ECS 178 -- Geometric Modeling

Unit 7 -- Transitioning to Subdivision Curves

But Subdivision can do much more

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Unit 7 -- Transitioning from B-splines to Subdivision Curves

Section Description Video Notes Exercises

Transforming from B-Splines to Subdivision

Why

Chaikin's Curve

In 1974, George Chaikin gave a talk at the University of Utah, and the topic of this talk has been transformed into what we know today as Subdivision Curves.

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Hat

Working with the Uniform B-Spline Curve

The uniform B-spline curve, generated from a uniform set of knots, has some properties that we can utilize to generate subdivision curves.

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Matrix

A Matrix Representation of the Uniform B-Spline Curve

Because the blending functions of the Uniform B-spline curve are just shifted versions of each other, this enables us to write the Uniform B-spline curve in a matrix form.

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Basis

Subdivision Algorithms are refinement schemes. What are refinement schemes?

Like Chaikin's method, these schemes take a set of points representing a control point set, and refine them into a new control point set, typically with more elements.

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