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Use Hermite instead of Bezier for glTF spline interpolation #93597

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Jun 29, 2024
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Use Hermite instead of Bezier for glTF spline interpolation #93597

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25 changes: 14 additions & 11 deletions modules/gltf/gltf_document.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -5785,15 +5785,17 @@ struct SceneFormatImporterGLTFInterpolate {
return 0.5f * ((2.0f * p1) + (-p0 + p2) * t + (2.0f * p0 - 5.0f * p1 + 4.0f * p2 - p3) * t2 + (-p0 + 3.0f * p1 - 3.0f * p2 + p3) * t3);
}

T bezier(T start, T control_1, T control_2, T end, float t) {
/* Formula from Wikipedia article on Bezier curves. */
const real_t omt = (1.0 - t);
const real_t omt2 = omt * omt;
const real_t omt3 = omt2 * omt;
T hermite(T start, T tan_start, T end, T tan_end, float t) {
/* Formula from the glTF 2.0 specification. */
const real_t t2 = t * t;
const real_t t3 = t2 * t;

return start * omt3 + control_1 * omt2 * t * 3.0 + control_2 * omt * t2 * 3.0 + end * t3;
const real_t h00 = 2.0 * t3 - 3.0 * t2 + 1.0;
const real_t h10 = t3 - 2.0 * t2 + t;
const real_t h01 = -2.0 * t3 + 3.0 * t2;
const real_t h11 = t3 - t2;

return start * h00 + tan_start * h10 + end * h01 + tan_end * h11;
}
};

Expand All @@ -5814,7 +5816,7 @@ struct SceneFormatImporterGLTFInterpolate<Quaternion> {
return p1.slerp(p2, c).normalized();
}

Quaternion bezier(const Quaternion start, const Quaternion control_1, const Quaternion control_2, const Quaternion end, const float t) {
Quaternion hermite(const Quaternion start, const Quaternion tan_start, const Quaternion end, const Quaternion tan_end, const float t) {
ERR_FAIL_COND_V_MSG(!start.is_normalized(), Quaternion(), vformat("The start quaternion %s must be normalized.", start));
ERR_FAIL_COND_V_MSG(!end.is_normalized(), Quaternion(), vformat("The end quaternion %s must be normalized.", end));

Expand Down Expand Up @@ -5879,14 +5881,15 @@ T GLTFDocument::_interpolate_track(const Vector<real_t> &p_times, const Vector<T
return p_values[(p_times.size() - 1) * 3 + 1];
}

const float c = (p_time - p_times[idx]) / (p_times[idx + 1] - p_times[idx]);
const float td = (p_times[idx + 1] - p_times[idx]);
const float c = (p_time - p_times[idx]) / td;

const T &from = p_values[idx * 3 + 1];
const T c1 = from + p_values[idx * 3 + 2];
const T tan_from = td * p_values[idx * 3 + 2];
const T &to = p_values[idx * 3 + 4];
const T c2 = to + p_values[idx * 3 + 3];
const T tan_to = td * p_values[idx * 3 + 3];

return interp.bezier(from, c1, c2, to, c);
return interp.hermite(from, tan_from, to, tan_to, c);
} break;
}

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