/// <summary>
/// Returns the signed angle to the given vector, in radians.
/// The sign of the angle is positive in a counter-clockwise
/// direction and negative in a clockwise direction when viewed
/// from the side specified by the `axis`.
/// </summary>
/// <param name="to">The other vector to compare this vector to.</param>
/// <param name="axis">The reference axis to use for the angle sign.</param>
/// <returns>The signed angle between the two vectors, in radians.</returns>
public double SignedAngleTo(Vector3d to, Vector3d axis)
{
Vector3d crossTo = Cross(to);
double unsignedAngle = Mathd.Atan2(crossTo.Length(), Dot(to));
double sign = crossTo.Dot(axis);
return((sign < 0) ? -unsignedAngle : unsignedAngle);
}
public Transform2Dd InterpolateWith(Transform2Dd m, double c)
{
double r1 = Rotation;
double r2 = m.Rotation;
Vector2d s1 = Scale;
Vector2d s2 = m.Scale;
// Slerp rotation
var v1 = new Vector2d(Mathd.Cos(r1), Mathd.Sin(r1));
var v2 = new Vector2d(Mathd.Cos(r2), Mathd.Sin(r2));
double dot = v1.Dot(v2);
// Clamp dot to [-1, 1]
dot = dot < -1.0f ? -1.0f : (dot > 1.0f ? 1.0f : dot);
Vector2d v;
if (dot > 0.9995f)
{
// Linearly interpolate to avoid numerical precision issues
v = v1.LinearInterpolate(v2, c).Normalized();
}
else
{
double angle = c * Mathd.Acos(dot);
Vector2d v3 = (v2 - v1 * dot).Normalized();
v = v1 * Mathd.Cos(angle) + v3 * Mathd.Sin(angle);
}
// Extract parameters
Vector2d p1 = origin;
Vector2d p2 = m.origin;
// Construct matrix
var res = new Transform2Dd(Mathd.Atan2(v.y, v.x), p1.LinearInterpolate(p2, c));
Vector2d scale = s1.LinearInterpolate(s2, c);
res.x *= scale;
res.y *= scale;
return(res);
}
/// <summary>
/// Returns the angle between the line connecting the two points and the X axis, in radians.
/// </summary>
/// <param name="to">The other vector to compare this vector to.</param>
/// <returns>The angle between the two vectors, in radians.</returns>
public double AngleToPoint(Vector2d to)
{
return(Mathd.Atan2(y - to.y, x - to.x));
}
/// <summary>
/// Returns the angle to the given vector, in radians.
/// </summary>
/// <param name="to">The other vector to compare this vector to.</param>
/// <returns>The angle between the two vectors, in radians.</returns>
public double AngleTo(Vector2d to)
{
return(Mathd.Atan2(Cross(to), Dot(to)));
}
/// <summary>
/// Returns this vector's angle with respect to the X axis, or (1, 0) vector, in radians.
///
/// Equivalent to the result of <see cref="Mathd.Atan2(double, double)"/> when
/// called with the vector's `y` and `x` as parameters: `Mathd.Atan2(v.y, v.x)`.
/// </summary>
/// <returns>The angle of this vector, in radians.</returns>
public double Angle()
{
return(Mathd.Atan2(y, x));
}
/// <summary>
/// Returns the unsigned minimum angle to the given vector, in radians.
/// </summary>
/// <param name="to">The other vector to compare this vector to.</param>
/// <returns>The unsigned angle between the two vectors, in radians.</returns>
public double AngleTo(Vector3d to)
{
return(Mathd.Atan2(Cross(to).Length(), Dot(to)));
}