最小外接矩形思路以及实现

摘要：最小外接矩形外接矩形计算对一个凸多边形进行外接矩形计算，需要知道当前面的最大和最小值，即可获得外接矩形最小外接矩形计算对凸多边形的每一条边都绘制一个外接矩形求最小面积。

对一个凸多边形进行外接矩形计算，需要知道当前面的最大xy 和最小xy值，即可获得外接矩形

对凸多边形的每一条边都绘制一个外接矩形求最小面积。下图展示了计算流程

旋转基础算法实现

旋转点基础

 /**
     * 旋转点
     *
     * @param point 被旋转的点
     * @param center 旋转中心
     * @param angle 角度
     * @return 旋转后坐标
     */
    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));
    }

凸包算法实现

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

获得结果

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("==============旋转基点==============");
        System.out.println(new GeometryFactory().createPoint(c));
        System.out.println("==============旋转基点==============");
        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();
//            此处可以将 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);
    }

测试类

  @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());

    }

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