// Class methods
-double Vector::Dot(Vector v1, Vector v2)
+/*static*/ double Vector::Dot(Vector v1, Vector v2)
{
return (v1.x * v2.x) + (v1.y * v2.y) + (v1.z * v2.z);
}
-double Vector::Magnitude(Vector v1, Vector v2)
+/*static*/ double Vector::Magnitude(Vector v1, Vector v2)
{
double xx = v1.x - v2.x;
double yy = v1.y - v2.y;
// Returns the parameter of a point in space to this vector. If the parameter
// is between 0 and 1, the normal of the vector to the point is on the vector.
// Note: v1 is the tail, v2 is the head of the line (vector).
-double Vector::Parameter(Vector tail, Vector head, Vector p)
+/*static*/ double Vector::Parameter(Vector tail, Vector head, Vector p)
{
// Geometric interpretation:
// The parameterized point on the vector lineSegment is where the normal of
}
-// Return the normal to the linesegment formed by the passed in points.
-// (Not sure which is head or tail, or which hand the normal lies)
-// [v1 should be the tail, v2 should be the head, in which case the normal should
-// rotate anti-clockwise.]
+// Return the 2D normal to the linesegment formed by the passed in points.
+// The normal thus calculated should rotate anti-clockwise.
/*static*/ Vector Vector::Normal(Vector tail, Vector head)
{
Vector v = (head - tail).Unit();
return Vector(-v.y, v.x);
}
+
+/*static*/ double Vector::AngleBetween(Vector a, Vector b)
+{
+ // This is done using the following formula:
+ // (a . b) = ||a|| ||b|| cos(theta)
+ // However, have to check for two degenerate cases, where a = cb:
+ // 1, if c > 0, theta = 0; 2, if c < 0, theta = 180°.
+ // Also, the vectors a & b have to be non-zero.
+ // Also, have to check using an epsilon because acos will not return an
+ // exact value if the vectors are orthogonal
+ if (a.isZero() || b.isZero())
+ return 0;
+
+ return acos(a.Dot(b) / (a.Magnitude() * b.Magnitude()));
+}
+