3D Line-Plane Intersection

Question

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 th

Answer 1

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));
}