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java - 在一点上旋转平面

问题描述

我有一个 Java 类，它创建一个可以翻译、调整大小和旋转的虚拟屏幕（我们称之为地图）。
但是，当我旋转它时，它只会围绕 (0, 0) 旋转。
要将点转换到屏幕上，首先要旋转它，然后调整它的大小，然后再平移它。

private double dx; //offset in x and y
private double dy;
private double t; //rotation (radians)
private double sx; //scale of x and y
private double sy;
public double[] toScreen(double x, double y) //takes (x, y) on the map and gives (x1, y1) for the screen 
{
    double[] xy = {x, y};
    if(t != 0)
    {
        double distance = Math.hypot(xy[0], xy[1]);
        double theta = Math.atan2(xy[1], xy[0]) + t;
        xy[0] = Math.cos(theta)*distance;
        xy[1] = Math.sin(theta)*distance;
    }
    xy[0] *= sx;
    xy[1] *= sy;

    xy[0] += dx;
    xy[1] += dy;
    return xy;
}

要设置或更改旋转，您可以操作变量t，但它会在 (0, 0) 上旋转。
如果我制作一个方法，让 (x, y) 像public void changeRotation(double t, double x, double y).
我希望 (x, y) 成为地图坐标。该方法会是什么样子，您能解释一下它的作用吗？

标签： javarotationgeometryplane

解决方案

如果我理解正确，这就是您需要的：

/**
 * @param point  point (x,y) of the coordinates to be rotated
 * @param center point (x,y) of the center (pivot) coordinates
 * @param angle in radians
 * @return point (x,y) of the new (translated) coordinates 
 */
static Point2D.Double rotateAPoint(Point2D.Double point, Point2D.Double center, double angle){

    double newX = center.x + Math.cos(angle) * (point.x - center.x) -
                                        Math.sin(angle) * (point.y-center.y) ;
    double newY = center.y + Math.sin(angle) * (point.x - center.x) +
                                        Math.cos(angle) * (point.y - center.y) ;
    return new Point2D.Double(newX, newY);
}

尝试

Point2D.Double  point = new Point2D.Double(200,100);
Point2D.Double center = new Point2D.Double(100,100);
double angle = Math.PI/2 ; //90 degress
System.out.println(rotateAPoint(point, center, angle) );
System.out.println(rotateAPoint(point, center, -angle));

如果您更喜欢使用double[]：

/**
 * @param point  (x,y) of the coordinates to be rotated
 * @param center (x,y) of the center (pivot) coordinates
 * @param angle in radians
 * @return (x,y) of the new (translated) coordinates 
 */
static double[] rotateAPoint(double[] point, double[] center, double angle){

    double newX = center[0] + Math.cos(angle) * (point[0] - center[0]) -
                                        Math.sin(angle) * (point[0]-center[0]) ;
    double newY = center[1] + Math.sin(angle) * (point[1] - center[1]) +
                                        Math.cos(angle) * (point[1] - center[1]) ;
    return new double[]{newX, newY};
}

关于这里的数学解释

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