public Transform2D InterpolateWith(Transform2D m, real_t c)
{
real_t r1 = Rotation;
real_t r2 = m.Rotation;
Vector2 s1 = Scale;
Vector2 s2 = m.Scale;
// Slerp rotation
var v1 = new Vector2(Mathf.Cos(r1), Mathf.Sin(r1));
var v2 = new Vector2(Mathf.Cos(r2), Mathf.Sin(r2));
real_t dot = v1.Dot(v2);
// Clamp dot to [-1, 1]
dot = dot < -1.0f ? -1.0f : (dot > 1.0f ? 1.0f : dot);
Vector2 v;
if (dot > 0.9995f)
{
// Linearly interpolate to avoid numerical precision issues
v = v1.LinearInterpolate(v2, c).Normalized();
}
else
{
real_t 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
var res = new Transform2D(Mathf.Atan2(v.y, v.x), p1.LinearInterpolate(p2, c));
Vector2 scale = s1.LinearInterpolate(s2, c);
res.x *= scale;
res.y *= scale;
return(res);
}
/// <summary>
/// Interpolates this transform to the other <paramref name="transform"/> by <paramref name="weight"/>.
/// </summary>
/// <param name="transform">The other transform.</param>
/// <param name="weight">A value on the range of 0.0 to 1.0, representing the amount of interpolation.</param>
/// <returns>The interpolated transform.</returns>
public Transform2D InterpolateWith(Transform2D transform, real_t weight)
{
real_t r1 = Rotation;
real_t r2 = transform.Rotation;
Vector2 s1 = Scale;
Vector2 s2 = transform.Scale;
// Slerp rotation
var v1 = new Vector2(Mathf.Cos(r1), Mathf.Sin(r1));
var v2 = new Vector2(Mathf.Cos(r2), Mathf.Sin(r2));
real_t dot = v1.Dot(v2);
dot = Mathf.Clamp(dot, -1.0f, 1.0f);
Vector2 v;
if (dot > 0.9995f)
{
// Linearly interpolate to avoid numerical precision issues
v = v1.LinearInterpolate(v2, weight).Normalized();
}
else
{
real_t angle = weight * 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 = transform.origin;
// Construct matrix
var res = new Transform2D(Mathf.Atan2(v.y, v.x), p1.LinearInterpolate(p2, weight));
Vector2 scale = s1.LinearInterpolate(s2, weight);
res.x *= scale;
res.y *= scale;
return(res);
}