Interpolating Matrices

Question

Apologies if I am missing something very obvious (likely!) but is there anything wrong with interpolating between two matrices by:

    float d = (float)(targetTime.Ticks - keyframe_start.ticks) / (float)(keyframe_end.ticks - keyframe_start.ticks);
    return ((keyframe_start.Transform * (1 - d)) + (keyframe_end.Transform * d));

As in my app, when I try an use this to interpolate between two keyframes, the model begins to 'shrink' - the severity based on how far between the two keyframes the target time is; its worst when the transform split is ~50/50.

Answer 1

Put very simply, linear interpolation of matrices is not always a good idea. If you have an animation you are trying to accomplish, and you are using matrices to handle the bones rotation, you can't just take a linear combination of them. You'll need to use slerp, extract the axis of rotation and interpolate the angle and recalculate the rotation matrix, or you'll need to just use quaternions. Translation is linear, rotation is not (except for small angles theta).

Here is agood writeup on matrices and 3d applications

Answer 2

Interpolating the matrices like that isn't going to give a useful result, especially for anything involving a rotation. Ideally you want to decompose your animation into some other format (quaternion for rotation, for example) and then interpolate in that form before building the matrix.

Answer 3

Here is a graphical example of what I meant in the comment I wrote in the comment section of the OP's question. While the ticks representing the d values progress evenly from one vector to the other, the angular change (red lines) are not even. the changes near the middle of the sequence represent greater change than near the ends. so an animation of interpolated vectors will start slow, speed up near the middle, and slow down towards the end. If the angle between start and end is not great, it may not be noticeable.

The varying lengths of the interpolated vectors (red lines) are the reason your model was shrinking in places too as they will scale the model to their lengths.

If you used quaternions, the blue line would arc from vec A to vec B and each tick would cause equal angular change as well as an equal distance along the arc.