Function minterpolate::quasi_spherical_linear_interpolate

pub fn quasi_spherical_linear_interpolate<T>(
    input: f32, 
    inputs: &[f32], 
    outputs: &[T], 
    normalize: bool
) -> T where
    T: InterpolationPrimitive + Clone, 

Do quasi spherical linear interpolation.

This should only ever be used on quaternions, it will produce incorrect results for other data types. This will produce a result that compared to real spherical linear interpolation has an error around 10^-4, but runs much faster because it does no trigonometry or sqrt calls.

Algorithm was created by Jonathan Blow: Hacking Quaternions

f(d) = d <= 0.5 => lerp(p0, p1, y'(d)) f(d) = d > 0.5 => lerp(p0, p1, 1 - y'(1 - d)) y'(d) = 2 * k * d^2 - 3 * k * d + k + 1 k = worst_case_slope * (1 - attenuation * dot(p0, p1))^2 d = (t - t0) / (t1 - t0) p0 = output at left keyframe p1 = output at right keyframe t0 = input at left keyframe t1 = input at right keyframe

Parameters:

• input: the input value to the function
• inputs: list of discrete input values for each keyframe
• outputs: list of output values to interpolate between, for spherical linear interpolation this should be the same size as inputs
• normalize: if true, normalize the interpolated value before returning it