/// <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>
/// <param name="up">
/// The direction the normal should try to match.
/// </param>
public static Vector3 GetNormal(this CubicBezierSegment segment, CubicBezierTangentCoefficients coeffs, double t, Vector3 up)
{
Vector3 baseNormal = segment.GetNormal(coeffs, t);
Vector3 tangent = coeffs.GetTangent(t);
Vector3 upNormal = Vector3.Cross(Vector3.Cross(tangent, up), tangent).normalized;
if (Vector3.Angle(tangent, up) == 0f)
{
return(baseNormal);
}
float angle = Mathf.Min(Mathf.Abs(Vector3.Angle(tangent, up)), Mathf.Abs(Vector3.Angle(tangent, -up)));
float lerp = Mathf.Clamp01((angle + 5) / 45f);
return(AngleLerp(baseNormal, upNormal, lerp));
}
/// <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);
}
