Hermite Interpolation of Solid Orientations with Circular Blending Quaternion Curves

Construction methods are presented that generate Hermite interpolation quaternion curves on SO(3). Two circular curves C₁(t) and C₂(t), 0 ≤ t ≤ 1, are generated that interpolate two orientations q₁ and q₂, and have boundary angular velocities: C₁′(0) = ω₁ and C₂′(1) = ω₂, respectively. They are smoothly blended together on SO(3) to generate a Hermite quaternion curve Q(t) ∈ SO(3), 0 ≤ t ≤ 1, which satisfies the boundary conditions: Q(0) = q₁, Q(1) = ₂, Q′(0) = ω₁, and Q′ (1) = ω₂.