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

Just to expand on ZGorlock's answer, I have done the dot product, plus and scalse of 3D Vectors. The references for these calculations are Dot Product, Add two 3D vectors and Scaling. Note: Vec3D is just a custom class which has points: x, y and z.

/**
 * 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 Vec3D lineIntersection(Vec3D planePoint, Vec3D planeNormal, Vec3D linePoint, Vec3D lineDirection) {
    //ax × bx + ay × by
    int dot = (int) (planeNormal.x * lineDirection.x + planeNormal.y * lineDirection.y);
    if (dot == 0) {
        return null;
    }

    // Ref for dot product calculation: https://www.mathsisfun.com/algebra/vectors-dot-product.html
    int dot2 = (int) (planeNormal.x * planePoint.x + planeNormal.y * planePoint.y);
    int dot3 = (int) (planeNormal.x * linePoint.x + planeNormal.y * linePoint.y);
    int dot4 = (int) (planeNormal.x * lineDirection.x + planeNormal.y * lineDirection.y);

    double t = (dot2 - dot3) / dot4;

    float xs = (float) (lineDirection.x * t);
    float ys = (float) (lineDirection.y * t);
    float zs = (float) (lineDirection.z * t);
    Vec3D lineDirectionScale = new Vec3D( xs, ys, zs);

    float xa = (linePoint.x + lineDirectionScale.x);
    float ya = (linePoint.y + lineDirectionScale.y);
    float za = (linePoint.z + lineDirectionScale.z);

    return new Vec3D(xa, ya, za);
}