Java: 三角形旋转 - 不成功的概念

Question

我做错了什么？我得到不正确的结果（坐标）。

一个三角形（见下图：蓝色为原三角形，石灰为旋转后的三角形：克隆。边A为固定点）。

我使用的classes：

一个点class:

public class Point {
   private final double x;
   private final double y;
   public Point(double x, double y) {
      this.x = x;
      this.y = y;
   }
   public double getX() {
      return x;
   }
   public double getY() {
      return y;
   }
   @Override
   public String toString() {
       return "[(" + x + ") (" + y + ")]";
   }
}

一个抽象的 Object2D class:

public abstract class Object2D {
    Point[] point;
    public Point getPoint(int i) {
        return point[i];
    }
    public double getLowestX() {
        return Arrays.asList(point).stream()
            .mapToDouble(Point::getX)
            .min().getAsDouble();
    }
    public double getHighestX() {
        return Arrays.asList(point).stream()
            .mapToDouble(Point::getX)
            .max().getAsDouble();
    }
    public double getLowestY() {
        return Arrays.asList(point).stream()
            .mapToDouble(Point::getY)
            .min().getAsDouble();
    }
    public double getHighestY() {
        return Arrays.asList(point).stream()
            .mapToDouble(Point::getY)
            .max().getAsDouble();
    }
    public double getLength() {
        return getSide(getLowestX(), getHighestX());
    }
    public double getHeight() {
       return getSide(getLowestY(), getHighestY());
    }
    private double getSide(double v1, double v2) {
        return (v1 < v2) ? (0 - v1) + v2 : (0 - v2) + v1;
    }
    @Override
       public String toString() {
       StringBuilder sb = new StringBuilder();
       for (Point pt : point) sb.append(pt).append("\n");
       return sb.toString();
    }
}

一行class:

public class Line extends Object2D {
   public Line(Point point0, Point point1) {
      point = new Point[2];
      point[0] = point0;
      point[1] = point1;
   }
   public double getLineLength() {
      return Math.sqrt(Math.pow(getLength(), 2) + Math.pow(getHeight(), 2));
   }
}

我的三角形class:

public class Triangle extends Object2D {
    public Triangle(Point point0, Point point1, Point point2) {
        point = new Point[3];
        point[0] = point0;
        point[1] = point1;
        point[2] = point2;
    }
    public static Triangle getRotatedTriangle(Triangle triangle) {
       Point point0 = triangle.getPoint(0);
       Point point1 = triangle.getPoint(1);
       Point point2 = triangle.getPoint(2);
       Line baseLine = new Line(point0, point1);
       double rotationHeight = baseLine.getHeight();
       double baseLength = baseLine.getLineLength();
       double sinA = rotationHeight / baseLength;
       double angle = Math.asin(sinA);
       double cosA = Math.cos(angle);                  
       point1 = new Point(
            (point1.getX() * cosA - point1.getY() * sinA),
            (point1.getX() * sinA + point1.getY() * cosA));
       point2 = new Point(
            (point2.getX() * cosA - point2.getY() * sinA),
            (point2.getX() * sinA + point2.getY() * cosA));
       return new Triangle(point0, point1, point2);
   }
}

当然还有我的主要 class:

public class TestDrive {
      public static void main(String[] args) {
          Triangle triangle = new Triangle (
             new Point(-6.5, -1.5),
             new Point(2.5, 7.5),
             new Point(6.5, -5.5)
          );
          System.out.println(triangle);
          System.out.println(Triangle.getRotatedTriangle(triangle));
      }
}

Answer 1

您在代码中犯了 2 个错误：

您尝试以角度 α 旋转，而您应该以角度 -α 旋转（因为您是顺时针旋转）。
您的乘法矩阵不正确：您的代码将围绕 XY 平面的原点执行旋转，而不是围绕点 A 旋转。对于由旋转矩阵 R 旋转的点 (x, y)围绕中心 (a, b)，新旋转点 (x', y') 的正确公式将是 (x', y') = R * (x - a, y - b) + (a, b).

这应该足以让您更正代码。作为参考，这是我为旋转三角形得到的解决方案：

[(-6.5) (-1.5)]
[(6.227922061357855) (-1.5000000000000009)]
[(-0.1360389693210724) (-13.520815280171309)]

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