3D 线面交点

Question

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)。我想要一个可以由标准编程语言(我使用的是 Java)解释的等式(无论多长)。

Answer 1

这是Java中的一种方法，可以找到直线和平面之间的交点。有一些不包括在内的向量方法，但它们的功能是不言自明的。

/**
 * 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));
}