Bug 1501: Apply intersection tests for non-convex shapes to reject new CCW and non-circulcircle triangulation candidates in our Delaunay tessellator

<https://jogamp.org/bugzilla//show_bug.cgi?id=1501#c6>

The used Delaunay tessellation works well with (almost) convex shapes.
In case e.g. a glyph gets to the extremes like 'M' in FreeMono
or any other complex Chinese symbol - it may just simply happen
that the new non-circumcircle triangle point crosses the inner (hope)
or outer boundaries of the given polygon.

Applying further constraint at Loop.cut() resolves most cases
by rejecting the proposed CCW and non-circumcircle triangle candidate
if its new two line-segments intersects with the original polygon.

This results in mostly proper rendered Chinese fonts and also
FreeMono is now readable - overal remaining bugs in Glyphs is low.

+++

Of course, this intersection test is costly around >= O(log(n)*n) costs,
practically adding a measured ~65% processing time.
E.g. for FontView01 using FreeSerif.ttf
- orig total took 1430.817638ms, per-glyph 0.2236ms, glyphs 6399
- fix  total took 2377.337359ms, per-glyph 0.371517ms, glyphs 6399

Pure Glyph/Shape instantiation shows > 2x costs:
 750 ms 100% convex (fake)
1875 ms   0% convex (fake)
1870 ms  13% convex 824/6399

+++

Hence it is desired to either
(1) Manually mark a polygon non-convex to add described intersection test for accuracy.
    Also may be used to just drop the additional costs despite the lack of correctness.

PROVIDED

(2) Determine non-convex nature of a polygon with a and overall less expensive algorithm.
    If considerably cheaper, this could reduce O(log(n) * n) -> O(n) or even O(log n).

Added convex/non-convex classification while ignoring off-curve points,
but only ~13% of FreeSerif is pure convex,
hence there is no benefit with this classification type.

It might be desired to attempt other classes, i.e.
being rendered in non-convex mode w/o intersection tests.
See
- GENERALIZED DELAUNAY TRIANGULATIONS OF NON-CONVEX DOMAINS
  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/28782/0000614.pdf;sequence=1

- https://en.wikipedia.org/wiki/List_of_self-intersecting_polygons
- https://en.wikipedia.org/wiki/Complex_polygon

3 files changed, 123 insertions, 26 deletions

diff --git a/src/jogl/classes/com/jogamp/graph/curve/OutlineShape.java b/src/jogl/classes/com/jogamp/graph/curve/OutlineShape.java
index d481af24c..18e7328ce 100644
--- a/src/jogl/classes/com/jogamp/graph/curve/OutlineShape.java
+++ b/src/jogl/classes/com/jogamp/graph/curve/OutlineShape.java
@@ -1,5 +1,5 @@
 /**
- * Copyright 2010-2023 JogAmp Community. All rights reserved.
+ * Copyright 2010-2024 JogAmp Community. All rights reserved.
  *
  * Redistribution and use in source and binary forms, with or without modification, are
  * permitted provided that the following conditions are met:
@@ -135,15 +135,20 @@ public final class OutlineShape implements Comparable<OutlineShape> {
     /** Initial {@link #getSharpness()} value, which can be modified via {@link #setSharpness(float)}. */
     public static final float DEFAULT_SHARPNESS = 0.5f;
 
-    public static final int DIRTY_BOUNDS = 1 << 0;
+    private static final int DIRTY_BOUNDS = 1 << 0;
     /**
      * Modified shape, requires to update the vertices and triangles, here: vertices.
      */
-    public static final int DIRTY_VERTICES  = 1 << 1;
+    private static final int DIRTY_VERTICES  = 1 << 1;
     /**
      * Modified shape, requires to update the vertices and triangles, here: triangulation.
      */
-    public static final int DIRTY_TRIANGLES  = 1 << 2;
+    private static final int DIRTY_TRIANGLES  = 1 << 2;
+    /**
+     * Modified shape, requires to update the convex determination
+     */
+    private static final int DIRTY_CONVEX  = 1 << 3;
+    private static final int OVERRIDE_CONVEX  = 1 << 4;
 
     /** The list of {@link Outline}s that are part of this
      *  outline shape.
@@ -154,6 +159,7 @@ public final class OutlineShape implements Comparable<OutlineShape> {
     private final ArrayList<Triangle> triangles;
     private final ArrayList<Vertex> vertices;
     private int addedVerticeCount;
+    private boolean convexFlag;
 
     private VerticesState outlineState;
 
@@ -181,6 +187,7 @@ public final class OutlineShape implements Comparable<OutlineShape> {
         this.triangles = new ArrayList<Triangle>();
         this.vertices = new ArrayList<Vertex>();
         this.addedVerticeCount = 0;
+        this.convexFlag = true;
         this.dirtyBits = 0;
         this.sharpness = DEFAULT_SHARPNESS;
     }
@@ -214,6 +221,7 @@ public final class OutlineShape implements Comparable<OutlineShape> {
         vertices.clear();
         triangles.clear();
         addedVerticeCount = 0;
+        convexFlag = true;
         dirtyBits = 0;
     }
 
@@ -221,7 +229,7 @@ public final class OutlineShape implements Comparable<OutlineShape> {
     public final void clearCache() {
         vertices.clear();
         triangles.clear();
-        dirtyBits |= DIRTY_TRIANGLES | DIRTY_VERTICES;
+        dirtyBits |= DIRTY_TRIANGLES | DIRTY_VERTICES | DIRTY_CONVEX;
     }
 
     /** Returns the number of {@link Outline}s. */
@@ -254,6 +262,50 @@ public final class OutlineShape implements Comparable<OutlineShape> {
     }
 
     /**
+     * Returns cached or computed result whether all {@code polyline}s of {@link #getOutline(int)} are of convex shape, see {@link Outline#isConvex()}.
+     * <p>
+     * A polyline with less than 3 elements is marked convex for simplicity,
+     * since a non-convex complex shape may need to pass intersection testing within triangulation.
+     * </p>
+     * <p>
+     * The result is cached.
+     * </p>
+     * @see #setOverrideConvex(boolean)
+     * @see #clearOverrideConvex()
+     */
+    public boolean isConvex() {
+        if( 0 == ( OVERRIDE_CONVEX & dirtyBits ) ) {
+            if( 0 != ( DIRTY_CONVEX & dirtyBits ) ) {
+                convexFlag = true;
+                final int sz = this.getOutlineCount();
+                for(int i=0; i<sz && convexFlag; ++i) {
+                    convexFlag = getOutline(i).isConvex();
+                }
+                dirtyBits &= ~DIRTY_CONVEX;
+            }
+        }
+        return convexFlag;
+    }
+    /**
+     * Overrides {@link #isConvex()} using the given value instead of computing via {@link Outline#isConvex()}.
+     * @see #clearOverrideConvex()
+     * @see #isConvex()
+     */
+    public void setOverrideConvex(final boolean convex) {
+        dirtyBits |= OVERRIDE_CONVEX;
+        convexFlag = convex;
+    }
+    /**
+     * Clears the {@link #isConvex()} override done by {@link #setOverrideConvex(boolean)}
+     * @see #setOverrideConvex(boolean)
+     * @see #isConvex()
+     */
+    public void clearOverrideConvex() {
+        dirtyBits &= ~OVERRIDE_CONVEX;
+        dirtyBits |= DIRTY_CONVEX;
+    }
+
+    /**
      * Add a new empty {@link Outline}
      * to the end of this shape's outline list.
      * <p>If the {@link #getLastOutline()} is empty already, no new one will be added.</p>
@@ -308,7 +360,7 @@ public final class OutlineShape implements Comparable<OutlineShape> {
                     bbox.resize(outline.getBounds());
                 }
                 // vertices.addAll(outline.getVertices()); // FIXME: can do and remove DIRTY_VERTICES ?
-                dirtyBits |= DIRTY_TRIANGLES | DIRTY_VERTICES;
+                dirtyBits |= DIRTY_TRIANGLES | DIRTY_VERTICES | DIRTY_CONVEX;
                 return;
             }
         }
@@ -316,7 +368,7 @@ public final class OutlineShape implements Comparable<OutlineShape> {
         if( 0 == ( dirtyBits & DIRTY_BOUNDS ) ) {
             bbox.resize(outline.getBounds());
         }
-        dirtyBits |= DIRTY_TRIANGLES | DIRTY_VERTICES;
+        dirtyBits |= DIRTY_TRIANGLES | DIRTY_VERTICES | DIRTY_CONVEX;
     }
 
     /**
@@ -351,7 +403,7 @@ public final class OutlineShape implements Comparable<OutlineShape> {
             throw new NullPointerException("outline is null");
         }
         outlines.set(position, outline);
-        dirtyBits |= DIRTY_BOUNDS | DIRTY_TRIANGLES | DIRTY_VERTICES;
+        dirtyBits |= DIRTY_BOUNDS | DIRTY_TRIANGLES | DIRTY_VERTICES | DIRTY_CONVEX;
     }
 
     /**
@@ -362,7 +414,7 @@ public final class OutlineShape implements Comparable<OutlineShape> {
      * @throws IndexOutOfBoundsException if position is out of range (position < 0 || position >= getOutlineNumber())
      */
     public final Outline removeOutline(final int position) throws IndexOutOfBoundsException {
-        dirtyBits |= DIRTY_BOUNDS | DIRTY_TRIANGLES | DIRTY_VERTICES;
+        dirtyBits |= DIRTY_BOUNDS | DIRTY_TRIANGLES | DIRTY_VERTICES | DIRTY_CONVEX;
         return outlines.remove(position);
     }
 
@@ -396,7 +448,7 @@ public final class OutlineShape implements Comparable<OutlineShape> {
             bbox.resize(v.getCoord());
         }
         // vertices.add(v); // FIXME: can do and remove DIRTY_VERTICES ?
-        dirtyBits |= DIRTY_TRIANGLES | DIRTY_VERTICES;
+        dirtyBits |= DIRTY_TRIANGLES | DIRTY_VERTICES | DIRTY_CONVEX;
     }
 
     /**
@@ -412,7 +464,7 @@ public final class OutlineShape implements Comparable<OutlineShape> {
         if( 0 == ( dirtyBits & DIRTY_BOUNDS ) ) {
             bbox.resize(v.getCoord());
         }
-        dirtyBits |= DIRTY_TRIANGLES | DIRTY_VERTICES;
+        dirtyBits |= DIRTY_TRIANGLES | DIRTY_VERTICES | DIRTY_CONVEX;
     }
 
     /**
@@ -516,7 +568,7 @@ public final class OutlineShape implements Comparable<OutlineShape> {
      */
     public final void closeLastOutline(final boolean closeTail) {
         if( getLastOutline().setClosed( closeTail ) ) {
-            dirtyBits |= DIRTY_TRIANGLES | DIRTY_VERTICES;
+            dirtyBits |= DIRTY_TRIANGLES | DIRTY_VERTICES | DIRTY_CONVEX;
         }
     }
 
@@ -956,6 +1008,9 @@ public final class OutlineShape implements Comparable<OutlineShape> {
         return vertices;
     }
 
+    public static void printPerf(final PrintStream out) {
+        // jogamp.graph.curve.tess.Loop.printPerf(out);
+    }
     private void triangulateImpl() {
         if( 0 < outlines.size() ) {
             sortOutlines();
@@ -963,6 +1018,7 @@ public final class OutlineShape implements Comparable<OutlineShape> {
 
             triangles.clear();
             final Triangulator triangulator2d = Triangulation.create();
+            triangulator2d.setConvexShape( isConvex() );
             for(int index = 0; index<outlines.size(); index++) {
                 triangulator2d.addCurve(triangles, outlines.get(index), sharpness);
             }
@@ -997,6 +1053,12 @@ public final class OutlineShape implements Comparable<OutlineShape> {
         }
         if(Region.DEBUG_INSTANCE) {
             System.err.println("OutlineShape.getTriangles().X: "+triangles.size()+", updated "+updated);
+            if( updated ) {
+                int i=0;
+                for(final Triangle t : triangles) {
+                    System.err.printf("- [%d]: %s%n", i++, t);
+                }
+            }
         }
         return triangles;
     }
@@ -1117,5 +1179,4 @@ public final class OutlineShape implements Comparable<OutlineShape> {
             }
         }
     }
-
 }
diff --git a/src/jogl/classes/com/jogamp/graph/curve/tess/Triangulator.java b/src/jogl/classes/com/jogamp/graph/curve/tess/Triangulator.java
index 20fe9bfd9..eaebde076 100644
--- a/src/jogl/classes/com/jogamp/graph/curve/tess/Triangulator.java
+++ b/src/jogl/classes/com/jogamp/graph/curve/tess/Triangulator.java
@@ -49,6 +49,9 @@ import com.jogamp.graph.geom.Triangle;
  */
 public interface Triangulator {
 
+    /** Mark the to be triangulated shape convex or non-convex, causing further processing costs if non-convex like intersection tests. Default is assuming a convex shape. */
+    public void setConvexShape(boolean convex);
+
     /**
      * Add a curve to the list of Outlines
      * describing the shape
diff --git a/src/jogl/classes/com/jogamp/graph/geom/Outline.java b/src/jogl/classes/com/jogamp/graph/geom/Outline.java
index 1b36bfc24..8c39004a0 100644
--- a/src/jogl/classes/com/jogamp/graph/geom/Outline.java
+++ b/src/jogl/classes/com/jogamp/graph/geom/Outline.java
@@ -1,5 +1,5 @@
 /**
- * Copyright 2010-2023 JogAmp Community. All rights reserved.
+ * Copyright 2010-2024 JogAmp Community. All rights reserved.
  *
  * Redistribution and use in source and binary forms, with or without modification, are
  * permitted provided that the following conditions are met:
@@ -57,7 +57,11 @@ public class Outline implements Comparable<Outline> {
     private final AABBox bbox;
     private boolean dirtyBBox;
     private Winding winding;
-    private boolean dirtyWinding;
+    private boolean convexFlag;
+    private int dirtyBits;
+
+    private static final int DIRTY_WINDING = 1 << 0;
+    private static final int DIRTY_CONVEX  = 1 << 0;
 
     /**Create an outline defined by control vertices.
      * An outline can contain off Curve vertices which define curved
@@ -69,7 +73,8 @@ public class Outline implements Comparable<Outline> {
         bbox = new AABBox();
         dirtyBBox = false;
         winding = Winding.CCW;
-        dirtyWinding = false;
+        convexFlag = false;
+        dirtyBits = 0;
     }
 
     /**
@@ -79,7 +84,8 @@ public class Outline implements Comparable<Outline> {
         final int count = src.vertices.size();
         vertices = new ArrayList<Vertex>(count);
         winding = Winding.CCW;
-        dirtyWinding = true;
+        convexFlag = false;
+        dirtyBits = DIRTY_WINDING | DIRTY_CONVEX;
         for(int i=0; i<count; i++) {
             vertices.add( src.vertices.get(i).copy() );
         }
@@ -99,9 +105,15 @@ public class Outline implements Comparable<Outline> {
     public Outline(final Outline src, final Winding enforce) {
         final int count = src.vertices.size();
         vertices = new ArrayList<Vertex>(count);
-        final Winding had_winding = src.getWinding();;
+        final Winding had_winding = src.getWinding();
         winding = had_winding;
-        dirtyWinding = false;
+        if( 0 == ( src.dirtyBits & DIRTY_CONVEX ) ) {
+            convexFlag = src.convexFlag;
+            dirtyBits = 0;
+        } else {
+            convexFlag = false;
+            dirtyBits = DIRTY_CONVEX;
+        }
         if( enforce != had_winding ) {
             for(int i=count-1; i>=0; --i) {
                 vertices.add( src.vertices.get(i).copy() );
@@ -138,11 +150,14 @@ public class Outline implements Comparable<Outline> {
     }
 
     /**
-     * Compute the winding of the {@link #getLastOutline()} using the {@link VectorUtil#area2d(ArrayList)} function over all of its vertices.
+     * Returns the cached or computed winding of this {@link Outline}s {@code polyline} using {@link VectorUtil#area(ArrayList)}.
+     * <p>
+     * The result is cached.
+     * </p>
      * @return {@link Winding#CCW} or {@link Winding#CW}
      */
     public final Winding getWinding() {
-        if( !dirtyWinding ) {
+        if( 0 == ( dirtyBits & DIRTY_WINDING ) ) {
             return winding;
         }
         final int count = getVertexCount();
@@ -151,10 +166,29 @@ public class Outline implements Comparable<Outline> {
         } else {
             winding = VectorUtil.getWinding( getVertices() );
         }
-        dirtyWinding = false;
+        dirtyBits &= ~DIRTY_WINDING;
         return winding;
     }
 
+    /**
+     * Returns the cached or computed result whether this {@link Outline}s {@code polyline} has a convex shape using {@link VectorUtil#isConvex(ArrayList, boolean)}.
+     * <p>
+     * A polyline with less than 3 elements is marked convex for simplicity,
+     * since a non-convex complex shape may need to pass intersection testing within triangulation.
+     * </p>
+     * <p>
+     * The result is cached.
+     * </p>
+     */
+    public boolean isConvex() {
+        if( 0 == ( dirtyBits & DIRTY_CONVEX ) ) {
+            return convexFlag;
+        }
+        convexFlag = VectorUtil.isConvex1( getVertices(), true );
+        dirtyBits &= ~DIRTY_CONVEX;
+        return convexFlag;
+    }
+
     public final int getVertexCount() {
         return vertices.size();
     }
@@ -183,7 +217,7 @@ public class Outline implements Comparable<Outline> {
         if(!dirtyBBox) {
             bbox.resize(vertex.getCoord());
         }
-        dirtyWinding = true;
+        dirtyBits |= DIRTY_WINDING | DIRTY_CONVEX;
     }
 
     /** Replaces the {@link Vertex} element at the given {@code position}.
@@ -200,7 +234,7 @@ public class Outline implements Comparable<Outline> {
         }
         vertices.set(position, vertex);
         dirtyBBox = true;
-        dirtyWinding = true;
+        dirtyBits |= DIRTY_WINDING | DIRTY_CONVEX;
     }
 
     public final Vertex getVertex(final int index){
@@ -219,7 +253,7 @@ public class Outline implements Comparable<Outline> {
      */
     public final Vertex removeVertex(final int position) throws IndexOutOfBoundsException {
         dirtyBBox = true;
-        dirtyWinding = true;
+        dirtyBits |= DIRTY_WINDING | DIRTY_CONVEX;
         return vertices.remove(position);
     }
 
@@ -372,5 +406,4 @@ public class Outline implements Comparable<Outline> {
             out.printf("- OL[%d]: %s%n", vi, v);
         }
     }
-
 }