java - 计算 3 个点 (x,y) 的曲率

Question

我有一个二维欧氏空间。给出三点。

例如(p2为中点):

Point2D p1 = new Point2D.Double(177, 289);
Point2D p2 = new Point2D.Double(178, 290);
Point2D p3 = new Point2D.Double(178, 291);

现在我想计算 curvature对于这三点。

double curvature = calculateCurvature(p1, p2, p3);

如何做到这一点？有没有现成的方法(没有java外部库)？

• 曲率:https://en.wikipedia.org/wiki/Curvature
• 门格尔曲率: https://en.wikipedia.org/wiki/Menger_curvature

Answer 1

对于门格尔曲率，公式是对的there在维基百科文章中:

curvature = 4*triangleArea/(sideLength1*sideLength2*sideLength3)

您究竟尝试了哪些代码？

根据您的 3 分计算这 4 个值应该不难。

Here有一些有用的方法:

/**
 * Returns twice the signed area of the triangle a-b-c.
 * @param a first point
 * @param b second point
 * @param c third point
 * @return twice the signed area of the triangle a-b-c
 */
public static double area2(Point2D a, Point2D b, Point2D c) {
    return (b.x-a.x)*(c.y-a.y) - (b.y-a.y)*(c.x-a.x);
}

/**
 * Returns the Euclidean distance between this point and that point.
 * @param that the other point
 * @return the Euclidean distance between this point and that point
 */
public double distanceTo(Point2D that) {
    double dx = this.x - that.x;
    double dy = this.y - that.y;
    return Math.sqrt(dx*dx + dy*dy);
}

没什么可做的。警告:area2 返回带符号的 double ，具体取决于您的点的方向(顺时针或逆时针)。