Gradual utilization of Quaternion

I am currently exploring methods to apply incremental rotations to a dynamically changing orientation without using slerp.

Specifics: In a 3D space, I have an object with quaternion Q describing its orientation. As the object rotates, it receives updates from a server indicating the correct orientation at different time points – for example, at t1, the orientation was Q1 and should be corrected to K1.

Replacing Q1 with K1 directly leads to a non-smooth visual transition. Instead, I aim to gradually correct from Q1 to K1 over 10 steps without using slerp due to the dynamic nature of Q1. This involves deriving an incremental correction termed dK until the next server update is received.

The current method to derive dK consists of:

  1. delK = K1 * Q1.conjugate()
  2. dk = delK / 10

At step 2, delK is converted into an axis+angle representation, the angle is divided by 10, and then converted back to a quaternion.

Question 1: Is the aforementioned approach mathematically sound?

Question 2: Instances have been observed where dk is not a minor correction and may rotate in the opposite direction. What could be causing this anomaly?

This pertains to client-side prediction implementation in JavaScript utilizing incheon.

javascriptthree.jsgame-enginequaternionscannon.js

Answer №1

Consider implementing a "slerp towards" solution to simplify your 10-step approach:

Q = slerp(Q, Q1, 1 - Math.pow(smoothingRatio, deltaTime)

This method smoothly interpolates Q towards Q1 regardless of frame rate, allowing for dynamic adjustments. After 1 second of interpolation, the remaining fraction of the distance to Q1 will be determined by smoothingRatio. For more information, check out this resource.

In cases where rotations exceed 180 degrees per update, the closest axis of rotation may differ from that on the server. To address this, consider increasing update frequency or restricting rotational speed.

If updates include angular velocity data, client-side prediction can be enhanced to mitigate issues like opposite direction rotation. By continuously rotating the quaternion based on the received angular velocity, predictive accuracy can be improved.

For quaternion integration, consider using the Quaternion#integrate function available in Cannon.js.

// Rotate Q along the provided angular velocity from the last update
Q = Q.integrate(angularVelocity, deltaTime, Vec3.ZERO);

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