nlerp

NLERP, short for Normalized Linear Interpolation, is a method used to interpolate between two orientations represented as quaternions. It blends the two quaternions linearly and then normalizes the result to unit length, producing a unit quaternion that represents a smooth rotation. It is commonly employed in computer graphics and animation where fast orientation blending is desirable.

The standard formula is NLERP(q0, q1, t) = normalize((1 − t) q0 + t q1). To ensure the interpolation follows the shortest rotational path, it is common to negate q1 when the dot product dot(q0, q1) is negative before performing the interpolation. If either input quaternion is not unit length, it should be normalized first, although working with unit quaternions is typical in practice.

Compared with SLERP (spherical linear interpolation), NLERP is computationally cheaper because it avoids trigonometric functions and the division by sin(angle). However, NLERP does not interpolate along a great-circle arc and does not preserve constant angular velocity, which can lead to non-uniform motion for larger rotations. As a result, NLERP is often used when performance is critical and exact constant-speed rotation is not required, or for small-angle inter-polations.

Applications of NLERP include real-time graphics, game engines, and animation pipelines for blending orientations between keyframes. Users should be mindful of its limitations regarding speed consistency and the potential need for normalization and shortest-path handling to obtain correct results.