central_difference_tangents()

MAYAFLUX_API void MayaFlux::Kinesis::central_difference_tangents	(	std::span< const double >	points,
		size_t	dim,
		size_t	count,
		std::vector< double > &	tangents
	)

Tangents of a sampled curve by finite difference, coordinate-major.

Parameters

points	Coordinate-major, dim * count doubles.
dim	Coordinate count per sample, at least 1.
count	Sample count, at least 2.
tangents	Resized to dim * count, coordinate-major.

For curves whose samples did not come straight from CurveEvaluator's analytic derivative, most importantly after reparameterize_planar has resampled by arc length, which leaves analytic tangents attached to the original parameter values. Uniformly spaced samples make the central difference well conditioned; the endpoints take the one sided difference.

Like the analytic tangents, these are directions and not rates.

Definition at line 334 of file MotionCurves.cpp.

{
    if (dim == 0 || count < 2 || points.size() < dim * count) {
        tangents.assign(dim * count, 0.0);
        return;
    }
 
    tangents.resize(dim * count);
 
    for (size_t d = 0; d < dim; ++d) {
        const double* row = points.data() + d * count;
        double* out = tangents.data() + d * count;
 
        for (size_t i = 0; i < count; ++i) {
            const size_t a = i == 0 ? 0 : i - 1;
            const size_t b = i + 1 < count ? i + 1 : count - 1;
            out[i] = row[b] - row[a];
        }
    }
}

References a, b, count, out, and points.

Referenced by MayaFlux::Nodes::GpuSync::TopologyGeneratorNode::build_interpolated_path(), and MayaFlux::Nodes::GpuSync::PathGeneratorNode::write_curve_segment().

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