High Quality Content by WIKIPEDIA articles! Slerp has a geometric formula independent of quaternions, and independent of the dimension of the space in which the arc is embedded. This formula, a symmetric weighted sum credited to Glenn Davis, is based on the fact that any point on the curve must be a linear combination of the ends. Let p0 and p1 be the first and last points of the arc, and let t be the parameter, 0 ? t ? 1. Compute ? as the angle subtended by the arc, so that cos ? = p0 ? p1, the n-dimensional dot product of the unit vectors from the origin to the ends. The geometric formula is then mathrm{Slerp}(p_0,p_1; t) = frac{sin {[(1-t)Omega}]}{sin Omega} p_0 + frac{sin [tOmega]}{sin Omega} p_1. The symmetry can be seen in the fact that Slerp(p0,p1;t) = Slerp(p1,p0;1?t). In the limit ? ? 0, this formula reduces to the corresponding symmetric formula for linear interpolation,mathrm{lerp}(p_0,p_1; t) = (1-t) p_0 + t p_1.,!

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