commit 8f5116ec8e2d3bb9fe215d41b5ce2880d9f5092d
Author: leszek <leszek@koltunski.pl>
Date:   Fri Mar 1 23:58:33 2024 +0100

    Major improvement for the FactorySticker: now all changes to border thickness & size of corners should work.

diff --git a/src/main/java/org/distorted/objectlib/helpers/FactorySticker.java b/src/main/java/org/distorted/objectlib/helpers/FactorySticker.java
index abe9da0a..6feab6ad 100644
--- a/src/main/java/org/distorted/objectlib/helpers/FactorySticker.java
+++ b/src/main/java/org/distorted/objectlib/helpers/FactorySticker.java
@@ -14,6 +14,7 @@ import static org.distorted.objectlib.main.TwistyObject.COLOR_STROKE;
 import android.graphics.Canvas;
 import android.graphics.Color;
 import android.graphics.Paint;
+import android.graphics.Path;
 import android.graphics.PorterDuff;
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
@@ -22,7 +23,6 @@ public class FactorySticker
   {
   private static FactorySticker mThis;
   private static final float PI = (float)Math.PI;
-  private float mOX, mOY, mR;
   private int mTexHeight;
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
@@ -42,15 +42,14 @@ public class FactorySticker
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
+// This agrees with startAngle and sweepAngle arguments to Canvas.drawArc(), i.e. it is 0 at the +x
+// axis, and grows clockwise to 2*PI.
 
   private float computeAngle(float dx, float dy)
     {
-    double angle = Math.atan2(dy,dx);
-    float ret = (float)(3*PI/2-angle);
-
-    if( ret>2*PI ) ret-= 2*PI;
-
-    return ret;
+    float theta = (float)Math.atan2(-dy,dx);
+    if( theta<0 ) theta += 2*PI;
+    return theta;
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
@@ -62,14 +61,129 @@ public class FactorySticker
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
 
-  private void computeCircleCoords(float x1,float y1, float x2, float y2, float alpha)
+  private float[][] computeCircles(float[][] vertices, float[] angles)
     {
-    float ctg= 1.0f/((float)Math.tan(alpha));
-    mOX = 0.5f*(x1+x2) - ctg*0.5f*(y1-y2);
-    mOY = 0.5f*(y1+y2) + ctg*0.5f*(x1-x2);
-    float dx = mOX-x1;
-    float dy = mOY-y1;
-    mR = (float)Math.sqrt(dx*dx+dy*dy);
+    int length = vertices.length;
+    float[][] output = new float[length][3];
+
+    for(int vert=0; vert<length; vert++)
+      {
+      int next = vert<length-1 ? vert+1 : 0;
+      float[] cv = vertices[vert];
+      float[] nv = vertices[next];
+      float currX = cv[0];
+      float currY = cv[1];
+      float nextX = nv[0];
+      float nextY = nv[1];
+
+      float angle = getAngle(angles,vert);
+      computeCircle(currX,currY,nextX,nextY,angle,output[vert]);
+      }
+
+    return output;
+    }
+
+///////////////////////////////////////////////////////////////////////////////////////////////////
+// Input: circle segment from point C=(cx,cy) to point N=(nx,ny) ; if angle==0, then it is a
+// straight line. Otherwise it is a true circle segment. If O=(ox,oy) is the center of this circle
+// and R>0 is its radius, then |angle| is the angle CON (in radians); if angle>0, then O is to the
+// left of vector PC, otherwise it is to the right.
+//
+// Output: if angle!=0, output[0]=ox, output[1]=oy, output[2]=R.
+// Otherwise we have a straight line y=ax+b and output[0]=a, output[1]=b and output[2]=0.
+// [ special case when line is vertical, i.e. x=c: output=(c,0,-1) ]
+
+  private void computeCircle(float cx, float cy, float nx, float ny, float angle, float[] output)
+    {
+    if( angle != 0 )
+      {
+      float ctg= 1.0f/((float)Math.tan(angle/2));
+      float ox = 0.5f*(cx+nx) + ctg*0.5f*(cy-ny);
+      float oy = 0.5f*(cy+ny) - ctg*0.5f*(cx-nx);
+      float dx = ox-cx;
+      float dy = oy-cy;
+      float r = (float)Math.sqrt(dx*dx+dy*dy);
+
+      output[0] = ox;
+      output[1] = oy;
+      output[2] = r;
+      }
+    else
+      {
+      float dx = nx-cx;
+      float dy = ny-cy;
+
+      if( dx*dx > 0.000001f )
+        {
+        output[0] = dy/dx;
+        output[1] = (nx*cy-cx*ny)/dx;
+        output[2] = 0;
+        }
+      else
+        {
+        output[0] = cx;
+        output[1] =  0;
+        output[2] = -1;
+        }
+      }
+    }
+
+///////////////////////////////////////////////////////////////////////////////////////////////////
+
+  private float[][][] computeInnerVertices(float[][] circles, float[][] vertices, float[] radii, float corners,
+                                           float[] strokes, float borders, float[][] corner_circles)
+    {
+    int prev, next, length = circles.length;
+    float[][][] output = new float[length][2][2];
+
+    for(int curr=0; curr<length; curr++)
+      {
+      float[] currC = corner_circles[curr];
+      prev = curr==0 ? length-1 : curr-1;
+      next = curr==length-1 ? 0 : curr+1;
+      float radius = radii[curr]*corners + strokes[curr]*borders/2;
+      computeCornerCircle(circles[prev],circles[curr], vertices[prev], vertices[curr], vertices[next], radius, currC );
+      computeInnerVertex(circles[prev],currC,output[curr][0]);
+      computeInnerVertex(circles[curr],currC,output[curr][1]);
+      }
+
+    return output;
+    }
+
+///////////////////////////////////////////////////////////////////////////////////////////////////
+// Return the angle the vector tangent to the circle at point T='tangent_point' makes with the
+// +x axis. (i.e. float from 0 to 2PI going clockwise, same format as in Canvas.drawArc).
+// If the 'circle' is really a straight line, return the angle from O=other_point to T, two
+// points which lie on this line.
+// Otherwise, the direction of the vector points as we go from O to T (along the shorter arc).
+// What to do when the two points are opposite on the circle and two arcs are equal? Go CCW.
+//
+// If C (cx,cy) is the center of the circle, compute vector CT = (vx,vy), then the perpendicular
+// V'= (-vy,vx) and choose V' or -V' depending on which one forms angle of less than 90 degrees
+// with vector TO = (tx,ty).
+
+  private float computeDir(float[] circle, float[] tangent_point, float[] other_point)
+    {
+    if( circle[2]<=0 )
+      {
+      float dx = tangent_point[0] - other_point[0];
+      float dy = tangent_point[1] - other_point[1];
+      return computeAngle(dx,dy);
+      }
+    else
+      {
+      float vx = tangent_point[0] - circle[0];
+      float vy = tangent_point[1] - circle[1];
+      float tx = tangent_point[0] - other_point[0];
+      float ty = tangent_point[1] - other_point[1];
+
+      float ret= (-vy*tx+vx*ty >=0) ? computeAngle(-vy,vx) : computeAngle(vy,-vx);
+
+      //android.util.Log.e("D", "tangent: "+tangent_point[0]+" "+tangent_point[1]+" other="+other_point[0]+" "+other_point[1]);
+      //android.util.Log.e("D","circle: "+circle[0]+" "+circle[1]+" "+circle[2]+" ret="+ret);
+
+      return ret;
+      }
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
@@ -77,7 +191,8 @@ public class FactorySticker
 // Guaranteed to intersect in two points. Find the intersection. Which one? the one that's closer
 // to (nearx,neary).
 
-  private void findCircleIntersection(float x1,float y1, float r1, float x2, float y2, float r2, float nearx, float neary )
+  private void findCircleIntersection(float x1,float y1, float r1, float x2, float y2, float r2,
+                                      float nearx, float neary, float[] output )
     {
     float dx = x2-x1;
     float dy = y2-y1;
@@ -104,251 +219,469 @@ public class FactorySticker
 
       if( d1<d2 )
         {
-        mOX = ox1;
-        mOY = oy1;
+        output[0] = ox1;
+        output[1] = oy1;
         }
       else
         {
-        mOX = ox2;
-        mOY = oy2;
+        output[0] = ox2;
+        output[1] = oy2;
         }
       }
     else
       {
-      mOX = x1;
-      mOY = y1;
+      output[0] = nearx;
+      output[1] = neary;
       }
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
+// circle1: center (x,y) radius r; line: y=ax+b (if c==0) or x=a (otherwise)
+// Guaranteed to intersect in two points. Find the intersection. Which one? the one that's closer
+// to (nearx,neary).
+// (vx,vy) is the point of intersection of the (a,b,c) line and the line perpendicular to it
+// passing through (x,y)
 
-  private void drawCurrSide(Canvas canvas, Paint paint, int left, int bottom, float stroke,
-                            float pX, float pY, float cX, float cY, float pAngle)
+  private void findCircleLineIntersection(float x,float y, float r, float a, float b, float c,
+                                          float nearx, float neary, float[] output )
     {
-    pX = (0.5f+pX)*mTexHeight;
-    pY = (0.5f-pY)*mTexHeight;
-    cX = (0.5f+cX)*mTexHeight;
-    cY = (0.5f-cY)*mTexHeight;
+    float vx,vy,m;
+    float ox1,ox2,oy1,oy2;
 
-    if( pAngle==0 )
+    if( c==0 )
       {
-      float aX = pX-cX;
-      float aY = pY-cY;
-      float aLen = (float)Math.sqrt(aX*aX+aY*aY);
-      aX /= aLen;
-      aY /= aLen;
-
-      // draw a little more - 0.5f*stroke*(aX,aY) more - so
-      // that we draw over the rounded corners (Kilominx!)
-      float corr = stroke*0.5f;
-      canvas.drawLine(left+pX,bottom-pY,left+cX-corr*aX,bottom-cY+corr*aY,paint);
+      vx = (x + a*(y-b)) / (a*a + 1);
+      vy = (a*x + a*a*y + b) / (a*a + 1);
+      m = a;
       }
     else
       {
-      computeCircleCoords(pX,pY,cX,cY,pAngle);
-      float ox = mOX;
-      float oy = mOY;
-      float r  = mR;
+      vx = a;
+      vy = y;
+      m = 0;
+      }
 
-      float dx = ox-pX;
-      float dy = oy-pY;
-      float startA = computeAngle(-dy,dx);
-      float sweepA = 2*pAngle;
+    float dx = x-vx;
+    float dy = y-vy;
+    float d = (float)Math.sqrt(dx*dx+dy*dy);
+    float f = (float)Math.sqrt(r*r-d*d);
+    float e = f / ((float)Math.sqrt(m*m+1));
 
-      startA *= 180/PI;
-      sweepA *= 180/PI;
+    if( c==0 )
+      {
+      ox1 = vx - e;
+      oy1 = vy - e*m;
+      ox2 = vx + e;
+      oy2 = vy + e*m;
+      }
+    else
+      {
+      ox1 = vx;
+      oy1 = vy - f;
+      ox2 = vx;
+      oy2 = vy + f;
+      }
 
-      canvas.drawArc( left+ox-r, bottom-oy-r, left+ox+r, bottom-oy+r, startA, sweepA, false, paint);
+    dx = nearx-ox1;
+    dy = neary-oy1;
+    float d1 = dx*dx+dy*dy;
+    dx = nearx-ox2;
+    dy = neary-oy2;
+    float d2 = dx*dx+dy*dy;
+
+    if( d1<d2 )
+      {
+      output[0] = ox1;
+      output[1] = oy1;
+      }
+    else
+      {
+      output[0] = ox2;
+      output[1] = oy2;
       }
+
+    // android.util.Log.e("D", "findCircleLineIntersection circle="+x+" "+y+" "+r+" line="+a+" "+b+" "+c+" result: "+output[0]+" "+output[1]);
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
-// quotient in (0,1).
-// quotient==0 --> ret=curvature; quotient==1 --> ret=0.
+// line1: y=a1x+b1 (if c1==0) or x=a1 (otherwise)
+// line2: y=a2x+b2 (if c2==0) or x=a2 (otherwise)
+// Guaranteed to intersect. Find the intersection point.
 
-  private float computeQuotientOfCurvature(float quotient, float curvature)
+  private void findLineIntersection(float a1,float b1, float c1, float a2, float b2, float c2, float[] output )
     {
-    if( curvature!=0 )
+    if( c1==0 && c2==0 )
+      {
+      if( a1==a2 ) android.util.Log.e("E", "1 error in findLineIntersection: lines parallel" );
+      else
+        {
+        float x = (b2-b1)/(a1-a2);
+        float y = a1*x+b1;
+        output[0] = x;
+        output[1] = y;
+        }
+      }
+    else if( c1==0 )
       {
-      double sinC = Math.sin(curvature);
-      float arcsin = (float)Math.asin(quotient*sinC);
-      return curvature-arcsin;
+      output[0] = a2;
+      output[1] = a1*a2 + b1;
+      }
+    else if( c2==0 )
+      {
+      output[0] = a1;
+      output[1] = a2*a1 + b2;
+      }
+    else
+      {
+      android.util.Log.e("E", "2 error in findLineIntersection: lines parallel" );
       }
-    return curvature;
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
 
-  private float computeSideAngle(float vX, float vY, float radius, float curvature)
+  private void computeIntersection(float[] circle1, float[] circle2, float[] point, float[] output)
     {
-    float quotient = radius/(float)Math.sqrt(vX*vX + vY*vY);
-    float ret = computeAngle(vX,-vY)-computeQuotientOfCurvature(quotient,curvature);
+    float x1 = circle1[0];
+    float y1 = circle1[1];
+    float r1 = circle1[2];
+    float x2 = circle2[0];
+    float y2 = circle2[1];
+    float r2 = circle2[2];
+
+    if( r1>0 && r2>0 ) findCircleIntersection(x1,y1,r1,x2,y2,r2,point[0],point[1],output);
+    else
+      {
+           if( r1>0 ) findCircleLineIntersection(x1,y1,r1,x2,y2,r2,point[0],point[1],output);
+      else if( r2>0 ) findCircleLineIntersection(x2,y2,r2,x1,y1,r1,point[0],point[1],output);
+      else            findLineIntersection(x2,y2,r2,x1,y1,r1,output);
+      }
+    }
 
-    while( ret>=2*PI ) ret -= 2*PI;
-    while( ret<0     ) ret += 2*PI;
+///////////////////////////////////////////////////////////////////////////////////////////////////
+// Input: a circle (true or line) in usual format and two points on it.
+//
+// If it is a straight line, return a straight line which is parallel to it and moved by either
+// |move| to the 'left' (if move<0) or |move| to the right (otherwise).
+// 'left' or 'right' are defined: we are looking from point1 towards point2.
+//
+// If it is a true circle, then return a true circle which has the same center and radius either
+// smaller by |move| or larger by |move| - depending on:
+// if we're looking from point1 towards point2 (along the shorter arc) - notice on which side, left
+// or right of the vector of movement anchored at point1, the outside of the circle is.
+//
+// Make the radius smaller iff:
+// it is on the left and move<0 or it is on the right and move>0.
+
+  private float[] moveCircle(float[] circle, float[] point1, float[] point2, float move)
+    {
+    float radius = circle[2];
 
-    return ret;
+    if( radius>0 )
+      {
+      float vx = point2[0]-point1[0];
+      float vy = point2[1]-point1[1];
+      float wx = circle[0]-point1[0];
+      float wy = circle[1]-point1[1];
+      boolean left = (wx*vy <= wy*vx);
+      float m = left ? move : -move;
+      return new float[] {circle[0],circle[1],radius+m};
+      }
+    else
+      {
+      if( radius==0 )
+        {
+        float a = circle[0];
+        float m = point2[0]>point1[0] ? -move : move;
+        float f = m*((float)Math.sqrt(a*a+1));
+        return new float[] {circle[0],circle[1]+f,0};
+        }
+      else
+        {
+        float m = point2[1]>point1[1] ? move : -move;
+        return new float[] {circle[0]+m,0,-1};
+        }
+      }
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
+// Compute the 3-tuple describing a 'corner_circle' (i.e. the one which actually makes the corner
+// of the sticker round). Format similar to the one in computeCircle() but:
+// 1. here if radius=0 then it is a 'nothing', empty circle of radius 0 and not a line
+// 2. there is the 4th float: 0 means 'this corner circle's center is inside the sticker (so outside
+// of the circle is outside of the sticker), 1 - otherwise. We need this knowledge later on when
+// blacking out the outsides of the round corners.
+
+  private void computeCornerCircle(float[] prev_edge_circle, float[] curr_edge_circle,
+                                   float[] pvert, float[] cvert, float[] nvert, float radius, float[] output)
+    {
+    if( radius<=0 )
+      {
+      output[0] = cvert[0];
+      output[1] = cvert[1];
+      output[2] = 0;
+      output[3] = 0; // ??
+      }
+    else
+      {
+      float pdir = computeDir(prev_edge_circle,cvert,pvert);
+      float cdir = computeDir(curr_edge_circle,cvert,nvert);
+/*
+      boolean pl = (cdir<pdir-PI || (cdir>pdir && cdir<pdir+PI));
+      boolean cl = (pdir<cdir-PI || (pdir>cdir && pdir<cdir+PI));
+
+      android.util.Log.e("D", "prev edge circle: "+prev_edge_circle[0]+" "+prev_edge_circle[1]+" "+prev_edge_circle[2]);
+      android.util.Log.e("D", "from: "+cvert[0]+" "+cvert[1]);
+      android.util.Log.e("D", "to  : "+pvert[0]+" "+pvert[1]);
+      android.util.Log.e("D", "dir : "+pdir+" left: "+pl);
+
+      android.util.Log.e("D", "curr edge circle: "+curr_edge_circle[0]+" "+curr_edge_circle[1]+" "+curr_edge_circle[2]);
+      android.util.Log.e("D", "from: "+cvert[0]+" "+cvert[1]);
+      android.util.Log.e("D", "to  : "+nvert[0]+" "+nvert[1]);
+      android.util.Log.e("D", "dir : "+cdir+" left: "+cl);
+*/
+      float tmp = Math.abs(pdir-cdir);
+      float diff= Math.abs(PI-tmp);
+
+      if( diff > (17*PI/18) )  // the two consecutive edges are 'almost' parallel, do not round the corner
+        {
+        output[0] = cvert[0];
+        output[1] = cvert[1];
+        output[2] = 0;
+        output[3] = 0;
+        }
+      else
+        {
+        boolean pleft = (cdir<pdir-PI || (cdir>pdir && cdir<pdir+PI));
+        boolean cleft = (pdir<cdir-PI || (pdir>cdir && pdir<cdir+PI));
+
+        float[] moved_prev_edge = moveCircle(prev_edge_circle, cvert, pvert, pleft ? radius : -radius);
+        float[] moved_curr_edge = moveCircle(curr_edge_circle, cvert, nvert, cleft ? radius : -radius);
+
+        computeIntersection(moved_curr_edge,moved_prev_edge,cvert,output);
+        output[2] = radius;
+        output[3] = pleft ? 0:1;
+/*
+        android.util.Log.e("D", "computeCornerCircle pdir="+pdir+" cdir="+cdir);
+        android.util.Log.e("D", "prev edge circ: "+prev_edge_circle[0]+" "+prev_edge_circle[1]+" "+prev_edge_circle[2]+" pleft="+pleft);
+        android.util.Log.e("D", "moved_prev: "+moved_prev_edge[0]+" "+moved_prev_edge[1]+" "+moved_prev_edge[2]);
+        android.util.Log.e("D", "curr edge circ: "+curr_edge_circle[0]+" "+curr_edge_circle[1]+" "+curr_edge_circle[2]+" cleft="+cleft);
+        android.util.Log.e("D", "moved_curr: "+moved_curr_edge[0]+" "+moved_curr_edge[1]+" "+moved_curr_edge[2]);
+
+        android.util.Log.e("D", "pvert: "+pvert[0]+" "+pvert[1]);
+        android.util.Log.e("D", "cvert: "+cvert[0]+" "+cvert[1]);
+        android.util.Log.e("D", "nvert: "+nvert[0]+" "+nvert[1]);
+
+        android.util.Log.d("D", "intersection: "+output[0]+" "+output[1]);
+*/
+        }
+      }
+    }
 
-  private float angleMidpoint(float angle1, float angle2)
+///////////////////////////////////////////////////////////////////////////////////////////////////
+// input:
+// 1) a 3-tuple representing circles (or possibly a degenerate circle, i.e. straight line)
+// in the same format as described in the output of 'computeCircle()'
+// 2) another 3-tuple describing the connecting 'corner_circle'. This time if its radius>0, then
+// it is a proper corner_circle which makes the respecting corner round. Otherwise the circle is
+// not there and the corner stays sharp.
+//
+// Compute the tangent point (vx,vy) where circle and corner circle touch.
+// Output: output[0]=vx, output[1]=vy.
+
+  private void computeInnerVertex(float[] edge_circle, float[] corner_circle, float[] output)
     {
-    float diff = angle2-angle1;
-    if( diff<0 ) diff = -diff;
-    float avg = (angle1+angle2)/2;
+    float cx = corner_circle[0];
+    float cy = corner_circle[1];
+    float cr = corner_circle[2];
+    float ex = edge_circle[0];
+    float ey = edge_circle[1];
+    float er = edge_circle[2];
+
+    if( er>0 )  // the edge is curved, i.e. edge_circle is a true circle segment and not a line.
+      {
+      float dx = ex-cx;
+      float dy = ey-cy;
+      float len = (float)Math.sqrt(dx*dx + dy*dy);
 
-    if( diff>PI )
+      if( len>0 )
+        {
+        float b = cr/len;
+        if( len<er ) b = -b;  // the corner circle can be inside the edge circle,
+                              // then we need to subtract, or outside - then add.
+
+        output[0] = cx + b*dx;
+        output[1] = cy + b*dy;
+        }
+      else
+        {
+        android.util.Log.e("D", "error in computeInnerVertex: len=0");
+        }
+      }
+    else if( er==0 )  // non-vertical line
+      {
+      float tmp = ex*ex+1;
+      output[0] = (ex*(cy-ey)+cx)/tmp;
+      output[1] = (ex*(cx+ex*cy)+ey)/tmp;
+      }
+    else   // vertical line
       {
-      avg -= PI;
-      if( avg<0 ) avg += 2*PI;
+      output[0] = ex;
+      output[1] = cy;
       }
 
-    return avg;
+    //android.util.Log.e("D", "corner c: "+cx+" "+cy+" "+cr+" edge c: "+ex+" "+ey+" "+er+" output: "+output[0]+" "+output[1]);
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
+// black out the outside of the round corner. It is guaranteed to be outside of the sticker.
 
-  private void drawRoundCorner(Canvas canvas, Paint paint, int color, int left, int bottom,
-                               float stroke, float borders, float radius, float corners, float cX, float cY, float pA, float cA)
+  private void blackOutCorner(Canvas canvas, Paint paint, int left, int bott, float[] vert1,
+                              float[] vert2, float[] vert, float[] circle)
     {
-    final boolean isConvex = ((pA<cA && cA<pA+PI) || (pA<cA+2*PI && cA+2*PI<pA+PI));
-    float startA, stopA, centerA, alpha, D;
-
-    cX = (0.5f+cX)*mTexHeight;
-    cY = (0.5f-cY)*mTexHeight;
-
-    radius *= (isConvex ? corners : borders);
-    stroke *= borders;
-    final float A = isConvex ? 4.0f : 2.0f;
-
-    float r = radius*mTexHeight + stroke/2;    // distance from the center of the circle arc of
-                                               // which we are drawing to the center of the edge line
-    float R = radius*mTexHeight + A*stroke/2;  // distance from the center of the circle to the center
-                                               // of the arc being drawn; the arc is A times thicker.
-
-    if( isConvex )
-      {
-      startA = cA;
-      stopA  = pA;
-      if( startA>2*PI ) startA -= 2*PI;
-      if( stopA >2*PI ) stopA  -= 2*PI;
-      centerA= angleMidpoint(pA,cA) - PI/2;
-      if( centerA<0 ) centerA += 2*PI;
-      float diff = cA-centerA;
-      if( diff<0 ) diff += 2*PI;
-      alpha = diff> PI/2 ? PI-diff : diff;
-      D = (float)(r/Math.sin(alpha));
+    float v1x = left+(0.5f+vert1[0])*mTexHeight;
+    float v1y = bott-(0.5f-vert1[1])*mTexHeight;
+    float v2x = left+(0.5f+vert2[0])*mTexHeight;
+    float v2y = bott-(0.5f-vert2[1])*mTexHeight;
+    float vx  = left+(0.5f+vert[0])*mTexHeight;
+    float vy  = bott-(0.5f-vert[1])*mTexHeight;
+    float ox  = left+(0.5f+circle[0])*mTexHeight;
+    float oy  = bott-(0.5f-circle[1])*mTexHeight;
+    float or  = circle[2]*mTexHeight;
+
+    float dx = vx-ox;
+    float dy = vy-oy;
+    float d  = (float)Math.sqrt(dx*dx+dy*dy);
+    float v3x = ox + or*dx/d;
+    float v3y = oy + or*dy/d;
+
+    Path path = new Path();
+    path.moveTo(v1x,v1y);
+    path.lineTo(v3x,v3y);
+    path.lineTo(v2x,v2y);
+    path.lineTo(vx,vy);
+    path.close();
+
+    canvas.drawLine(v1x,v1y,vx,vy,paint);
+    canvas.drawLine(v2x,v2y,vx,vy,paint);
+
+    paint.setStrokeWidth(1);
+    paint.setStyle(Paint.Style.FILL_AND_STROKE);
+    canvas.drawPath(path, paint);
+    paint.setStyle(Paint.Style.STROKE);
+    }
+
+///////////////////////////////////////////////////////////////////////////////////////////////////
+// draw a circle segment from vert1 to vert2. 'circle' describes the center and radius of the segment.
+
+  private void drawCircleSegment(Canvas canvas, Paint paint, int left, int bottom, float[] vert1, float[] vert2, float[] circle)
+    {
+    float v1x = (0.5f+vert1[0])*mTexHeight;
+    float v1y = (0.5f-vert1[1])*mTexHeight;
+    float v2x = (0.5f+vert2[0])*mTexHeight;
+    float v2y = (0.5f-vert2[1])*mTexHeight;
+
+    float R = circle[2]*mTexHeight;
+
+    if( R>0 )
+      {
+      float oX = (0.5f+circle[0])*mTexHeight;
+      float oY = (0.5f-circle[1])*mTexHeight;
+
+      float startA = computeAngle(oX-v1x, oY-v1y) + PI;
+      float stopA  = computeAngle(oX-v2x, oY-v2y) + PI;
+
+      float sweepA = stopA-startA;
+      while( sweepA<-PI ) sweepA += 2*PI;
+      while( sweepA> PI ) sweepA -= 2*PI;
+
+      //sweepA = -sweepA;
+
+      startA *= 180/PI;
+      sweepA *= 180/PI;
+
+//android.util.Log.e("D", "drawing arc ox="+oX+" oy="+oY+" R="+R+" startA="+startA+" sweepA="+sweepA+" stopA="+(stopA*(180/PI)));
+//android.util.Log.e("D", "drawing arc v1="+v1x+" , "+v1y+" v2="+v2x+" , "+v2y+" tex: "+mTexHeight);
+
+      canvas.drawArc( left+oX-R, bottom-oY-R, left+oX+R, bottom-oY+R, startA, sweepA, false, paint);
       }
     else
       {
-      startA = pA + PI;
-      stopA  = cA + PI;
-      centerA= angleMidpoint(pA,cA) + PI/2;
-      if( centerA>=2*PI ) centerA -= 2*PI;
-      float diff = centerA-cA;
-      if( diff<0 ) diff += 2*PI;
-      alpha = diff> PI/2 ? PI-diff : diff;
-      D = (float)((r-stroke)/Math.sin(alpha));
+//android.util.Log.e("D", "drawing line from "+v1x+" , "+v1y+" to "+v2x+" , "+v2y);
+
+      canvas.drawLine( left+v1x, bottom-v1y, left+v2x, bottom-v2y, paint);
       }
+    }
+/*
+///////////////////////////////////////////////////////////////////////////////////////////////////
 
-    float sweepA = startA-stopA;
-    if( sweepA<0 ) sweepA += 2*PI;
-    sweepA = -sweepA;
+  private void printCircle(float[] circle, String marker)
+    {
+    String str = "";
 
-    float sinA = (float)(Math.sin(centerA));
-    float cosA = (float)(Math.cos(centerA));
-    float oX= cX + D*sinA;
-    float oY= cY + D*cosA;
+    if( circle[2]>0 ) str=" true circle "+circle[0]+" "+circle[1]+" "+circle[2];
+    else              str=" line "+circle[0]+" "+circle[1]+" "+circle[2];
 
-    startA *= 180/PI;
-    sweepA *= 180/PI;
+    if( circle.length>3 ) str+= (circle[3]==0 ? " INSIDE" : " OUTSIDE");
 
-    if( !isConvex ) paint.setColor(color);
-    paint.setStrokeWidth(A*stroke);
-    canvas.drawArc( left+oX-R, bottom-oY-R, left+oX+R, bottom-oY+R, startA, sweepA, false, paint);
-    if( !isConvex ) paint.setColor(COLOR_STROKE);
+    android.util.Log.e("D", marker+" "+str);
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
-// TODO: this doesn't really support proper drawing of rounded corners in case two neighbouring
-// strokes are not equal to each other.
 
-  private void drawEdge(Canvas canvas, Paint paint, int left, int bottom, int color, float[] strokes,
+  private void printVertices(float[][] v, String marker)
+    {
+    String str = (v[0][0]+","+v[0][1]+" "+v[1][0]+","+v[1][1]);
+    android.util.Log.e("D", marker+" "+str);
+    }
+*/
+///////////////////////////////////////////////////////////////////////////////////////////////////
+
+  private void drawEdge(Canvas canvas, Paint paint, int left, int bottom, float[] strokes,
                         float[][] vertices, float[] angles, float[] radii, float borders, float corners )
     {
     int length = vertices.length;
 
-    float prevX = vertices[length-1][0];
-    float prevY = vertices[length-1][1];
-    float currX = vertices[0][0];
-    float currY = vertices[0][1];
-    float nextX = vertices[1][0];
-    float nextY = vertices[1][1];
-    float prevA = getAngle(angles,length-1);
-    float currA = getAngle(angles,0);
+    float[][]     edge_circles = computeCircles(vertices,angles);
+    float[][]   corner_circles = new float[length][4];
+    float[][][] inner_vertices = computeInnerVertices(edge_circles,vertices,radii,corners,strokes,borders,corner_circles);
 
-    for(int vert=0; vert<length; vert++)
+    //for(int c=0; c<edge_circles.length; c++) printCircle(edge_circles[c], "EDGE "+c);
+    //for(int c=0; c<corner_circles.length; c++) printCircle(corner_circles[c], "CORNER "+c);
+    //for(int c=0; c<inner_vertices.length; c++) printVertices(inner_vertices[c], "VERTICES "+c);
+
+    for(int curr=0; curr<length; curr++)
       {
-      float stroke = borders*strokes[vert]*mTexHeight;
+      int next = curr==length-1 ? 0 : curr+1;
+      float currStroke = borders*strokes[curr]*mTexHeight;
+      float radius     = corner_circles[next][2]*mTexHeight;
 
-      if( stroke>0 )
+      if( currStroke>0 )
         {
-        paint.setStrokeWidth(stroke);
-        drawCurrSide(canvas, paint, left, bottom, stroke, prevX, prevY, currX, currY, prevA);
+        paint.setStrokeWidth(currStroke);
+        drawCircleSegment( canvas, paint, left, bottom, inner_vertices[curr][1], inner_vertices[next][0], edge_circles[curr]);
         }
 
-      prevX = currX;
-      prevY = currY;
-      currX = nextX;
-      currY = nextY;
-      prevA = currA;
-      currA = getAngle(angles, vert==length-1 ? 0 : vert+1);
-      int ind = ( vert+2 < length ? vert+2 : 0);
-      nextX = vertices[ind][0];
-      nextY = vertices[ind][1];
-      }
-
-    prevX = vertices[length-1][0];
-    prevY = vertices[length-1][1];
-    currX = vertices[0][0];
-    currY = vertices[0][1];
-    nextX = vertices[1][0];
-    nextY = vertices[1][1];
-
-    prevA = getAngle(angles,length-1);
-    currA = getAngle(angles,0);
+      if( radius>0 )
+        {
+        float nextStroke = borders*strokes[next]*mTexHeight;
+        if( nextStroke<currStroke ) paint.setStrokeWidth(nextStroke);
+        drawCircleSegment( canvas, paint, left, bottom, inner_vertices[next][0], inner_vertices[next][1], corner_circles[next]);
 
-    for(int vert=0; vert<length; vert++)
-      {
-      float stroke = strokes[vert]*mTexHeight;
-      int prev = vert==0 ? length-1 : vert-1;
-      float rp = radii[prev];
-      float rv = radii[vert];
-      float prevAngle = computeSideAngle(currX-prevX,currY-prevY,rp,-prevA);
-      float currAngle = computeSideAngle(nextX-currX,nextY-currY,rv,+currA);
-
-      if( rv>0 && stroke>0 )
-        drawRoundCorner(canvas,paint,color,left,bottom,stroke,borders,rv,corners,currX,currY,prevAngle,currAngle);
-
-      prevX = currX;
-      prevY = currY;
-      currX = nextX;
-      currY = nextY;
-      prevA = currA;
-      currA = getAngle(angles, vert==length-1 ? 0 : vert+1);
-      int ind = ( vert+2 < length ? vert+2 : 0);
-      nextX = vertices[ind][0];
-      nextY = vertices[ind][1];
+        if( corner_circles[next][3]==0 )
+          blackOutCorner( canvas, paint, left, bottom, inner_vertices[next][0], inner_vertices[next][1], vertices[next], corner_circles[next] );
+        }
       }
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
 // PUBLIC
+///////////////////////////////////////////////////////////////////////////////////////////////////
 
   public void drawRoundedPolygons(Canvas canvas, Paint paint, int left, int bottom, int color,
                                   int height, ObjectSticker sticker, float borders, float corners)
     {
+    //android.util.Log.d("D", "DRAW ROUNDED POLYGONS");
+
     mTexHeight = height;
 
     float[][] strokes    = sticker.getStrokes();
@@ -372,7 +705,7 @@ public class FactorySticker
     for(int l=0; l<numLoops; l++)
       {
       float[] ang = (angles==null? null : angles[l]);
-      drawEdge(canvas, paint, left, bottom, color, strokes[l], vertices[l], ang, radii[l], borders, corners);
+      drawEdge(canvas, paint, left, bottom, strokes[l], vertices[l], ang, radii[l], borders, corners);
       }
 
     canvas.restore();
diff --git a/src/main/java/org/distorted/objectlib/objects/TwistyCoinHexahedron.java b/src/main/java/org/distorted/objectlib/objects/TwistyCoinHexahedron.java
index fbfc8aa7..3acad199 100644
--- a/src/main/java/org/distorted/objectlib/objects/TwistyCoinHexahedron.java
+++ b/src/main/java/org/distorted/objectlib/objects/TwistyCoinHexahedron.java
@@ -95,11 +95,11 @@ public class TwistyCoinHexahedron extends ShapeHexahedron
     {
     boolean icon = isInIconMode();
 
-    float S1 = icon ? 0.21f : 0.10f;
-    float S2 = icon ? 0.23f : 0.15f;
-    float S3 = icon ? 0.23f : 0.15f;
+    float S1 = icon ? 0.21f : 0.12f;
+    float S2 = icon ? 0.21f : 0.07f;
+    float S3 = icon ? 0.21f : 0.12f;
 
-    return new float[][][] { {{ S2,S1,S1,S2,S2 }} , {{S3,S3,S3,S3}} , {{S3,S3}} };
+    return new float[][][] { {{ S1,S1,S1,S1,S1 }} , {{S2,S2,S2,S2}} , {{S3,S3}} };
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
@@ -680,7 +680,7 @@ public class TwistyCoinHexahedron extends ShapeHexahedron
 
   public float[][][] getStickerAngles()
     {
-    float D = (float)(Math.PI/4);
+    float D = (float)(Math.PI/2);
     return new float[][][] { {{ 0,0,0,-D,0 }} , {{-D,-D,-D,-D}} , {{D,D}} };
     }
 
diff --git a/src/main/java/org/distorted/objectlib/objects/TwistyCoinTetrahedron.java b/src/main/java/org/distorted/objectlib/objects/TwistyCoinTetrahedron.java
index c9ad97cf..1fcb9677 100644
--- a/src/main/java/org/distorted/objectlib/objects/TwistyCoinTetrahedron.java
+++ b/src/main/java/org/distorted/objectlib/objects/TwistyCoinTetrahedron.java
@@ -713,10 +713,9 @@ public class TwistyCoinTetrahedron extends ShapeTetrahedron
 
   public float[][][] getStickerAngles()
     {
-    float D1 = (float)(Math.PI/3);
-    float D2 = (float)(Math.PI/5);
-    float D3 = (float)(Math.PI/6);
-    return new float[][][] { {{ 0,0,0,-D1,0 }} , {{D2,D2,D2}} , {{D1,D3}} };
+    float D1 = (float)(2*Math.PI/3);
+    float D2 = (float)(Math.PI/3);
+    return new float[][][] { {{ 0,0,0,-D1,0 }} , {{D2,D2,D2}} , {{D1,D2}} };
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
diff --git a/src/main/java/org/distorted/objectlib/objects/TwistyCrazy2x2.java b/src/main/java/org/distorted/objectlib/objects/TwistyCrazy2x2.java
index f3c1ea3a..02057b05 100644
--- a/src/main/java/org/distorted/objectlib/objects/TwistyCrazy2x2.java
+++ b/src/main/java/org/distorted/objectlib/objects/TwistyCrazy2x2.java
@@ -563,7 +563,7 @@ public class TwistyCrazy2x2 extends ShapeHexahedron
 
   public float[][][] getStickerAngles()
     {
-    float D = (float)(Math.PI/4);
+    float D = (float)(Math.PI/2);
     return new float[][][] { {{ 0,0,0,-D,0 }} , {{ 0,0,D }} };
     }
 
diff --git a/src/main/java/org/distorted/objectlib/objects/TwistyCrazy3x3.java b/src/main/java/org/distorted/objectlib/objects/TwistyCrazy3x3.java
index f8462d3e..0faef975 100644
--- a/src/main/java/org/distorted/objectlib/objects/TwistyCrazy3x3.java
+++ b/src/main/java/org/distorted/objectlib/objects/TwistyCrazy3x3.java
@@ -959,8 +959,8 @@ public class TwistyCrazy3x3 extends ShapeHexahedron
 
   public float[][][] getStickerAngles()
     {
-    float D1 = (float)(Math.PI/8);
-    float D2 = (float)(Math.PI/6);
+    float D1 = (float)(Math.PI/4);
+    float D2 = (float)(Math.PI/3);
     return new float[][][] { {{ 0,0,0,-D1,0 }} , {{ 0,0,0,-D2 }} , {{0,0,0,0}} , {{ 0,0,0,D2 }} , {{ 0,0,D1 }} };
     }
 
diff --git a/src/main/java/org/distorted/objectlib/objects/TwistyIvy.java b/src/main/java/org/distorted/objectlib/objects/TwistyIvy.java
index a4f9e30b..0f1046a7 100644
--- a/src/main/java/org/distorted/objectlib/objects/TwistyIvy.java
+++ b/src/main/java/org/distorted/objectlib/objects/TwistyIvy.java
@@ -438,7 +438,7 @@ public class TwistyIvy extends ShapeHexahedron
 
   public float[][][] getStickerAngles()
     {
-    float D = (float)(Math.PI/4);
+    float D = (float)(Math.PI/2);
     return new float[][][] { {{ 0,0,-D }} , {{ D,D }} };
     }
 
diff --git a/src/main/java/org/distorted/objectlib/objects/TwistyJing.java b/src/main/java/org/distorted/objectlib/objects/TwistyJing.java
index aa552d39..327ab638 100644
--- a/src/main/java/org/distorted/objectlib/objects/TwistyJing.java
+++ b/src/main/java/org/distorted/objectlib/objects/TwistyJing.java
@@ -68,21 +68,22 @@ public class TwistyJing extends ShapeTetrahedron
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
-// make the 'center' sticker artificially smaller, so that we paint over the area in the center of the face.
 
   @Override
-  public void adjustStickerCoords()
+  protected float[][][] getStickerRadii()
     {
     int type = getObjectType();
 
-    if( type==JING_3 || type==JING_5 )
+    if( type==JING_3 )
       {
-      float CENTER_CORR = (type==JING_3 ? 0.85f : 0.76f);
-      int index = (type==JING_3 ? 3 : 5);
-
-      mStickerCoords[index][0][2][0] *= CENTER_CORR;
-      mStickerCoords[index][0][2][1] *= CENTER_CORR;
+      float R = 0.06f;
+      float L = 0.16f;
+      float[][] t1 = {{ R,R,R,R }};
+      float[][] t2 = {{ R,R,L,R }};
+      return new float[][][] { t1,t1,t1,t2 };
       }
+
+    return super.getStickerRadii();
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
diff --git a/src/main/java/org/distorted/objectlib/objects/TwistyKilominx.java b/src/main/java/org/distorted/objectlib/objects/TwistyKilominx.java
index ed868fe5..96178770 100644
--- a/src/main/java/org/distorted/objectlib/objects/TwistyKilominx.java
+++ b/src/main/java/org/distorted/objectlib/objects/TwistyKilominx.java
@@ -34,17 +34,18 @@ public class TwistyKilominx extends TwistyDodecahedron
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
-// make the 'center' sticker artificially smaller, so that we paint over the area in the center of the face.
 
   @Override
-  public void adjustStickerCoords()
+  protected float[][][] getStickerRadii()
     {
     int[] numLayers = getNumLayers();
-    int index = numLayers[0]==3 ? 0:3;
-    float CENTER_CORR = 0.9f;
+    float R = 0.18f;
+    float L = 0.50f;
+    float[][] t1 = {{ R,L,R,R }};
+    float[][] t2 = {{ R,R,R,R }};
 
-    mStickerCoords[index][0][1][0] *= CENTER_CORR;
-    mStickerCoords[index][0][1][1] *= CENTER_CORR;
+    if( numLayers[0]==3 ) return new float[][][] { t1 };
+    else                  return new float[][][] { t2,t2,t2,t1 };
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
@@ -532,10 +533,11 @@ public class TwistyKilominx extends TwistyDodecahedron
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
+// we override getStickerRadii() anyway
 
   public float getStickerRadius()
     {
-    return 0.18f;
+    return 0.0f;
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
diff --git a/src/main/java/org/distorted/objectlib/objects/TwistyO2.java b/src/main/java/org/distorted/objectlib/objects/TwistyO2.java
index 3009041a..82f7c82c 100644
--- a/src/main/java/org/distorted/objectlib/objects/TwistyO2.java
+++ b/src/main/java/org/distorted/objectlib/objects/TwistyO2.java
@@ -59,7 +59,6 @@ public class TwistyO2 extends ShapeHexahedron
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
-// ditto, manually provide the sticker coordinates.
 
   @Override
   public void adjustStickerCoords()
@@ -69,16 +68,18 @@ public class TwistyO2 extends ShapeHexahedron
     final float C = 0.50f;
 
     // stickers with holes are not collapsed into one; we need to repeat this 6 times
-    float[][][] t = new float[][][] { { { A,-A},{A,A},{-A, A},{-A,-A} } , { {B,0},{-B,0} } };
-    mStickerCoords = new float[][][][] { t,t,t,t,t,t, { { { C,0},{-C,0} } } };
+    // the hole loop needs to be first so that FactorySticker draws it first; otherwise there's a
+    // slight artifact.
+    float[][][] t = new float[][][] {  {{B,0},{-B,0}} , {{ A,-A},{A,A},{-A, A},{-A,-A}} };
+    mStickerCoords = new float[][][][] { t,t,t,t,t,t, {{{ C,0},{-C,0}}} };
   }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
 
   public float[][][] getStickerAngles()
     {
-    float A = (float)(Math.PI/2);
-    float[][] t = new float[][] { {0,0,0,0},{-A,-A} };
+    float A = (float)(Math.PI*0.999f);
+    float[][] t = new float[][] { {-A,-A},{0,0,0,0} };
     return new float[][][] { t,t,t,t,t,t,{{A,A}} };
     }
 
diff --git a/src/main/java/org/distorted/objectlib/objects/TwistyPyraminxDiamond.java b/src/main/java/org/distorted/objectlib/objects/TwistyPyraminxDiamond.java
index 529e5b78..e2cd649a 100644
--- a/src/main/java/org/distorted/objectlib/objects/TwistyPyraminxDiamond.java
+++ b/src/main/java/org/distorted/objectlib/objects/TwistyPyraminxDiamond.java
@@ -51,6 +51,17 @@ public class TwistyPyraminxDiamond extends ShapeOctahedron
     super(iconMode, meta.getNumLayers()[0], quat, move, scale, meta, asset);
     }
 
+///////////////////////////////////////////////////////////////////////////////////////////////////
+
+  @Override
+  protected float[][][] getStickerRadii()
+    {
+    float R1 = 0.13f;
+    float R2 = 0.00f;
+    float R3 = 0.13f;
+    return new float[][][] { {{ R3,R3,R3,R2,R3,R3 }} , {{ R1,R1,R1 }} };
+    }
+
 ///////////////////////////////////////////////////////////////////////////////////////////////////
 
   @Override
@@ -340,17 +351,18 @@ public class TwistyPyraminxDiamond extends ShapeOctahedron
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
+// overriding getStickerRadii()
 
   public float getStickerRadius()
     {
-    return 0.12f;
+    return 0.0f;
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
 
   public float getStickerStroke()
     {
-    return isInIconMode() ? 0.20f : 0.10f;
+    return isInIconMode() ? 0.20f : 0.11f;
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
diff --git a/src/main/java/org/distorted/objectlib/objects/TwistyPyraminxDuo.java b/src/main/java/org/distorted/objectlib/objects/TwistyPyraminxDuo.java
index 3b9bc49f..92aa7642 100644
--- a/src/main/java/org/distorted/objectlib/objects/TwistyPyraminxDuo.java
+++ b/src/main/java/org/distorted/objectlib/objects/TwistyPyraminxDuo.java
@@ -53,6 +53,17 @@ public class TwistyPyraminxDuo extends ShapeTetrahedron
     super(iconMode, meta.getNumLayers()[0], quat, move, scale, meta, asset);
     }
 
+///////////////////////////////////////////////////////////////////////////////////////////////////
+
+  @Override
+  protected float[][][] getStickerRadii()
+    {
+    float R1 = 0.10f;
+    float R2 = 0.02f;
+    float R3 = 0.10f;
+    return new float[][][] { {{ R3,R3,R3,R2,R3,R3 }} , {{ R1,R1,R1 }} };
+    }
+
 ///////////////////////////////////////////////////////////////////////////////////////////////////
 
   @Override
@@ -299,10 +310,11 @@ public class TwistyPyraminxDuo extends ShapeTetrahedron
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
+// doesn't matter, we override getStickerRadii()
 
   public float getStickerRadius()
     {
-    return 0.07f;
+    return 0.0f;
     }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
diff --git a/src/main/java/org/distorted/objectlib/objects/TwistyVoid.java b/src/main/java/org/distorted/objectlib/objects/TwistyVoid.java
index 84c3e1c8..a5f456c8 100644
--- a/src/main/java/org/distorted/objectlib/objects/TwistyVoid.java
+++ b/src/main/java/org/distorted/objectlib/objects/TwistyVoid.java
@@ -448,7 +448,7 @@ public class TwistyVoid extends ShapeHexahedron
 
   public float[][][] getStickerAngles()
     {
-    float D = (float)(Math.PI/6);
+    float D = (float)(Math.PI/3);
     return new float[][][] { {{ 0,D,0 }} , {{ 0,0,0,-D }} };
     }
 
diff --git a/src/main/res/raw/coih_3_object.json b/src/main/res/raw/coih_3_object.json
index c563b9bd..8536d697 100644
--- a/src/main/res/raw/coih_3_object.json
+++ b/src/main/res/raw/coih_3_object.json
@@ -1 +1 @@
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diff --git a/src/main/res/raw/coin_3_object.json b/src/main/res/raw/coin_3_object.json
index 0328137f..c2c513c7 100644
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index f5feaf09..16c95b75 100644
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index 476325d1..77fbdb02 100644
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diff --git a/src/main/res/raw/kilo_3_object.json b/src/main/res/raw/kilo_3_object.json
index e2ce7efd..516bf4fd 100644
--- a/src/main/res/raw/kilo_3_object.json
+++ b/src/main/res/raw/kilo_3_object.json
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index c71afb52..a5e7ba96 100644
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diff --git a/src/main/res/raw/o2_2_object.json b/src/main/res/raw/o2_2_object.json
index 942ad5c1..1f740011 100644
--- a/src/main/res/raw/o2_2_object.json
+++ b/src/main/res/raw/o2_2_object.json
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diff --git a/src/main/res/raw/traj_4.dmesh b/src/main/res/raw/traj_4.dmesh
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Binary files a/src/main/res/raw/traj_4.dmesh and b/src/main/res/raw/traj_4.dmesh differ
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index 7f1dcde9..4c1abdc2 100644
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diff --git a/src/main/res/raw/void_3_object.json b/src/main/res/raw/void_3_object.json
index 8f76c4ba..af4e9aaa 100644
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