public Transform2D orthonormalized()
{
Transform2D on = this;
Vector2 onX = on.x;
Vector2 onY = on.y;
onX.normalize();
onY = onY - onX * (onX.dot(onY));
onY.normalize();
on.x = onX;
on.y = onY;
return(on);
}
public Transform2D interpolate_with(Transform2D m, float c)
{
float r1 = Rotation;
float r2 = m.Rotation;
Vector2 s1 = Scale;
Vector2 s2 = m.Scale;
// Slerp rotation
Vector2 v1 = new Vector2(Mathf.cos(r1), Mathf.sin(r1));
Vector2 v2 = new Vector2(Mathf.cos(r2), Mathf.sin(r2));
float dot = v1.dot(v2);
// Clamp dot to [-1, 1]
dot = (dot < -1.0f) ? -1.0f : ((dot > 1.0f) ? 1.0f : dot);
Vector2 v = new Vector2();
if (dot > 0.9995f)
{
// Linearly interpolate to avoid numerical precision issues
v = v1.linear_interpolate(v2, c).normalized();
}
else
{
float angle = c * Mathf.acos(dot);
Vector2 v3 = (v2 - v1 * dot).normalized();
v = v1 * Mathf.cos(angle) + v3 * Mathf.sin(angle);
}
// Extract parameters
Vector2 p1 = Origin;
Vector2 p2 = m.Origin;
// Construct matrix
Transform2D res = new Transform2D(Mathf.atan2(v.y, v.x), p1.linear_interpolate(p2, c));
Vector2 scale = s1.linear_interpolate(s2, c);
res.x *= scale;
res.y *= scale;
return(res);
}
public Vector2 basis_xform_inv(Vector2 v)
{
return(new Vector2(x.dot(v), y.dot(v)));
}