/// <summary> /// Spherical linear interpolation. /// /// Assumes q1 and q2 are normalized and that t in [0,1]. /// /// This method does interpolate along the shortest arc /// between q1 and q2. /// </summary> /// <param name="q1"></param> /// <param name="q2"></param> /// <param name="t">[0,1]</param> /// <returns>Interpolant</returns> public static Rot3f SlerpShortest( Rot3f q1, Rot3f q2, double t ) { Rot3f q3 = q2; float cosomega = Fun.Clamp(Rot3f.Dot(q1, q3), -1, 1); if (cosomega < 0.0) { cosomega = -cosomega; q3 *= -1; //q3 = -q3; } if (cosomega >= 1.0) { // Special case: q1 and q2 are the same, so just return one of them. // This also catches the case where cosomega is very slightly > 1.0 return(q1); } double sinomega = System.Math.Sqrt(1 - cosomega * cosomega); Rot3f result = new Rot3f(); if (sinomega * double.MaxValue > 1) { double omega = System.Math.Acos(cosomega); float s1 = (float)(System.Math.Sin((1.0 - t) * omega) / sinomega); float s2 = (float)(System.Math.Sin(t * omega) / sinomega); result = s1 * q1 + s2 * q3; } else if (cosomega > 0) { // omega == 0 float s1 = 1.0f - (float)t; float s2 = (float)t; result = s1 * q1 + s2 * q3; } else { // omega == -pi result.X = -q1.Y; result.Y = q1.X; result.Z = -q1.W; result.W = q1.Z; float s1 = (float)System.Math.Sin((0.5 - t) * System.Math.PI); float s2 = (float)System.Math.Sin(t * System.Math.PI); result = s1 * q1 + s2 * result; } return(result); }