/**
* Returns reflection of this vector through a plane specified by a point on the plane and a
* vector normal to the plane.
*
* @param x0 point on the plane
* @param normal normal to the plane
* @return reflected position
*/
public Vector3d reflectionThroughPlaneAt(Vector3d x0, Vector3d normal) {
Vector3d x1 = this.minus(x0);
double alpha = -2 * x1.dotProduct(normal) / normal.dotProduct(normal);
Vector3d reflection = Vector3d.linearCombination(1, this, alpha, normal);
return reflection;
}
/** Returns cosine of the angle between this vector and vector v. */
public double cosAngleWith(Vector3d v) {
if (isZero() || v.isZero()) {
return 1;
}
double cosAngle = dotProduct(v) / (norm() * v.norm());
cosAngle = Math.min(1, Math.max(-1, cosAngle));
return cosAngle;
}
public static Vector3d linearCombination(
double a1, Vector3d v1, double a2, Vector3d v2, double a3, Vector3d v3) {
Vector3d v =
new Vector3d(
(a1 * v1.getX()) + (a2 * v2.getX()) + (a3 * v3.getX()),
(a1 * v1.getY()) + (a2 * v2.getY()) + (a3 * v3.getY()),
(a1 * v1.getZ()) + (a2 * v2.getZ()) + (a3 * v3.getZ()));
return v;
}
/**
* Returns the projection of this vector onto the vector v. Lenient version treats zero vector for
* v as (1,0,0) in order to avoid returning vector containing NaN values.
*/
public Vector3d projectionOnto(Vector3d v, boolean isLenient) {
if (isLenient && v.isZero()) {
v = new Vector3d(1, 0, 0);
}
return projectOnto(v);
}
public static Vector3d linearCombination(double a1, Vector3d v1, double a2, Vector3d v2) {
return new Vector3d(
(a1 * v1.getX()) + (a2 * v2.getX()),
(a1 * v1.getY()) + (a2 * v2.getY()),
(a1 * v1.getZ()) + (a2 * v2.getZ()));
}
/**
* Returns the projection of this vector onto the vector v.
*
* @see #projectionOnto(Vector2d, boolean) for lenient handling of v
*/
public Vector3d projectOnto(Vector3d v) {
double scale = dotProduct(v) / v.normSquared();
return v.scaledBy(scale);
}