最小外接矩形思路以及實現

最小外接矩形

外接矩形計算

對一個凸多邊形進行外接矩形計算，需要知道當前面的最大xy 和最小xy值，即可獲得外接矩形

最小外接矩形計算

對凸多邊形的每一條邊都繪製一個外接矩形求最小面積。下圖展示了計算流程

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計算流程

1. 旋轉基礎算法實現

   • 旋轉點基礎

    /**
        * 旋轉點
        *
        * @param point 被旋轉的點
        * @param center 旋轉中心
        * @param angle 角度
        * @return 旋轉後坐標
        */
       public static Coordinate get(Coordinate point, Coordinate center, double angle) {
           double cos = Math.cos(angle);
           double sin = Math.sin(angle);
           double x = point.x;
           double y = point.y;
           double centerX = center.x;
           double centerY = center.y;
           return new Coordinate(centerX + cos * (x - centerX) - sin * (y - centerY),
                   centerY + sin * (x - centerX) + cos * (y - centerY));
       }

1. 凸包算法實現

   Geometry hull = (new ConvexHull(geom)).getConvexHull();

2. 獲得結果

   public static Polygon get(Geometry geom, GeometryFactory gf) {
           Geometry hull = (new ConvexHull(geom)).getConvexHull();
           if (!(hull instanceof Polygon)) {
               return null;
           }
           Polygon convexHull = (Polygon) hull;
           System.out.println(convexHull);
   
           // 直接使用中心值
           Coordinate c = geom.getCentroid().getCoordinate();
           System.out.println("==============旋轉基點==============");
           System.out.println(new GeometryFactory().createPoint(c));
           System.out.println("==============旋轉基點==============");
           Coordinate[] coords = convexHull.getExteriorRing().getCoordinates();
   
           double minArea = Double.MAX_VALUE;
           double minAngle = 0;
           Polygon ssr = null;
           Coordinate ci = coords[0];
           Coordinate cii;
           for (int i = 0; i < coords.length - 1; i++) {
               cii = coords[i + 1];
               double angle = Math.atan2(cii.y - ci.y, cii.x - ci.x);
               Polygon rect = (Polygon) Rotation.get(convexHull, c, -1 * angle, gf).getEnvelope();
               double area = rect.getArea();
   //            此處可以將 rotationPolygon 放到list中求最小值
   //            Polygon rotationPolygon = Rotation.get(rect, c, angle, gf);
   //            System.out.println(rotationPolygon);
               if (area < minArea) {
                   minArea = area;
                   ssr = rect;
                   minAngle = angle;
               }
               ci = cii;
           }
   
           return Rotation.get(ssr, c, minAngle, gf);
       }

3. 測試類

     @Test
       public void test() throws Exception{
           GeometryFactory gf = new GeometryFactory();
           String wkt = "POLYGON ((87623.0828822501 73753.4143904365,87620.1073981973 73739.213216548,87629.1690996309 73730.4220136646,87641.882531493 73727.3112803367,87643.0997749692 73714.8683470248,87662.0346734872 73725.0120426595,87669.0676357939 73735.1557382941,87655.9484561064 73735.9672339449,87676.9120937514 73747.4634223308,87651.8909778525 73740.8362078495,87659.4649372597 73755.4431295634,87644.4522677204 73748.680665807,87645.5342619215 73760.7178512935,87635.2553170117 73750.9799034842,87630.5215923822 73760.3121034681,87623.0828822501 73753.4143904365))";
           Polygon read = (Polygon) new WKTReader().read(wkt);
           Polygon polygon = MinimumBoundingRectangle.get(read, gf);
   
   //        System.out.println(polygon);
   //        System.out.println(polygon.getArea());
   
       }

注

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