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8
What is the goal of Subdivision techniques? Explain Subdivision using the Lane-Riesenfeld technique!
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
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
Karteninfo:
Autor: janisborn
Oberthema: Informatik
Thema: Computergrafik
Schule / Uni: RWTH Aachen
Ort: Aachen
Veröffentlicht: 18.05.2022