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We interpret a sequence of points as the control points of a B-Spline curve

Now, we want to describe the same curve with a higher number of control points.

We define two operators on the sequence

Doubling

Averaging


To determine the new vertex positions, we compute weighted positions based on even / odd rules.

Subdivision Operators
Linear (primal)

Quadratic Spline (dual)

Cubic Spline (primal)


TODO: Fix this explanation

Consider the B-Spline basis function .
It is a piecewise linear function between




We can write as an affine combination of the same function with parameter :


We can do this for uniform B-Spline basis functions in general:

where