## Gift-Wrap Convex Hull Bounding Polygon

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### Gift-Wrap Convex Hull Bounding Polygon

I ported a Java implementation of the gift-wrap algorithm to LibGDX. This basically takes a cloud of points (which could consist in a set of Box2D fixtures, for example) and it generates a bounding polygon that is a convex hull (with all the useful inherent properties of non-concave polygons).

Enjoy Code: Select all
`Array<Array<Vector2>> polygons; // e.g. existing Box2D fixturesArray<Vector2> pointsCloud= new Array<Vector2>(polygons.size * 3); // capacity initialization, assuming 3 vertices per polygon (triangles)for (int j = 0; j < polygons.size; j++) {    Array<Vector2> polygon = polygons.get(j);    for (int i = 0; i < polygon.size; i++) {        Vector2 point = polygon.get(i);        boolean pointAlreadyInCloud = false;        for (int k = 0; k < pointsCloud.size; k++) {            Vector2 pointInCloud = pointsCloud.get(k);            if (pointInCloud.x == point.x && pointInCloud.y == point.y) {                pointAlreadyInCloud = true;                break;            }        }        if (!pointAlreadyInCloud)                pointsCloud.add(point);    }}Array<Vector2> convexHull = BoundingPolygon.createGiftWrapConvexHull(pointsCloud);`

Code: Select all
`import com.badlogic.gdx.math.Vector2;import com.badlogic.gdx.utils.Array;public class BoundingPolygon {   /**    * Find the convex hull of a point cloud using "Gift-wrap" algorithm - start    * with an external point, and walk around the outside edge by testing    * angles. Runs in O(N*S) time where S is number of sides of resulting    * polygon. Worst case: point cloud is all vertices of convex polygon ->    * O(N^2). There may be faster algorithms to do this, should you need one -    * this is just the simplest. You can get O(N log N) expected time if you    * try, I think, and O(N) if you restrict inputs to simple polygons. Returns    * null if number of vertices passed is less than 3. Results should be    * passed through convex decomposition afterwards to ensure that each shape    * has few enough points to be used in Box2d. May be buggy with colinear    * points on hull, but we check angle with an equality resolver that always    * picks the longer edge (this seems to be working, but it sometimes creates    * an extra edge along a line).    */   public static Array<Vector2> createGiftWrapConvexHull(         Array<Vector2> points) {      assert (points.size > 2);      int[] edgeList = new int[points.size];      int numEdges = 0;      float minY = Float.MAX_VALUE;      int minYIndex = points.size;      for (int i = 0; i < points.size; ++i) {         Vector2 point = points.get(i);         if (point.y < minY) {            minY = point.y;            minYIndex = i;         }      }      int startIndex = minYIndex;      int winIndex = -1;      float dx = -1.0f;      float dy = 0.0f;      while (winIndex != minYIndex) {         float newdx = 0.0f;         float newdy = 0.0f;         float maxDot = -2.0f;         Vector2 point2 = points.get(startIndex);         for (int i = 0; i < points.size; ++i) {            if (i == startIndex)               continue;            Vector2 point1 = points.get(i);            newdx = point1.x - point2.x;            newdy = point1.y - point2.y;            float nrm = (float) Math.sqrt(newdx * newdx + newdy * newdy);            nrm = (nrm == 0.0f) ? 1.0f : nrm;            newdx /= nrm;            newdy /= nrm;            float newDot = newdx * dx + newdy * dy;            if (newDot > maxDot) {               maxDot = newDot;               winIndex = i;            }         }         edgeList[numEdges] = winIndex;         numEdges++;         Vector2 point3 = points.get(winIndex);         dx = point3.x - point2.x;         dy = point3.y - point2.y;         float nrm = (float) Math.sqrt(dx * dx + dy * dy);         nrm = (nrm == 0.0f) ? 1.0f : nrm;         dx /= nrm;         dy /= nrm;         startIndex = winIndex;      }      Array<Vector2> polygon = new Array<Vector2>(numEdges);      for (int i = 0; i < numEdges; i++) {         Vector2 point4 = points.get(edgeList[i]);         polygon.add(point4.cpy());      }      if (polygon.size <= 3)         return polygon;      float tolerance = 2.0f / 180.0f * (float) Math.PI; // 2 degrees      Array<Integer> toRemove = null;      for (int i = 0; i < polygon.size; ++i) {         int lower = (i == 0) ? (polygon.size - 1) : (i - 1);         int middle = i;         int upper = (i == polygon.size - 1) ? (0) : (i + 1);         Vector2 pointMiddle = polygon.get(middle);         Vector2 pointLower = polygon.get(lower);         Vector2 pointUpper = polygon.get(upper);         float dx0 = pointMiddle.x - pointLower.x;         float dy0 = pointMiddle.y - pointLower.y;         float dx1 = pointUpper.x - pointMiddle.x;         float dy1 = pointUpper.y - pointMiddle.y;         float norm0 = (float) Math.sqrt(dx0 * dx0 + dy0 * dy0);         float norm1 = (float) Math.sqrt(dx1 * dx1 + dy1 * dy1);         if (!(norm0 > 0.0f && norm1 > 0.0f)               && (toRemove == null || (polygon.size - toRemove.size) > 3)) {            // Merge identical points            if (toRemove == null)               toRemove = new Array<Integer>();            toRemove.add(i);         }         dx0 /= norm0;         dy0 /= norm0;         dx1 /= norm1;         dy1 /= norm1;         float cross = dx0 * dy1 - dx1 * dy0;         float dot = dx0 * dx1 + dy0 * dy1;         if (Math.abs(cross) < tolerance && dot > 0               && (toRemove == null || (polygon.size - toRemove.size) > 3)) {            if (toRemove == null)               toRemove = new Array<Integer>();            toRemove.add(i);         }      }      if (toRemove == null || toRemove.size == 0)         return polygon;      for (int i = 0; i < toRemove.size; ++i) {         int index = toRemove.get(i);         polygon.removeIndex(index - i);      }      return polygon;   }}`
daniel.weck

Posts: 57
Joined: Mon Mar 21, 2011 8:18 am

### Re: Gift-Wrap Convex Hull Bounding Polygon

Original source code:

http://farseerphysics.codeplex.com/Sour ... 41#1436512

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daniel.weck

Posts: 57
Joined: Mon Mar 21, 2011 8:18 am