kochanekBartels
Converts this polyline into a Kochanek-Bartels spline, after Kochanek and Bartels, "Interpolating splines with local tension, continuity, and bias control" (SIGGRAPH 1984): a cubic Hermite spline through all points whose tangents are shaped by a tension, continuity and bias, see TCB. With all three 0 it is the uniform Catmull-Rom spline.
At point pᵢ, with Δ₋ = pᵢ - pᵢ₋₁ and Δ₊ = pᵢ₊₁ - pᵢ, the curve arrives with tangent (1-t)(1-c)(1+b)/2·Δ₋ + (1-t)(1+c)(1-b)/2·Δ₊ and leaves with tangent (1-t)(1+c)(1+b)/2·Δ₋ + (1-t)(1-c)(1-b)/2·Δ₊. The two are equal, so the curve is C1, only for continuity 0. Every edge is parametrized over 0, 1, as in the paper without its adjustment for uneven keyframe spacing. The ends of an open polyline take the missing edge as the mirror image of the edge next to it, so with all parameters 0 the curve leaves the first point along the first edge.
Parameters
whether the polyline is closed, the last point should then not repeat the first
the tension at every point
the continuity at every point
the bias at every point
the polarity of the resulting contour
Converts this polyline into a Kochanek-Bartels spline with a tension, continuity and bias per point, see List.kochanekBartels.
Parameters
the tension, continuity and bias at every point
Converts this 3D polyline into a Kochanek-Bartels spline, for instance for a camera path, see List.kochanekBartels.
Converts this 3D polyline into a Kochanek-Bartels spline with a tension, continuity and bias per point.