/// <summary>
/// Gets the tangent at a point along the curve.
/// </summary>
/// <returns>The tangent at the given time.</returns>
/// <param name="coeffs">The precalculated coefficients of the curve.</param>
/// <param name="t">
/// The time along the curve, where t=0 is the start point, and t=1 is the end point. Note that t can be extrapolated
/// beyond these bounds.
/// </param>
public static Vector3 GetTangent(this CubicBezierTangentCoefficients coeffs, double t)
{
Vector3 velocity = (float)(t * t) * coeffs.Coeff1 + ((float)t) * coeffs.Coeff2 + coeffs.Coeff3;
// If the velocity is 0, we look at the acceleration of the path to determine which direction the path is about
// to travel to.
if (velocity.magnitude < float.Epsilon)
{
Vector3 acceleration = coeffs.GetAcceleration(t);
// If acceleration is 0, the entire path is probably a single point.
if (acceleration.magnitude < float.Epsilon)
{
if (coeffs.Coeff1.magnitude < float.Epsilon)
{
return(Vector3.forward);
}
return(coeffs.Coeff1.normalized);
}
return(acceleration.normalized);
}
return(velocity.normalized);
}
/// <summary>
/// Gets a normal for a given segment. Note that there are an infinite number of possible normals, this method just
/// produces a locally consistent normal.
/// </summary>
/// <returns>A normal at a given point.</returns>
/// <param name="segment">The segment to calculate the tangent of.</param>
/// <param name="segment">The precalculated coefficients of the curve.</param>
/// <param name="t">
/// The time along the curve, where t=0 is the start point, and t=1 is the end point. Note that t can be extrapolated
/// beyond these bounds.
/// </param>
public static Vector3 GetNormal(this CubicBezierSegment segment, CubicBezierTangentCoefficients coeffs, double t)
{
Vector3 currentTangent = coeffs.GetTangent(t);
Vector3 normal;
if (currentTangent == Vector3.zero)
{
Vector3 acceleration = coeffs.GetAcceleration(t);
currentTangent = acceleration;
}
// The tangent doesn't change, (such in the case of a straight line).
// We pick a vector which shouldn't be parallel to the tangent, and
// use the cross product with the tangent to find a normal.
normal = currentTangent;
normal.x = -currentTangent.y;
normal.y = -currentTangent.z;
normal.z = currentTangent.x;
normal = Vector3.Cross(currentTangent, normal).normalized;
return(normal);
}