摘要：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和最小值，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制一個外接矩形求最小面積。

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

對凸多邊形的每一條邊都繪制一個外接矩形求最小面積。下圖展示了計算流程

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 旋轉后坐標
     */
    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));
    }

凸包算法實現

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

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);
    }

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());

    }

本文代碼及可視化代碼均放在 gitee 碼云上 歡迎star & fork