compute_path_curvature()

MAYAFLUX_API std::vector< Kakshya::LineVertex > MayaFlux::Kinesis::compute_path_curvature	(	const std::vector< Kakshya::LineVertex > &	path_vertices,
		float	curvature_scale,
		size_t	stride = 1
	)

Compute curvature vectors along a path (2nd derivative approximation)

Parameters

path_vertices	Sequential vertices defining curve
curvature_scale	Magnitude scaling factor
stride	Sample every stride-th vertex

Returns

Line segments representing discrete curvature

Curvature at i approximated by: (v[i+1] - 2*v[i] + v[i-1])

Definition at line 333 of file GeometryPrimitives.cpp.

{
    if (path_vertices.size() < 3 || stride == 0) {
        return {};
    }
 
    std::vector<Kakshya::LineVertex> curvatures;
    curvatures.reserve((path_vertices.size() - 2) / stride * 2);
 
    for (size_t i = 1; i < path_vertices.size() - 1; i += stride) {
        glm::vec3 p_prev = path_vertices[i - 1].position;
        glm::vec3 p_curr = path_vertices[i].position;
        glm::vec3 p_next = path_vertices[i + 1].position;
 
        glm::vec3 curvature = (p_next - 2.0F * p_curr + p_prev) * curvature_scale;
 
        glm::vec3 color = path_vertices[i].color;
        float thickness = path_vertices[i].thickness;
 
        curvatures.push_back({ .position = p_curr,
            .color = color,
            .thickness = thickness });
 
        curvatures.push_back({ .position = p_curr + curvature,
            .color = color,
            .thickness = thickness });
    }
 
    return curvatures;
}

Referenced by MayaFlux::Nodes::GpuSync::LineSegmentsNode::add_curvature().

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