Quaternion Slerp Interpolation Calculator
Spherical linear interpolation between two orientations at parameter t — smooth, constant-speed rotation blending.
Slerp interpolates rotations at constant angular speed along the shortest great-circle arc on the quaternion hypersphere — the gold standard for smooth camera and animation blends. It flips one quaternion if needed to take the short way (≤180°) and falls back to lerp for nearly-identical orientations to avoid divide-by-zero.
Formula
About Quaternion Slerp Interpolation Calculator
Slerp — spherical linear interpolation — is how you smoothly blend between two orientations, the technique behind every camera ease, animation transition and orientation filter. Unlike naively interpolating Euler angles (which wobbles and can gimbal-lock) or lerping quaternions (which speeds up mid-arc), slerp moves at constant angular velocity along the shortest great-circle arc on the quaternion hypersphere. This calculator computes the interpolated, normalized quaternion at any t between 0 and 1, automatically taking the short way around (≤180°) and falling back to linear interpolation when the orientations are nearly identical to avoid numerical blow-up.
How to use Quaternion Slerp Interpolation Calculator
- 1Enter your values into Quaternion Slerp Interpolation Calculator — sensible, domain-typical defaults are pre-filled so you see a real result immediately.
- 2The result recomputes live using the formula shown on the page; there is no button to press.
- 3Adjust any input to compare scenarios, then read the worked example to see the substituted numbers.
Why use Quaternion Slerp Interpolation Calculator?
- ✓Computes Quaternion Slerp Interpolation instantly in your browser — no sign-up, no upload, no server round-trip.
- ✓100% free and unlimited, with the exact formula shown: slerp(q1,q2,t) = [sin((1−t)Ω).
- ✓Runs entirely client-side, so every value you enter stays private on your device.
- ✓Live recompute as you type, with a worked example and authoritative references for trust.
Frequently asked questions
Why use slerp instead of interpolating Euler angles?+
Euler interpolation wobbles, doesn't take the shortest path, and breaks at gimbal lock — angles can swing the long way or produce visible tumbling. Slerp moves smoothly and directly along the true shortest rotation between orientations at constant speed, which is why it's the standard for animation, camera moves and any orientation blend that needs to look natural.
What does the 'shortest path' handling do?+
Because q and −q are the same rotation, two orientations have two arcs between them (one ≤180°, one ≥180°). Slerp checks the dot product and flips one quaternion's sign if it's negative, guaranteeing it interpolates along the short arc. Without this, a small rotation difference could animate as a nearly-full spin the wrong way.
When does slerp fall back to lerp?+
When the two quaternions are almost identical (dot product near 1), the angle between them is tiny, sin(Ω) approaches zero, and the slerp formula divides by it — numerically unstable. For such small angles, plain normalized linear interpolation (nlerp) is visually indistinguishable and safe, so implementations switch to it, as this tool does above dot ≈ 0.9995.
Slerp vs nlerp — which should I use?+
Slerp gives exactly constant angular velocity but costs trig and a division; nlerp (normalized lerp) is cheaper and commutative but slightly varies speed mid-arc. For single transitions and cameras, slerp's smoothness is worth it. For blending many animation poses per frame (skeletal animation), nlerp's speed and the negligible visual difference usually win.
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