Add TriangleFunctions.innerHexagon

Author: dr-jts

modules/app/src/main/java/org/locationtech/jtstest/function/TriangleFunctions.java

@@ -11,7 +11,9 @@
  */
 package org.locationtech.jtstest.function;
 
+import org.locationtech.jts.algorithm.Orientation;
 import org.locationtech.jts.geom.Coordinate;
+import org.locationtech.jts.geom.CoordinateArrays;
 import org.locationtech.jts.geom.Geometry;
 import org.locationtech.jts.geom.GeometryFactory;
 import org.locationtech.jts.geom.LineSegment;
@@ -112,12 +114,65 @@ public static Geometry angleBisectors(Geometry g)
     return geomFact.createMultiLineString(line);
   }
 
-
   private static Coordinate[] trianglePts(Geometry g)
   {
-    Coordinate[] pts = g.getCoordinates();
+    Coordinate[] pts = CoordinateArrays.copyDeep(g.getCoordinates());
+    if (Orientation.isCCW(pts)) {
+      CoordinateArrays.reverse(pts);
+    }
     if (pts.length < 3)
       throw new IllegalArgumentException("Input geometry must have at least 3 points");
     return pts;
   }
+  
+  /**
+   * Constructs the inner hexagon of a triangle, 
+   * created by intersecting the chords of the triangle running from each vertex to
+   * points a distance of (side / nSections) from each end of the opposite side.
+   * 
+   * When the parameter is 3 this provides a visualization of
+   * Marion Walter's Theorem (https://en.wikipedia.org/wiki/Marion_Walter#Recognition).
+   * The theorem states that if each side of an arbitrary triangle is trisected 
+   * and lines are drawn to the opposite vertices, 
+   * the area of the hexagon created in the middle is one-tenth the area of the original triangle.
+   * 
+   * @param g a triangle
+   * @param nSections the number of sections to divide each side into (>= 3)
+   * @return the inner hexagon
+   */
+  public static Geometry innerHexagon(Geometry g, int nSections) {
+    Coordinate[] pts = trianglePts(g);
+    //-- return empty polygon for degenerate cases
+    if (nSections < 3) {
+      return g.getFactory().createEmpty(2);
+    }
+    
+    LineSegment side0 = new LineSegment(pts[0], pts[1]);
+    LineSegment side1 = new LineSegment(pts[1], pts[2]);
+    LineSegment side2 = new LineSegment(pts[2], pts[0]);
+    
+    double frac = 1.0 / nSections;
+    LineSegment chord0a = chord(pts[0], side1, frac);
+    LineSegment chord0b = chord(pts[0], side1, 1.0 - frac);
+    LineSegment chord1a = chord(pts[1], side2, frac);
+    LineSegment chord1b = chord(pts[1], side2, 1.0 - frac);
+    LineSegment chord2a = chord(pts[2], side0, frac);
+    LineSegment chord2b = chord(pts[2], side0, 1.0 - frac);
+    
+    Coordinate[] hexPts = new Coordinate[7];
+    hexPts[0] = chord0a.intersection(chord1b);
+    hexPts[1] = chord0a.intersection(chord2b);
+    hexPts[2] = chord1a.intersection(chord2b);
+    hexPts[3] = chord1a.intersection(chord0b);
+    hexPts[4] = chord2a.intersection(chord0b);
+    hexPts[5] = chord2a.intersection(chord1b);
+    hexPts[6] = hexPts[0].copy();
+    
+    return g.getFactory().createPolygon(hexPts);
+  }
+
+  private static LineSegment chord(Coordinate apex, LineSegment side, double frac) {
+    Coordinate opp = side.pointAlong(frac);
+    return new LineSegment(apex, opp);
+  }
 }