Interpolating solid orientations with circular blending quaternion curves

This paper presents a method to smoothly interpolate a given sequence of solid orientations using circular blending quaternion curves. Given three solid orientations, a circular quaternion curve is constructed that interpolates the three orientations. Therefore, given four orientations q i?1 ; q i ; q i+1 ; q i+2 , there are two circular quaternion curves C i and C i+1 which interpolate the triples of orientations (q i?1 ; q i ; q i+1) and (q i ; q i+1 ; q i+2), respectively; thus, both C i and C i+1 interpolate the two orientations q i and q i+1. Using a similar method to the parabolic blending of Overhauser 16], we generate a quaternion curve Q i (t) which interpolates the two orientations q i and q i+1 while smoothly blending the two circular quaternion curves C i (t) and C i+1 (t) with a blending function f (t) of degree (2k ? 1). The quaternion curve Q i has the same derivatives (up to order k) with C i at q i and with C i+1 at q i+1 , respectively. By connecting the quaternion curve segments Q i 's in a connected sequence, we generate a C k-continuous quaternion path which smoothly interpolates a given sequence of solid orientations. 1 Figure 1: Keyframe Animation of a 3D Character \K".