Make Points along Spline (vuo.point.make.spline)

Adds more points in between the list of input points.

This node produces an approximation of a cubic Hermite spline. The curve is continuous and passes through each control point (unlike, say, Bézier and B-splines, where the curve merely passes near the control points). The shape of the curve at a given point is affected by the point before and the point after it.

Changing the Tension and Continuity values has a similar effect on the path, but each differs in the way it affects the placement of the interpolated points: increasing Tension causes the interpolated points to bunch up near the control points (resulting in smooth deceleration and acceleration when used to control motion), whereas decreasing Continuity causes sharp transitions while maintaining spacing (enabling sudden motion changes, like bouncing).

Setting Continuity to -1 results in linear interpolation (evenly spaced points along straight lines between the input points).

Setting Tension, Continuity, and Bias all to 0 results in a Catmull–Rom spline.

This particular spline formulation — the Tension/Continuity/Bias parameterization — was developed by Doris H. U. Kochanek and Richard H. Bartels in their 1984 SIGGRAPH paper.

Keywords: Catmull-Rom, Kochanek–Bartels, TCB, cardinal, cubic, curve, hermite, interpolate, keyframe, linear, list, math, number, shape

Example composition:

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