fix: 2D polygon volume algorithm (#2811)

Co-authored-by: Octavia Togami <otogami@gradle.com>

Author: TiagoFar78

worldedit-core/src/main/java/com/sk89q/worldedit/regions/Polygonal2DRegion.java

@@ -19,15 +19,14 @@
 
 package com.sk89q.worldedit.regions;
 
+import com.google.common.math.IntMath;
 import com.sk89q.worldedit.math.BlockVector2;
 import com.sk89q.worldedit.math.BlockVector3;
 import com.sk89q.worldedit.regions.iterator.FlatRegion3DIterator;
 import com.sk89q.worldedit.regions.iterator.FlatRegionIterator;
 import com.sk89q.worldedit.util.formatting.text.TranslatableComponent;
 import com.sk89q.worldedit.world.World;
 
-import java.math.BigDecimal;
-import java.math.RoundingMode;
 import java.util.ArrayList;
 import java.util.Collections;
 import java.util.Iterator;
@@ -220,11 +219,37 @@ public BlockVector3 getMaximumPoint() {
 
     @Override
     public long getVolume() {
+        if (points.size() <= 2) {
+            return 0;
+        }
+
+        long concreteArea = concreteArea();
+        int b = boundaryPoints();
+        long i = interiorPoints(concreteArea, b);
+        long latticeArea = i + b;
+
+        return latticeArea * (maxY - minY + 1);
+    }
+
+    private int boundaryPoints() {
+        int j = points.size() - 1;
+        int boundaryPoints = 0;
+        for (int i = 0; i < points.size(); i++) {
+            int x = Math.abs(points.get(i).x() - points.get(j).x());
+            int z = Math.abs(points.get(i).z() - points.get(j).z());
+            boundaryPoints += IntMath.gcd(x, z);
+            j = i;
+        }
+
+        return boundaryPoints;
+    }
+
+    // Trapezoid formula
+    private long concreteArea() {
         long area = 0;
-        int i;
         int j = points.size() - 1;
 
-        for (i = 0; i < points.size(); ++i) {
+        for (int i = 0; i < points.size(); i++) {
             BlockVector2 iPoint = points.get(i);
             BlockVector2 jPoint = points.get(j);
             long x = jPoint.x() + (long) iPoint.x();
@@ -233,11 +258,12 @@ public long getVolume() {
             j = i;
         }
 
-        return BigDecimal.valueOf(area)
-                .multiply(BigDecimal.valueOf(0.5))
-                .abs()
-                .setScale(0, RoundingMode.FLOOR)
-                .longValue() * (maxY - minY + 1);
+        return Math.abs(area) / 2;
+    }
+
+    // Pick's theorem
+    private long interiorPoints(long concreteArea, long boundaryPoints) {
+        return concreteArea - boundaryPoints / 2 + 1;
     }
 
     @Override

worldedit-core/src/test/java/com/sk89q/worldedit/regions/Polygonal2DRegionTest.java

@@ -0,0 +1,90 @@
+/*
+ * WorldEdit, a Minecraft world manipulation toolkit
+ * Copyright (C) sk89q <http://www.sk89q.com>
+ * Copyright (C) WorldEdit team and contributors
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+package com.sk89q.worldedit.regions;
+
+import com.sk89q.worldedit.math.BlockVector2;
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.Arguments;
+import org.junit.jupiter.params.provider.MethodSource;
+
+import java.util.ArrayList;
+import java.util.List;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+public class Polygonal2DRegionTest {
+
+    @ParameterizedTest
+    @MethodSource("areaTestData")
+    void testArea(int[][] coordinates, long expectedVolume) {
+        List<BlockVector2> points = toPoints(coordinates);
+        Polygonal2DRegion region = new Polygonal2DRegion(null, points, 0, 0);
+
+        assertEquals(expectedVolume, region.getVolume());
+    }
+
+    static List<Arguments> areaTestData() {
+        return List.of(
+                Arguments.of(new int[][]{{0, 0}, {0, 1}, {1, 1}, {1, 0}}, 4), // square
+                Arguments.of(new int[][]{{0, 0}, {2, 2}, {2, 0}}, 6), // triangle
+                Arguments.of(new int[][]{{6, 3}, {6, 1}, {0, 0}}, 10), // polygon with separated parts
+                Arguments.of(new int[][]{{-1, 1}, {4, 1}, {4, -3}, {-1, -3}}, 30), // x < 0
+                Arguments.of(new int[][]{
+                        {0, 9}, {6, 9}, {6, 0}, {1, 2}, {4, 4}, {3, 7}, {0, 5},
+                }, 47), // concave
+                Arguments.of(new int[][]{
+                        {0, 4}, {2, 6}, {4, 6}, {6, 4}, {6, 2}, {4, 0}, {2, 0}, {0, 2},
+                }, 37), // octagon
+                Arguments.of(new int[][]{
+                        {0, 0}, {2, 2}, {2, 4}, {0, 6}, {6, 6}, {4, 4}, {4, 2}, {6, 0},
+                }, 33), // hourglass
+                Arguments.of(new int[][]{
+                        {0, 5}, {11, 5}, {11, 0}, {9, 0}, {9, 4}, {7, 4}, {7, 1}, {6, 1},
+                        {6, 2}, {4, 2}, {4, 1}, {3, 1}, {3, 0}, {1, 0}, {1, 3}, {0, 3},
+                }, 60), // checks if new direction is well assigned
+                Arguments.of(new int[][]{
+                        {0, 5}, {2, 3}, {5, 3}, {7, 1}, {0, 1},
+                }, 24), // horizontal and downwards
+                Arguments.of(new int[][]{
+                        {0, 0}, {2, 2}, {4, 2}, {6, 4}, {6, 0},
+                }, 21), // horizontal and upwards
+                Arguments.of(new int[][]{
+                        {0, 5}, {3, 5}, {2, 3}, {5, 3}, {7, 5}, {7, 1}, {0, 1},
+                }, 34), // horizontal with upwards and downwards
+                Arguments.of(new int[][]{
+                        {0, 5}, {3, 5}, {2, 3}, {4, 3}, {5, 3}, {7, 5}, {7, 1}, {0, 1},
+                }, 34), // horizontal, upwards, downwards, redundant point
+                Arguments.of(new int[][]{
+                        {1, 3}, {3, 3}, {4, 5}, {6, 8}, {7, 6}, {9, 6}, {12, 8}, {11, 6}, {11, 4},
+                        {10, 2}, {8, 0}, {6, 1}, {9, 4}, {6, 3}, {4, 1}, {3, 0}, {1, 1},
+                }, 55) // complex polygon
+        );
+    }
+
+    private static List<BlockVector2> toPoints(int[]... coordinates) {
+        List<BlockVector2> points = new ArrayList<>();
+        for (int[] coordinate : coordinates) {
+            points.add(BlockVector2.at(coordinate[0], coordinate[1]));
+        }
+
+        return points;
+    }
+
+}