      throw new NurbsException(28);
+
+    if( v1.param[1] < v2.param[1] )
+      return 0;
+    else if( v1.param[1] > v2.param[1] )
+      return 1;
+
+    while( true ) {
+      if( v1next.param[0] < v2next.param[0] ) {
+        assert( v1.param[0] <= v1next.param[0] );
+        assert( v2.param[0] <= v1next.param[0] );
+        switch( bbox( v2, v2next, v1next, 1 ) ) {
+        case -1:
+          return 0;
+        case 0:
+          sgn = ccw( v1next, v2, v2next );
+          if( sgn != -1 ) {
+            return sgn;
+          } else {
+            v1i = v1nexti--;
+            v1 = j1.pwlArc.pts[v1i];
+            v1next = j1.pwlArc.pts[v1nexti];
+            if( v1 == v1last ) {
+              return 0; // ill-conditioned, guess answer
+            }
+          }
+          break;
+        case 1:
+          return 1;
+        }
+      } else if( v1next.param[0] > v2next.param[0] ) {
+        assert( v1.param[0] <= v2next.param[0] );
+        assert( v2.param[0] <= v2next.param[0] );
+        switch( bbox( v1, v1next, v2next, 1 ) ) {
+        case -1:
+          return 1;
+        case 0:
+          sgn = ccw( v1next, v1, v2next );
+          if( sgn != -1 ) { 
+            return sgn;
+          } else {
+            v2i = v2nexti++;
+            v2 = j2.pwlArc.pts[v2i];
+            v2next = j2.pwlArc.pts[v2nexti];
+            if( v2 == v2last ) {
+              return 0; // ill-conditioned, guess answer
+            }
+          }
+          break;
+        case 1:
+          return 0;
+        }
+      } else {
+        if( v1next.param[1] < v2next.param[1] )
+          return 0;
+        else if( v1next.param[1] > v2next.param[1] )
+          return 1;
+        else {
+          v2i = v2nexti++;
+          v2 = j2.pwlArc.pts[v2i];
+          v2next = j2.pwlArc.pts[v2nexti];
+          if( v2 == v2last ) {
+            return 0; // ill-conditioned, guess answer
+          }
+        }
+      }
+    }
+  }
+
+  public int ccwTurn_tl(Arc j1, Arc j2 ) {
+    int v1i             = j1.pwlArc.npts-1;
+    int v1lasti         = 0;
+    int v2i             = 0;
+    int v2lasti         = j2.pwlArc.npts-1;
+    int v1nexti         = v1i-1;
+    int v2nexti         = v2i+1;
+    TrimVertex v1       = j1.pwlArc.pts[v1i];
+    TrimVertex v1last   = j1.pwlArc.pts[v1lasti];
+    TrimVertex v2       = j2.pwlArc.pts[v2i];
+    TrimVertex v2last   = j2.pwlArc.pts[v2lasti];
+    TrimVertex v1next   = j1.pwlArc.pts[v1nexti];
+    TrimVertex v2next   = j2.pwlArc.pts[v2nexti];
+    int sgn;
+
+    assert( v1 != v1last );
+    assert( v2 != v2last );
+
+    // the arcs lie on the line (1 == v1.param[1])
+    if( v1.param[1] == v1next.param[1] && v2.param[1] == v2next.param[1] )
+      return 0;
+
+    if( v2next.param[1] > v2.param[1] || v1next.param[1] > v1.param[1] ) 
+      throw new NurbsException(28 );
+
+    if( v1.param[0] < v2.param[0] )
+      return 0;
+    else if( v1.param[0] > v2.param[0] )
+      return 1;
+
+    while( true ) {
+      if( v1next.param[1] > v2next.param[1] ) {
+        assert( v1.param[1] >= v1next.param[1] );
+        assert( v2.param[1] >= v1next.param[1] );
+        switch( bbox( v2next, v2, v1next, 0 ) ) {
+        case -1:
+          return 0;
+        case 0:
+          sgn = ccw( v1next, v2, v2next );
+          if( sgn != -1 ) 
+            return sgn;
+          else {
+            v1i = v1nexti--;
+            v1 = j1.pwlArc.pts[v1i];
+            v1next = j1.pwlArc.pts[v1nexti];
+            if( v1 == v1last ) {
+              return 0; // ill-conditioned, guess answer
+            }
+          }
+          break;
+        case 1:
+          return 1;
+        }
+      } else if( v1next.param[1] < v2next.param[1] ) {
+        switch( bbox( v1next, v1, v2next, 0 ) ) {
+        case -1:
+          return 1;
+        case 0:
+          sgn = ccw( v1next, v1, v2next );
+          if( sgn != -1 ) 
+            return sgn;
+          else {
+            v2i = v2nexti++;
+            v2 = j2.pwlArc.pts[v2i];
+            v2next = j2.pwlArc.pts[v2nexti];
+            if( v2 == v2last ) {
+              return 0; // ill-conditioned, guess answer
+            }
+          }
+          break;
+        case 1:
+          return 0;
+        }
+      } else {
+        if( v1next.param[0] < v2next.param[0] )
+          return 0;
+        else if( v1next.param[0] > v2next.param[0] )
+          return 1;
+        else {
+          v2i = v2nexti++;
+          v2 = j2.pwlArc.pts[v2i];
+          v2next = j2.pwlArc.pts[v2nexti];
+          if( v2 == v2last ) {
+            return 0; // ill-conditioned, guess answer
+          }
+        }
+      }
+    }
+  }
+
+  public int ccwTurn_tr(Arc j1, Arc j2) {
+    int v1i             = j1.pwlArc.npts-1;
+    int v1lasti         = 0;
+    int v2i             = 0;
+    int v2lasti         = j2.pwlArc.npts-1;
+    int v1nexti         = v1i-1;
+    int v2nexti         = v2i+1;
+    TrimVertex v1       = j1.pwlArc.pts[v1i];
+    TrimVertex v1last   = j1.pwlArc.pts[v1lasti];
+    TrimVertex v2       = j2.pwlArc.pts[v2i];
+    TrimVertex v2last   = j2.pwlArc.pts[v2lasti];
+    TrimVertex v1next   = j1.pwlArc.pts[v1nexti];
+    TrimVertex v2next   = j2.pwlArc.pts[v2nexti];
+    int sgn;
+
+    assert( v1 != v1last );
+    assert( v2 != v2last );
+
+    // the arcs lie on the line (1 == v1.param[1])
+    if( v1.param[1] == v1next.param[1] && v2.param[1] == v2next.param[1] )
+      return 0;
+
+    if( v2next.param[1] < v2.param[1] || v1next.param[1] < v1.param[1] )
+      throw new NurbsException( 28 );
+
+    if( v1.param[0] < v2.param[0] )
+      return 1;
+    else if( v1.param[0] > v2.param[0] )
+      return 0;
+
+    while( 1 ) {
+      if( v1next.param[1] < v2next.param[1] ) {
+        assert( v1.param[1] <= v1next.param[1] );
+        assert( v2.param[1] <= v1next.param[1] );
+        switch( bbox( v2, v2next, v1next, 0 ) ) {
+        case -1:
+          return 1;
+        case 0:
+          sgn = ccw( v1next, v2, v2next );
+          if( sgn != -1 ) {
+            return sgn;
+          } else {
+            v1i = v1nexti--;
+            v1 = j1.pwlArc.pts[v1i];
+            v1next = j1.pwlArc.pts[v1nexti];
+            if( v1 == v1last ) {
+              return 0; // ill-conditioned, guess answer
+            }
+          }
+          break;
+        case 1:
+          return 0;
+        }
+      } else if( v1next.param[1] > v2next.param[1] ) {
+        assert( v1.param[1] <= v2next.param[1] );
+        assert( v2.param[1] <= v2next.param[1] );
+        switch( bbox( v1, v1next, v2next, 0 ) ) {
+        case -1:
+          return 0;
+        case 0:
+          sgn = ccw( v1next, v1, v2next );
+          if( sgn != -1 ) { 
+            return sgn;
+          } else {
+            v2i = v2nexti++;
+            v2 = j2.pwlArc.pts[v2i];
+            v2next = j2.pwlArc.pts[v2nexti];
+            if( v2 == v2last ) {
+              return 0; // ill-conditioned, guess answer
+            }
+          }
+          break;
+        case 1:
+          return 1;
+        }
+      } else {
+        if( v1next.param[0] < v2next.param[0] )
+          return 1;
+        else if( v1next.param[0] > v2next.param[0] )
+          return 0;
+        else {
+          v2i = v2nexti++;
+          v2 = j2.pwlArc.pts[v2i];
+          v2next = j2.pwlArc.pts[v2nexti];
+          if( v2 == v2last ) {
+            return 0; // ill-conditioned, guess answer
+          }
+        }
+      }
+    }
+  }
+
+  public void set_domain_distance_u_rate(float u_rate) {
+    domain_distance_u_rate = u_rate;
+  }
+
+  public void set_domain_distance_v_rate(float v_rate) {
+    domain_distance_v_rate = v_rate;
+  }
+
+  public void set_is_domain_distance_sampling(int flag) {
+    is_domain_distance_sampling = flag;
+  }
+
+  //----------------------------------------------------------------------
+  // Internals only below this point
+  //
+
+  /**
+   * Determine which side of a line a jarc lies (for debugging only)
+   */
+  private int arc_classify( Arc jarc, int param, float value )
+  {
+    float tdiff, hdiff;
+    if( param == 0 ) {
+      tdiff = jarc.tail()[0] - value;
+      hdiff = jarc.head()[0] - value;
+    } else {
+      tdiff = jarc.tail()[1] - value;
+      hdiff = jarc.head()[1] - value;
+    }
+
+    if( tdiff > 0.0 ) {
+      if( hdiff > 0.0 ) {
+        return 0x11;
+      } else if( hdiff == 0.0 ) {
+        return 0x12;
+      } else {
+        return 0x10;
+      }
+    } else if( tdiff == 0.0 ) {
+      if( hdiff > 0.0 ) {
+        return 0x21;
+      } else if( hdiff == 0.0 ) {
+        return 0x22;
+      } else {
+        return 0x20;
+      }
+    } else {
+      if( hdiff > 0.0 ) {
+        return 0x01;
+      } else if( hdiff == 0.0 ) {
+        return 0x02;
+      } else {
+        return 0;
+      }
+    }
+  }
+
+  private void classify_headonleft_s( Bin bin, Bin in, Bin out, float val ) {
+    /* tail on line, head at left */
+    Arc j;
+
+    while( (j = bin.removearc()) != null ) {
+      assert( arc_classify( j, 0, val ) == 0x20 );
+
+      j.setitail();
+
+      float diff = j.prev.tail()[0] - val;
+      if( diff > 0.0 ) {
+        out.addarc( j );
+      } else if( diff < 0.0 ) {
+        if( ccwTurn_sl( j.prev, j ) != 0 )
+          out.addarc( j );
+        else
+          in.addarc( j );
+      } else {
+        if( j.prev.tail()[1] > j.prev.head()[1] )
+          in.addarc( j );
+        else
+          out.addarc( j );
+      }
+    }
+  }
+
+  private void classify_tailonleft_s( Bin bin, Bin in, Bin out, float val ) {
+    /* tail at left, head on line */
+    Arc j;
+
+    while( (j = bin.removearc()) != null ) {
+      assert( arc_classify( j, 1, val ) == 0x02 );
+      j.clearitail();
+
+      float diff = j.next.head()[1] - val;
+      if( diff > 0.0 ) {
+        in.addarc( j );
+      } else if( diff < 0.0 ) {
+        if( ccwTurn_tl( j, j.next ) != 0 )
+          out.addarc( j );
+        else
+          in.addarc( j );
+      } else {
+        if (j.next.tail()[0] > j.next.head()[0] )
+          out.addarc( j );
+        else
+          in.addarc( j );
+      }
+    }
+  }
+
+  private void classify_headonright_s( Bin bin, Bin in, Bin out, float val ) {
+    /* tail on line, head at right */
+    Arc j;
+
+    while( (j = bin.removearc()) != null ) {
+      assert( arc_classify( j, 0, val ) == 0x21 );
+    
+      j.setitail();
+
+      float diff = j.prev.tail()[0] - val;
+      if( diff > 0.0 ) { 
+        if( ccwTurn_sr( j.prev, j ) != 0 )
+          out.addarc( j );
+        else
+          in.addarc( j );
+      } else if( diff < 0.0 ) {
+        out.addarc( j );
+      } else {
+        if( j.prev.tail()[1] > j.prev.head()[1] )
+          out.addarc( j );
+        else
+          in.addarc( j );
+      }
+    }
+  }
+
+  private void classify_tailonright_s( Bin bin, Bin in, Bin out, float val ) {
+    /* tail at right, head on line */
+    Arc j;
+
+    while( (j = bin.removearc()) != null ) {
+      assert( arc_classify( j, 0, val ) == 0x12);
+	
+      j.clearitail();
+
+      float diff = j.next.head()[0] - val;
+      if( diff > 0.0 ) {
+        if( ccwTurn_sr( j, j.next ) != 0 )
+          out.addarc( j );
+        else
+          in.addarc( j );
+      } else if( diff < 0.0 ) {
+        in.addarc( j );
+      } else {
+        if( j.next.tail()[1] > j.next.head()[1] ) 
+          out.addarc( j );
+        else
+          in.addarc( j );
+      }
+    }
+  }
+
+  private void classify_headonleft_t( Bin bin, Bin in, Bin out, float val ) {
+    /* tail on line, head at left */
+    Arc j;
+
+    while( (j = bin.removearc()) != null ) {
+      assert( arc_classify( j, 1, val ) == 0x20 );
+      j.setitail();
+
+      float diff = j.prev.tail()[1] - val;
+      if( diff > 0.0 ) {
+        out.addarc( j );
+      } else if( diff < 0.0 ) {
+        if( ccwTurn_tl( j.prev, j ) != 0 )
+          out.addarc( j );
+        else
+          in.addarc( j );
+      } else {
+        if( j.prev.tail()[0] > j.prev.head()[0] )
+          out.addarc( j );
+        else
+          in.addarc( j );
+      }
+    }
+  }
+
+  private void classify_tailonleft_t( Bin bin, Bin in, Bin out, float val ) {
+    /* tail at left, head on line */
+    Arc j;
+
+    while( (j = bin.removearc()) != null ) {
+      assert( arc_classify( j, 1, val ) == 0x02 );
+      j.clearitail();
+
+      float diff = j.next.head()[1] - val;
+      if( diff > 0.0 ) {
+        in.addarc( j );
+      } else if( diff < 0.0 ) {
+        if( ccwTurn_tl( j, j.next ) != 0 )
+          out.addarc( j );
+        else
+          in.addarc( j );
+      } else {
+        if (j.next.tail()[0] > j.next.head()[0] )
+          out.addarc( j );
+        else
+          in.addarc( j );
+      }
+    }
+  }
+
+  private void classify_headonright_t( Bin bin, Bin in, Bin out, float val ) {
+    /* tail on line, head at right */
+    Arc j;
+
+    while( (j = bin.removearc()) != null ) {
+      assert( arc_classify( j, 1, val ) == 0x21 );
+    
+      j.setitail();
+
+      float diff = j.prev.tail()[1] - val;
+      if( diff > 0.0 ) { 
+        if( ccwTurn_tr( j.prev, j ) != 0 )
+          out.addarc( j );
+        else
+          in.addarc( j );
+      } else if( diff < 0.0 ) {
+        out.addarc( j );
+      } else {
+        if( j.prev.tail()[0] > j.prev.head()[0] )
+          in.addarc( j );
+        else
+          out.addarc( j );
+      }
+    }
+  }
+
+  private void classify_tailonright_t( Bin bin, Bin in, Bin out, float val ) {
+    /* tail at right, head on line */
+    Arc j;
+
+    while( (j = bin.removearc()) != null ) {
+      assert( arc_classify( j, 1, val ) == 0x12);
+	
+      j.clearitail();
+
+      float diff =  j.next.head()[1] - val;
+      if( diff > 0.0 ) {
+        if( ccwTurn_tr( j, j.next ) != 0 )
+          out.addarc( j );
+        else
+          in.addarc( j );
+      } else if( diff < 0.0 ) { 
+        in.addarc( j );
+      } else {
+        if( j.next.tail()[0] > j.next.head()[0] ) 
+          in.addarc( j );
+        else
+          out.addarc( j );
+      }
+    }
+  }
+
+  private int DIR_DOWN = 0;
+  private int DIR_SAME = 1;
+  private int DIR_UP   = 2;
+  private int DIR_NONE = 3;
+
+  private void tessellate( Arc_ptr, float );
+  private void monotonize( Arc_ptr , Bin & );
+  private int isMonotone( Arc_ptr  );
+  private int decompose( Bin &, float );
+
+
+  private Slicer slicer;
+  private ArcTessellator arctessellator;
+  //  private Pool arcpool;
+  //  private Pool bezierarcpool;
+  //  private Pool pwlarcpool;
+  //  private TrimVertexPool trimvertexpool;
+
+  private JumpBuffer* jumpbuffer;
+  private Renderhints& renderhints;
+  private Backend&  backend;
+
+  private Bin initialbin;
+  private Arc pjarc;
+  private int s_index;
+  private int t_index;
+  private Quilt *qlist;
+  private Flist spbrkpts;
+  private Flist tpbrkpts;
+  private Flist smbrkpts;
+  private Flist tmbrkpts;
+  private float stepsizes[4];
+  private int showDegenerate;
+  private int isArcTypeBezier;
+
+  // FIXME: NOT FINISHED
+  private void samplingSplit( Curvelist&, int );
+
+  private void subdivideInS( Bin source ) {
+    if( renderhints.display_method == N_OUTLINE_PARAM ) {
+      outline( source );
+      freejarcs( source );
+    } else {
+      setArcTypeBezier();
+      setNonDegenerate();
+      splitInS( source, spbrkpts.start, spbrkpts.end );
+    }
+  }
+
+  /**
+   * Splits a patch and a bin by an isoparametric line.
+   */
+  private void splitInS( Bin source, int start, int end ) {
+    if( source.isnonempty() ) {
+      if( start != end ) {
+        int  i = start + (end - start) / 2;
+        Bin left = new Bin();
+        Bin right = new Bin();
+        split( source, left, right, 0, spbrkpts.pts[i] );
+        splitInS( left, start, i );
+        splitInS( right, i+1, end );
+      } else {
+        if( start == spbrkpts.start || start == spbrkpts.end ) {
+          freejarcs( source );
+        } else if( renderhints.display_method == NurbsConsts.N_OUTLINE_PARAM_S ) {
+          outline( source );
+          freejarcs( source );
+        } else {
+          setArcTypeBezier();
+          setNonDegenerate();
+          s_index = start;
+          splitInT( source, tpbrkpts.start, tpbrkpts.end );
+        }
+      }
+    } 
+  }
+
+  /**
+   * Splits a patch and a bin by an isoparametric line.
+   */
+  private void splitInT( Bin source, int start, int end ) {
+    if( source.isnonempty() ) {
+      if( start != end ) {
+        int  i = start + (end - start) / 2;
+        Bin left = new Bin();
+        Bin right = new Bin();
+        split( source, left, right, 1, tpbrkpts.pts[i] );
+        splitInT( left, start, i );
+        splitInT( right, i+1, end );
+      } else {
+        if( start == tpbrkpts.start || start == tpbrkpts.end ) {
+          freejarcs( source );
+        } else if( renderhints.display_method == NurbsConsts.N_OUTLINE_PARAM_ST ) {
+          outline( source );
+          freejarcs( source );
+        } else {
+          t_index = start;
+          setArcTypeBezier();
+          setDegenerate();
+
+          float[] pta = new float[2];
+          float[] ptb = new float[2];
+          pta[0] = spbrkpts.pts[s_index-1];
+          pta[1] = tpbrkpts.pts[t_index-1];
+
+          ptb[0] = spbrkpts.pts[s_index];
+          ptb[1] = tpbrkpts.pts[t_index];
+          qlist.downloadAll( pta, ptb, backend );
+      
+          Patchlist patchlist = new Patchlist( qlist, pta, ptb );
+          /*
+            printf("-------samplingSplit-----\n");
+            source.show("samplingSplit source");
+          */
+          samplingSplit( source, patchlist, renderhints.maxsubdivisions, 0 );
+          setNonDegenerate();
+          setArcTypeBezier();
+        }
+      }
+    } 
+  }
+
+  /**
+   * Recursively subdivides patch, cull checks each subpatch  
+   */
+  private void samplingSplit( Bin source, Patchlist patchlist, int subdivisions, int param ) {
+    if( ! source.isnonempty() ) return;
+
+    if( patchlist.cullCheck() == Defines.CULL_TRIVIAL_REJECT ) {
+      freejarcs( source );
+      return;
+    }
+
+    patchlist.getstepsize();
+
+    if( renderhints.display_method == NurbsConsts.N_OUTLINE_PATCH ) {
+      tessellation( source, patchlist );
+      outline( source );
+      freejarcs( source );
+      return;
+    } 
+
+    //patchlist.clamp();
+
+    tessellation( source, patchlist );
+
+    if( patchlist.needsSamplingSubdivision() && (subdivisions > 0) ) {
+      if( ! patchlist.needsSubdivision( 0 ) )
+        param = 1;
+      else if( ! patchlist.needsSubdivision( 1 ) )
+        param = 0;
+      else
+        param = 1 - param;
+
+      Bin left = new Bin();
+      Bin right = new Bin();
+      float mid = ( patchlist.pspec[param].range[0] +
+                   patchlist.pspec[param].range[1] ) * 0.5;
+      split( source, left, right, param, mid );
+      Patchlist subpatchlist = new Patchlist( patchlist, param, mid );
+      samplingSplit( left, subpatchlist, subdivisions-1, param );
+      samplingSplit( right, patchlist, subdivisions-1, param );
+    } else {
+      setArcTypePwl();
+      setDegenerate();
+      nonSamplingSplit( source, patchlist, subdivisions, param );
+      setDegenerate();
+      setArcTypeBezier();
+    }
+  }
+
+  private void nonSamplingSplit( Bin source, Patchlist patchlist, int subdivisions, int param ) {
+    if( patchlist.needsNonSamplingSubdivision() && (subdivisions > 0) ) {
+      param = 1 - param;
+
+      Bin left = new Bin();
+      Bin right = new Bin();
+      float mid = ( patchlist.pspec[param].range[0] +
+                   patchlist.pspec[param].range[1] ) * 0.5;
+      split( source, left, right, param, mid );
+      Patchlist subpatchlist = new Patchlist( patchlist, param, mid );
+      if( left.isnonempty() )
+        if( subpatchlist.cullCheck() == Defines.CULL_TRIVIAL_REJECT ) 
+          freejarcs( left );
+        else
+          nonSamplingSplit( left, subpatchlist, subdivisions-1, param );
+      if( right.isnonempty() ) 
+        if( patchlist.cullCheck() == Defines.CULL_TRIVIAL_REJECT ) 
+          freejarcs( right );
+        else
+          nonSamplingSplit( right, patchlist, subdivisions-1, param );
+
+    } else {
+      // make bbox calls
+      patchlist.bbox();
+      backend.patch( patchlist.pspec[0].range[0], patchlist.pspec[0].range[1],
+                     patchlist.pspec[1].range[0], patchlist.pspec[1].range[1] );
+    
+      if( renderhints.display_method == NurbsConsts.N_OUTLINE_SUBDIV ) {
+        outline( source );
+        freejarcs( source );
+      } else {
+        setArcTypePwl();
+        setDegenerate();
+        findIrregularS( source );
+        monosplitInS( source, smbrkpts.start, smbrkpts.end );
+      }
+    }
+  }
+
+  /**
+   * Sets tessellation of interior and boundary of patch.
+   */
+  private void tessellation( Bin bin, Patchlist patchlist ) {
+    // tessellate unsampled trim curves
+    tessellate( bin, patchlist.pspec[1].sidestep[1], patchlist.pspec[0].sidestep[1],
+                patchlist.pspec[1].sidestep[0], patchlist.pspec[0].sidestep[0] );
+
+    // set interior sampling rates
+    slicer.setstriptessellation( patchlist.pspec[0].stepsize, patchlist.pspec[1].stepsize );
+
+    //added by zl: set the order which will be used in slicer.c++
+    slicer.set_ulinear( (patchlist.get_uorder() == 2));
+    slicer.set_vlinear( (patchlist.get_vorder() == 2));
+
+    // set boundary sampling rates
+    stepsizes[0] = patchlist.pspec[1].stepsize;
+    stepsizes[1] = patchlist.pspec[0].stepsize;
+    stepsizes[2] = patchlist.pspec[1].stepsize;
+    stepsizes[3] = patchlist.pspec[0].stepsize;
+  }
+
+  /**
+   * Splits a patch and a bin by an isoparametric line.
+   */
+  private void monosplitInS( Bin source, int start, int end ) {
+    if( source.isnonempty() ) {
+      if( start != end ) {
+        int  i = start + (end - start) / 2;
+        Bin left = new Bin();
+        Bin right = new Bin();
+        split( source, left, right, 0, smbrkpts.pts[i] );
+        monosplitInS( left, start, i );
+        monosplitInS( right, i+1, end );
+      } else {
+        if( renderhints.display_method == NurbsConsts.N_OUTLINE_SUBDIV_S ) {
+          outline( source );
+          freejarcs( source );
+        } else {
+          setArcTypePwl();
+          setDegenerate();
+          findIrregularT( source );
+          monosplitInT( source, tmbrkpts.start, tmbrkpts.end );
+        }
+      }
+    } 
+  }
+
+  /**
+   * Splits a patch and a bin by an isoparametric line.
+   */
+  private void monosplitInT( Bin source, int start, int end ) {
+    if( source.isnonempty() ) {
+      if( start != end ) {
+        int  i = start + (end - start) / 2;
+        Bin left = new Bin();
+        Bin right = new Bin();
+        split( source, left, right, 1, tmbrkpts.pts[i] );
+        monosplitInT( left, start, i );
+        monosplitInT( right, i+1, end );
+      } else {
+        if( renderhints.display_method == NurbsConsts.N_OUTLINE_SUBDIV_ST ) {
+          outline( source );
+          freejarcs( source );
+        } else {
+          /*
+            printf("*******render\n");
+            source.show("source\n");
+          */
+          render( source );
+          freejarcs( source );
+        }
+      }
+    } 
+  }
+
+  /**
+   * Renders the trimmed patch by outlining the boundary .
+   */
+  private void outline( Bin bin ) {
+    bin.markall();
+    for( Arc jarc=bin.firstarc(); jarc != null; jarc=bin.nextarc() ) {
+      if( jarc.ismarked() ) {
+        assert( jarc.check( ) );
+        Arc jarchead = jarc;
+        do {
+          slicer.outline( jarc );
+          jarc.clearmark();
+          jarc = jarc.prev;
+        } while (jarc != jarchead);
+      }
+    }
+  }
+
+  /**
+   * Frees all arcs in a bin.
+   */
+  private void freejarcs( Bin & ) {
+    bin.adopt();  /* XXX - should not be necessary */
+
+    Arc jarc;
+    while( (jarc = bin.removearc()) != null ) {
+      if( jarc.pwlArc != null ) jarc.pwlArc.deleteMe( ); jarc.pwlArc = null;
+      if( jarc.bezierArc != null) jarc.bezierArc.deleteMe( ); jarc.bezierArc = null;
+      jarc.deleteMe( );
+    }
+  }
+
+  /**
+   * Renders all monotone regions in a bin and frees the bin.
+   */
+  private void render( Bin bin ) {
+    bin.markall();
+
+    slicer.setisolines( ( renderhints.display_method == N_ISOLINE_S ) ? 1 : 0 );
+
+    for( Arc jarc=bin.firstarc(); jarc != null; jarc=bin.nextarc() ) {
+      if( jarc.ismarked() ) {
+        assert( jarc.check( ) != 0 );
+        Arc jarchead = jarc;
+        do {
+          jarc.clearmark();
+          jarc = jarc.next;
+        } while (jarc != jarchead);
+        slicer.slice( jarc );
+      }
+    }
+  }
+
+  private void split( Bin &, Bin &, Bin &, int, float );
+
+  /**
+   * Tessellates all Bezier arcs in a bin.
+   * <ol>
+   *   <li> only accepts linear Bezier arcs as input 
+   *   <li> the Bezier arcs are stored in the pwlArc structure
+   *   <li> only vertical or horizontal lines work
+   * </ol>
+   * should:
+   * <ol>
+   *   <li> represent Bezier arcs in BezierArc structure
+   *        (this requires a multitude of changes to the code)
+   *   <li> accept high degree Bezier arcs (hard)
+   *   <il> map the curve onto the surface to determine tessellation
+   *   <li> work for curves of arbitrary geometry
+   * </ol>
+   *----------------------------------------------------------------------------
+   */
+  private void tessellate( Bin bin, float rrate, float trate, float lrate, float brate ) {
+    for( Arc jarc=bin.firstarc(); jarc != null; jarc=bin.nextarc() ) {
+      if( jarc.isbezier( ) ) {
+        assert( jarc.pwlArc.npts == 2 );  
+        TrimVertex[] pts = jarc.pwlArc.pts;
+        float s1 = pts[0].param[0];
+        float t1 = pts[0].param[1];
+        float s2 = pts[1].param[0];
+        float t2 = pts[1].param[1];
+      
+        jarc.pwlArc.deleteMe( );
+        jarc.pwlArc = null;
+      
+        switch( jarc.getside() ) {
+        case Arc.SIDE_LEFT:
+          assert( s1 == s2 );
+          arctessellator.pwl_left( jarc, s1, t1, t2, lrate );
+          break;
+        case Arc.SIDE_RIGHT:
+          assert( s1 == s2 );
+          arctessellator.pwl_right( jarc, s1, t1, t2, rrate );
+          break;
+        case Arc.SIDE_TOP:
+          assert( t1 == t2 );
+          arctessellator.pwl_top( jarc, t1, s1, s2, trate );
+          break;
+        case Arc.SIDE_BOTTOM:
+          assert( t1 == t2 );
+          arctessellator.pwl_bottom( jarc, t1, s1, s2, brate );
+          break;
+        case Arc.SIDE_NONE:
+          throw new InternalError("Incorrect tesselation state");
+          break;
+        }
+        assert( ! jarc.isbezier() );
+        assert( jarc.check() != 0 );
+      }
+    }
+  }
+
+  private inline void setDegenerate( void ) { showDegenerate = 1; }
+  private inline void setNonDegenerate( void ) { showDegenerate = 0; }
+  private inline int showingDegenerate( void ) { return showDegenerate; }
+  private inline void setArcTypeBezier( void ) { isArcTypeBezier = 1; }
+  private inline void setArcTypePwl( void ) { isArcTypeBezier = 0; }
+  private inline int isBezierArcType( void ) { return isArcTypeBezier; }
+
+  /**
+   * If no user input trimming data, then create a trimming curve
+   * around the boundaries of the Quilt. The curve consists of four
+   * Jordan arcs, one for each side of the Quilt, connected, of
+   * course, head to tail.
+   */
+  private void makeBorderTrim( float[] from, float[] to ) {
+    float smin = from[0];
+    float smax = to[0];
+    float tmin = from[1];
+    float tmax = to[1];
+
+    pjarc = null;
+
+    Arc jarc = new Arc( Arc.SIDE_BOTTOM, 0 );
+    arctessellator.bezier( jarc, smin, smax, tmin, tmin );
+    initialbin.addarc( jarc  );
+    pjarc = jarc.append( pjarc );
+
+    jarc = new Arc( Arc.SIDE_RIGHT, 0 );
+    arctessellator.bezier( jarc, smax, smax, tmin, tmax );
+    initialbin.addarc( jarc  );
+    pjarc = jarc.append( pjarc );
+
+    jarc = new Arc( Arc.SIDE_TOP, 0 );
+    arctessellator.bezier( jarc, smax, smin, tmax, tmax );
+    initialbin.addarc( jarc  );
+    pjarc = jarc.append( pjarc );
+
+    jarc = new Arc( Arc.SIDE_LEFT, 0 );
+    arctessellator.bezier( jarc, smin, smin, tmax, tmin );
+    initialbin.addarc( jarc  );
+    jarc.append( pjarc );
+
+    assert( jarc.check() );
+  }
+
+  private void split( Bin &, int, const float *, int, int );
+  private void partition( Bin bin, Bin left, Bin intersections, Bin right, Bin unknown, int param, float value ) {
+    Bin  headonleft = new Bin();
+    Bin headonright = new Bin();
+    Bin tailonleft = new Bin();
+    Bin tailonright = new Bin();
+
+    for( Arc jarc = bin.removearc(); jarc != null; jarc = bin.removearc() ) {
+
+      float tdiff = jarc.tail()[param] - value;
+      float hdiff = jarc.head()[param] - value;
+
+      if( tdiff > 0.0 ) {
+        if( hdiff > 0.0 ) {
+          right.addarc( jarc  );
+        } else if( hdiff == 0.0 ) {
+          tailonright.addarc( jarc  );
+        } else {
+          Arc jtemp;
+          switch( arc_split(jarc, param, value, 0) ) {
+          case 2:
+            tailonright.addarc( jarc  );
+            headonleft.addarc( jarc.next  );
+            break;
+          case 31:
+            assert( jarc.head()[param] > value );
+            right.addarc( jarc  );
+            tailonright.addarc( jtemp = jarc.next  );
+            headonleft.addarc( jtemp.next  );
+            break;
+          case 32:
+            assert( jarc.head()[param] <= value );
+            tailonright .addarc( jarc  );
+            headonleft.addarc( jtemp = jarc.next  );
+            left.addarc( jtemp.next  );
+            break;
+          case 4:
+            right.addarc( jarc  );
+            tailonright.addarc( jtemp = jarc.next  );
+            headonleft.addarc( jtemp = jtemp.next  );
+            left.addarc( jtemp.next  );
+          }
+        }
+      } else if( tdiff == 0.0 ) {
+        if( hdiff > 0.0 ) {
+          headonright.addarc( jarc  );
+        } else if( hdiff == 0.0 ) {
+          unknown.addarc( jarc  );
+        } else {
+          headonleft.addarc( jarc  );
+        }
+      } else {
+        if( hdiff > 0.0 ) {
+          Arc jtemp;
+          switch( arc_split(jarc, param, value, 1) ) {
+          case 2:
+            tailonleft.addarc( jarc  );
+            headonright.addarc( jarc.next  );
+            break;
+          case 31:
+            assert( jarc.head()[param] < value );
+            left.addarc( jarc  );
+            tailonleft.addarc( jtemp = jarc.next  );
+            headonright.addarc( jtemp.next  );
+            break;
+          case 32:
+            assert( jarc.head()[param] >= value );
+            tailonleft.addarc( jarc  );
+            headonright.addarc( jtemp = jarc.next  );
+            right.addarc( jtemp.next  );
+            break;
+          case 4:
+            left.addarc( jarc  );
+            tailonleft.addarc( jtemp = jarc.next  );
+            headonright.addarc( jtemp = jtemp.next  );
+            right.addarc( jtemp.next  );
+          }
+        } else if( hdiff == 0.0 ) {
+          tailonleft.addarc( jarc  );
+        } else {
+          left.addarc( jarc  );
+        }
+      }
+    }
+    if( param == 0 ) {
+      classify_headonleft_s( headonleft, intersections, left, value );
+      classify_tailonleft_s( tailonleft, intersections, left, value );
+      classify_headonright_s( headonright, intersections, right, value );
+      classify_tailonright_s( tailonright, intersections, right, value );
+    } else {
+      classify_headonleft_t( headonleft, intersections, left, value );
+      classify_tailonleft_t( tailonleft, intersections, left, value );
+      classify_headonright_t( headonright, intersections, right, value );
+      classify_tailonright_t( tailonright, intersections, right, value );
+    }
+  }
+
+  /**
+   * Determine points of non-monotonicity in s direction.
+   */
+  private void findIrregularS( Bin bin ) {
+    assert( bin.firstarc() == null || bin.firstarc().check() );
+
+    smbrkpts.grow( bin.numarcs() );
+
+    for( Arc jarc=bin.firstarc(); jarc != null; jarc=bin.nextarc() ) {
+      float[] a = jarc.prev.tail();
+      float[] b = jarc.tail();
+      float[] c = jarc.head();
+
+      if( b[1] == a[1] && b[1] == c[1] ) continue;
+
+      //corrected code
+      if((b[1]<=a[1] && b[1] <= c[1]) ||
+         (b[1]>=a[1] && b[1] >= c[1]))
+        {
+          //each arc (jarc, jarc.prev, jarc.next) is a 
+          //monotone arc consisting of multiple line segements.
+          //it may happen that jarc.prev and jarc.next are the same,
+          //that is, jarc.prev and jarc form a closed loop.
+          //In such case, a and c will be the same.
+          if(a[0]==c[0] && a[1] == c[1])
+            {
+              if(jarc.pwlArc.npts >2)
+                {
+                  c = jarc.pwlArc.pts[jarc.pwlArc.npts-2].param;
+                }
+              else
+                {
+                  assert(jarc.prev.pwlArc.npts>2);
+                  a = jarc.prev.pwlArc.pts[jarc.prev.pwlArc.npts-2].param;
+                }
+        
+            }
+          if(area(a,b,c) < 0)
+            {
+              smbrkpts.add(b[0]);
+            }
+
+        }
+
+      /* old code, 
+         if( b[1] <= a[1] && b[1] <= c[1] ) {
+         if( ! ccwTurn_tr( jarc.prev, jarc ) )
+         smbrkpts.add( b[0] );
+         } else if( b[1] >= a[1] && b[1] >= c[1] ) {
+         if( ! ccwTurn_tl( jarc.prev, jarc ) )
+         smbrkpts.add( b[0] );
+         }
+      */
+
+    }
+
+    smbrkpts.filter();
+  }
+
+  /**
+   * Determines points of non-monotonicity in t direction where one
+   * arc is parallel to the s axis.
+   */
+  private void findIrregularT( Bin bin ) {
+    assert( bin.firstarc() == null || bin.firstarc().check() );
+
+    tmbrkpts.grow( bin.numarcs() );
+
+    for( Arc jarc=bin.firstarc(); jarc != null; jarc=bin.nextarc() ) {
+      float[] a = jarc.prev.tail();
+      float[] b = jarc.tail();
+      float[] c = jarc.head();
+
+      if( b[0] == a[0] && b[0] == c[0] ) continue;
+
+      if( b[0] <= a[0] && b[0] <= c[0] ) {
+        if( a[1] != b[1] && b[1] != c[1] ) continue; 
+        if( ccwTurn_sr( jarc.prev, jarc ) == 0)
+          tmbrkpts.add( b[1] );
+      } else if ( b[0] >= a[0] && b[0] >= c[0] ) {
+        if( a[1] != b[1] && b[1] != c[1] ) continue; 
+        if( ccwTurn_sl( jarc.prev, jarc ) == 0)
+          tmbrkpts.add( b[1] );
+      }
+    }
+    tmbrkpts.filter( );
+  }
+
+
+  private int bbox( TrimVertex a, TrimVertex b, TrimVertex c, int p ) {
+    return bbox( a.param[p], b.param[p], c.param[p],
+           a.param[1-p], b.param[1-p], c.param[1-p] );
+  }
+
+  private static int bbox( float sa, float sb, float sc, float ta, float tb, float tc ) {
+    assert( tc >= ta );
+    assert( tc <= tb );
+
+    if( sa < sb ) {
+      if( sc <= sa ) {
+        return -1;
+      } else if( sb <= sc ) {
+        return 1;
+      } else {
+        return 0;
+      }
+    } else if( sa > sb ) {
+      if( sc >= sa ) {
+        return 1;
+      } else if( sb >= sc ) {
+        return -1;
+      } else {
+        return 0;
+      }
+    } else {
+      if( sc > sa ) {
+        return 1;
+      } else if( sb > sc ) {
+        return -1;
+      } else {
+        return 0;
+      }
+    }
+  }
+  /**
+   * Determines how three points are oriented by computing their
+   * determinant.
+   *
+   * @return 1 if the vertices are ccw oriented, 0 if they are cw
+   * oriented, or -1 if the computation is ill-conditioned.
+   */
+  private static int ccw( TrimVertex a, TrimVertex b, TrimVertex c ) {
+    float d = TrimVertex.det3( a, b, c );
+    if( Math.abs(d) < 0.0001 ) return -1;
+    return (d < 0.0) ? 0 : 1;
+  }
+  private void join_s( Bin &, Bin &, Arc_ptr, Arc_ptr  );
+  private void join_t( Bin &, Bin &, Arc_ptr , Arc_ptr  );
+
+  private static void vert_interp( TrimVertex n, TrimVertex l, TrimVertex r, int p, float val ) {
+    assert( val > l.param[p]);
+    assert( val < r.param[p]);
+
+    n.nuid = l.nuid;
+
+    n.param[p] = val;
+    if( l.param[1-p] != r.param[1-p]  ) {
+      float ratio = (val - l.param[p]) / (r.param[p] - l.param[p]);
+      n.param[1-p] = l.param[1-p] + 
+        ratio * (r.param[1-p] - l.param[1-p]);
+    } else {
+      n.param[1-p] = l.param[1-p];
+    }
+  }
+
+  private static final int INTERSECT_VERTEX = 1;
+  private static final int INTERSECT_EDGE   = 2;
+
+  /**
+   * Finds intersection of pwlArc and isoparametric line.
+   */
+  private static int pwlarc_intersect( PwlArc pwlArc, int param, float value, int dir, int[] loc ) {
+    assert( pwlArc.npts > 0 );
+
+    if( dir != 0 ) {
+      TrimVertex[] v = pwlArc.pts;
+      int imin = 0; 
+      int imax = pwlArc.npts - 1;
+      assert( value > v[imin].param[param] );
+      assert( value < v[imax].param[param] );	
+      while( (imax - imin) > 1 ) {
+        int imid = (imax + imin)/2;
+        if( v[imid].param[param] > value )
+          imax = imid;
+        else if( v[imid].param[param] < value )
+          imin = imid;
+        else {
+          loc[1] = imid;
+          return INTERSECT_VERTEX;
+        }
+      }
+      loc[0] = imin;
+      loc[2] = imax;
+      return INTERSECT_EDGE;
+    } else {
+      TrimVertex[] v = pwlArc.pts;
+      int imax = 0; 
+      int imin = pwlArc.npts - 1;
+      assert( value > v[imin].param[param] );
+      assert( value < v[imax].param[param] );	
+      while( (imin - imax) > 1 ) {
+        int imid = (imax + imin)/2;
+        if( v[imid].param[param] > value )
+          imax = imid;
+        else if( v[imid].param[param] < value )
+          imin = imid;
+        else {
+          loc[1] = imid;
+          return INTERSECT_VERTEX;
+        }
+      }
+      loc[0] = imin;
+      loc[2] = imax;
+      return INTERSECT_EDGE;
+    }
+  }
+
+  private int arc_split( Arc jarc , int param, float value, int dir ) {
+    int maxvertex = jarc.pwlArc.npts;
+    Arc jarc1, jarc2, jarc3;
+    TrimVertex v = jarc.pwlArc.pts;
+
+    int[] loc = new int[3];
+    switch( pwlarc_intersect( jarc.pwlArc, param, value, dir, loc ) ) {
+
+      // When the parameter value lands on a vertex, life is sweet
+    case INTERSECT_VERTEX: {
+      jarc1 = new Arc( jarc, new PwlArc( maxvertex-loc[1], /* &v[loc[1]] */ v, loc[1] ) );
+      jarc.pwlArc.npts = loc[1] + 1;
+      jarc1.next = jarc.next;
+      jarc1.next.prev = jarc1;
+      jarc.next = jarc1;
+      jarc1.prev = jarc;
+      assert(jarc.check());
+      return 2;
+    }
+
+      // When the parameter value intersects an edge, we have to
+      // interpolate a new vertex.  There are special cases
+      // if the new vertex is adjacent to one or both of the
+      // endpoints of the arc.
+    case INTERSECT_EDGE: {
+      int i, j;
+      if( dir == 0 ) {
+        i = loc[0];
+        j = loc[2];
+      } else {
+        i = loc[2];
+        j = loc[0];
+      }
+
+      // The split is between vertices at index j and i, in that
+      // order (j < i)
+      
+      // JEB:  This code is my idea of how to do the split without
+      // increasing the number of links.  I'm doing this so that
+      // the is_rect routine can recognize rectangles created by
+      // subdivision.  In exchange for simplifying the curve list,
+      // however, it costs in allocated space and vertex copies.
+      
+      TrimVertex[] newjunk = TrimVertex.allocate(maxvertex -i+1 /*-j*/);
+      int k;
+      for(k=0; k<maxvertex-i; k++)
+        {
+          newjunk[k+1] = v[i+k];
+          newjunk[k+1].nuid = jarc.nuid;
+        }
+      
+      TrimVertex[] vcopy = TrimVertex.allocate(maxvertex);
+      for(k=0; k<maxvertex; k++)
+        {
+          vcopy[k].param[0] = v[k].param[0];
+          vcopy[k].param[1] = v[k].param[1];
+        }
+      jarc.pwlArc.pts=vcopy;
+
+      v[i].nuid = jarc.nuid;
+      v[j].nuid = jarc.nuid;
+      vert_interp( newjunk[0], v[loc[0]], v[loc[2]], param, value );
+
+      if( showingDegenerate() )
+        backend.triangle( v[i], newjunk[0], v[j] );
+
+      vcopy[j+1].param[0]=newjunk[0].param[0];
+      vcopy[j+1].param[1]=newjunk[0].param[1];
+
+
+      jarc1 = new Arc( jarc,
+                       new PwlArc(maxvertex-i+1 , newjunk ) );
+
+      jarc.pwlArc.npts = j+2;
+      jarc1.next = jarc.next;
+      jarc1.next.prev = jarc1;
+      jarc.next = jarc1;
+      jarc1.prev = jarc;
+      assert(jarc.check());
+
+      return 2;
+
+      /***
+      // JEB: This is the original version:
+
+      TrimVertex[] newjunk = TrimVertex.allocate(3);
+      v[i].nuid = jarc.nuid;
+      v[j].nuid = jarc.nuid;
+      newjunk[0] = v[j];
+      newjunk[2] = v[i];
+      vert_interp( &newjunk[1], &v[loc[0]], &v[loc[2]], param, value );
+
+      if( showingDegenerate() )
+        backend.triangle( &newjunk[2], &newjunk[1], &newjunk[0] );
+
+      // New vertex adjacent to both endpoints
+      if (maxvertex == 2) {
+        jarc1 = new(arcpool) Arc( jarc, new(pwlarcpool) PwlArc( 2, newjunk+1 ) );
+        jarc.pwlArc.npts = 2;
+        jarc.pwlArc.pts = newjunk;
+        jarc1.next = jarc.next;
+        jarc1.next.prev = jarc1;
+        jarc.next = jarc1;
+        jarc1.prev = jarc;
+        assert(jarc.check() != 0);
+
+        return 2;
+
+        // New vertex adjacent to ending point of arc
+      } else if (maxvertex - j == 2) {
+        jarc1 = new(arcpool) Arc( jarc, new(pwlarcpool) PwlArc( 2, newjunk ) );
+        jarc2 = new(arcpool) Arc( jarc, new(pwlarcpool) PwlArc( 2, newjunk+1 ) );
+        jarc.pwlArc.npts = maxvertex-1;
+        jarc2.next = jarc.next;
+        jarc2.next.prev = jarc2;
+        jarc.next = jarc1;
+        jarc1.prev = jarc;
+        jarc1.next = jarc2;
+        jarc2.prev = jarc1;
+        assert(jarc.check() != 0);
+        return 31;
+
+        // New vertex adjacent to starting point of arc
+      } else if (i == 1) {
+        jarc1 = new(arcpool) Arc( jarc, new(pwlarcpool) PwlArc( 2, newjunk+1 ) );
+        jarc2 = new(arcpool) Arc( jarc, 
+                                  new(pwlarcpool) PwlArc( maxvertex-1, &jarc.pwlArc.pts[1] ) );
+        jarc.pwlArc.npts = 2;
+        jarc.pwlArc.pts = newjunk;
+        jarc2.next = jarc.next;
+        jarc2.next.prev = jarc2;
+        jarc.next = jarc1;
+        jarc1.prev = jarc;
+        jarc1.next = jarc2;
+        jarc2.prev = jarc1;
+        assert(jarc.check() != 0);
+        return 32;
+
+        // It's somewhere in the middle
+      } else {
+        jarc1 = new(arcpool) Arc( jarc, new(pwlarcpool) PwlArc( 2, newjunk ) );
+        jarc2 = new(arcpool) Arc( jarc, new(pwlarcpool) PwlArc( 2, newjunk+1 ) );
+        jarc3 = new(arcpool) Arc( jarc, new(pwlarcpool) PwlArc( maxvertex-i, v+i ) );
+        jarc.pwlArc.npts = j + 1;
+        jarc3.next = jarc.next;
+        jarc3.next.prev = jarc3;
+        jarc.next = jarc1;
+        jarc1.prev = jarc;
+        jarc1.next = jarc2;
+        jarc2.prev = jarc1;
+        jarc2.next = jarc3;
+        jarc3.prev = jarc2;
+        assert(jarc.check() != 0);
+        return 4;
+      }
+      ***/
+    }
+    default:
+      return -1; //picked -1 since it's not used
+    }
+  }
+
+  private void check_s( Arc_ptr , Arc_ptr  );
+  private void check_t( Arc_ptr , Arc_ptr  );
+  private inline void link( Arc_ptr , Arc_ptr , Arc_ptr , Arc_ptr  );
+  private inline void simple_link( Arc_ptr , Arc_ptr  );
+
+  private Bin makePatchBoundary( const float[] from, const float[] to ) {
+    Bin ret = new Bin();
+    float smin = from[0];
+    float smax = to[0];
+    float tmin = from[1];
+    float tmax = to[1];
+
+    pjarc = 0;
+
+    Arc jarc = new Arc( arc_bottom, 0 );
+    arctessellator.bezier( jarc, smin, smax, tmin, tmin );
+    ret.addarc( jarc  );
+    pjarc = jarc.append( pjarc );
+
+    jarc = new(arcpool) Arc( arc_right, 0 );
+    arctessellator.bezier( jarc, smax, smax, tmin, tmax );
+    ret.addarc( jarc  );
+    pjarc = jarc.append( pjarc );
+
+    jarc = new(arcpool) Arc( arc_top, 0 );
+    arctessellator.bezier( jarc, smax, smin, tmax, tmax );
+    ret.addarc( jarc  );
+    pjarc = jarc.append( pjarc );
+
+    jarc = new(arcpool) Arc( arc_left, 0 );
+    arctessellator.bezier( jarc, smin, smin, tmax, tmin );
+    ret.addarc( jarc  );
+    jarc.append( pjarc );
+
+    assert( jarc.check() != 0 );
+    return ret;
+  }
+
+   /*in domain distance method, the tessellation is controled by two numbers:
+    *GLU_U_STEP: number of u-segments per unit u length of domain
+    *GLU_V_STEP: number of v-segments per unit v length of domain
+    *These two numbers are normally stored in mapdesc.maxs(t)rate.
+    *I (ZL) put these two numbers here so that I can optimize the untrimmed 
+    *case in the case of domain distance sampling.
+    *These two numbers are set by set_domain_distance_u_rate() and ..._v_..().
+    */
+  private float domain_distance_u_rate;
+  private float domain_distance_v_rate;
+  private int is_domain_distance_sampling;
+  
+}