3D 线面交点 [英] 3D Line-Plane Intersection

问题描述

如果给定一条线(由向量或线上的两个点表示)，我如何找到该线与平面相交的点?我在这方面找到了大量资源，但我无法理解那里的方程式(它们似乎不是标准代数).我想要一个可以被标准编程语言(我使用的是 Java)解释的等式(无论多长).

If given a line (represented by either a vector or two points on the line) how do I find the point at which the line intersects a plane? I've found loads of resources on this but I can't understand the equations there (they don't seem to be standard algebraic). I would like an equation (no matter how long) that can be interpreted by a standard programming language (I'm using Java).

推荐答案

这是 Java 中的一种方法，用于查找直线和平面之间的交点.有些向量方法没有包含在内，但它们的功能是不言自明的.

Here is a method in Java that finds the intersection between a line and a plane. There are vector methods that aren't included but their functions are pretty self explanatory.

/**
 * Determines the point of intersection between a plane defined by a point and a normal vector and a line defined by a point and a direction vector.
 *
 * @param planePoint    A point on the plane.
 * @param planeNormal   The normal vector of the plane.
 * @param linePoint     A point on the line.
 * @param lineDirection The direction vector of the line.
 * @return The point of intersection between the line and the plane, null if the line is parallel to the plane.
 */
public static Vector lineIntersection(Vector planePoint, Vector planeNormal, Vector linePoint, Vector lineDirection) {
    if (planeNormal.dot(lineDirection.normalize()) == 0) {
        return null;
    }

    double t = (planeNormal.dot(planePoint) - planeNormal.dot(linePoint)) / planeNormal.dot(lineDirection.normalize());
    return linePoint.plus(lineDirection.normalize().scale(t));
}

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