Merge pull request #25 from ref-humbold/convex-hull

Convex hull with Graham's scan

Author: ref-humbold

src/main/java/algolib/geometry/dim2/ConvexHull.java

@@ -1,10 +1,11 @@
 package algolib.geometry.dim2;
 
 import java.util.ArrayList;
-import java.util.Collections;
+import java.util.Comparator;
 import java.util.List;
+import java.util.stream.Collectors;
 
-/** Algorithm for convex hull in 2D (monotone chain). */
+/** Algorithm for convex hull in 2D (Graham's scan). */
 public final class ConvexHull
 {
     /**
@@ -17,38 +18,29 @@ public static List<Point2D> findConvexHull(List<Point2D> points)
         if(points.size() < 3)
             return List.of();
 
-        List<Point2D> sorted = new ArrayList<>(points);
+        Point2D minPoint = points.stream()
+                                 .min(Comparator.comparingDouble((Point2D pt) -> pt.y)
+                                                .thenComparingDouble(pt -> pt.x))
+                                 .orElseThrow();
+        Vector2D moving = Vector2D.between(Point2D.of(0, 0), minPoint);
+        List<Point2D> anglePoints = points.stream()
+                                          .map(pt -> Geometry2D.translate(pt, moving.negate()))
+                                          .collect(Collectors.toCollection(ArrayList::new));
 
-        Geometry2D.sortByX(sorted);
+        Geometry2D.sortByAngle(anglePoints);
 
-        List<Point2D> lowerHull = createHalfHull(sorted);
-
-        Collections.reverse(sorted);
-
-        List<Point2D> upperHull = createHalfHull(sorted);
-
-        lowerHull.remove(lowerHull.size() - 1);
-        upperHull.remove(upperHull.size() - 1);
-        lowerHull.addAll(upperHull);
-        return lowerHull;
-    }
-
-    // Computes half of convex hull for given points.
-    private static List<Point2D> createHalfHull(List<Point2D> points)
-    {
         List<Point2D> hull = new ArrayList<>();
 
-        for(Point2D pt : points)
+        for(Point2D pt : anglePoints)
         {
             while(hull.size() > 1
-                          && crossProduct(hull.get(hull.size() - 2), hull.get(hull.size() - 1), pt)
-                                     >= 0)
+                    && crossProduct(hull.get(hull.size() - 2), hull.get(hull.size() - 1), pt) >= 0)
                 hull.remove(hull.size() - 1);
 
             hull.add(pt);
         }
 
-        return hull;
+        return hull.stream().map(pt -> Geometry2D.translate(pt, moving)).toList();
     }
 
     private static double crossProduct(Point2D pt1, Point2D pt2, Point2D pt3)

src/test/java/algolib/geometry/dim2/ConvexHullTest.java

@@ -4,7 +4,7 @@
 import org.assertj.core.api.Assertions;
 import org.junit.jupiter.api.Test;
 
-// Tests: Algorithm for convex hull in 2D (monotone chain).
+// Tests: Algorithm for convex hull in 2D (Graham's scan).
 public class ConvexHullTest
 {
     @Test
@@ -55,9 +55,9 @@ public void findConvexHull_ThenPointsInHull()
 
         // then
         Assertions.assertThat(result)
-                  .containsExactly(Point2D.of(-8, -7), Point2D.of(-1, -8), Point2D.of(3, -6),
-                                   Point2D.of(6, -4), Point2D.of(10, 2), Point2D.of(5, 9),
-                                   Point2D.of(-5, 10), Point2D.of(-7, 7));
+                  .containsExactly(Point2D.of(-1, -8), Point2D.of(3, -6), Point2D.of(6, -4),
+                                   Point2D.of(10, 2), Point2D.of(5, 9), Point2D.of(-5, 10),
+                                   Point2D.of(-7, 7), Point2D.of(-8, -7));
     }
 
     @Test