Geometric Modeling Lectures Unit 8 -- Subdivision Curves Looking at curves in a different way!
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# Unit 8 -- Subdivision Curves

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## Subdivision Curves

### Splitting a Quadratic Uniform B-Spline Curve

We can use the matrix notation of a quadratic uniform B-spline curve to generate splitting matrices that separate the curve into two segments.

### Subdivision Curves based upon the Quadratic Uniform B-Spline Curve

We can develop a subdivision/refinement procedure based on quadratic uniform B-spline curves that looks exactly like Chaikin's algorithm.

### Splitting a Cubic Uniform B-Spline Curve

We can use the matrix notation of a cubic uniform B-spline curve to generate splitting matrices that separate the curve into two segments.

### Subdivision Curves based upon the Cubic Uniform B-Spline Curve

We can extend these methods to develop a subdivision/refinement procedure based on the cubic uniform B-spline curve.

### Vertex and Edge Points

We can classify points on the uniform cubic B-spline refinement in a simple way.

### Direct Calculation of Points on a Cubic Subdivision Curve

We can generate methods to directly calculate points on the curve, greatly simplifying the refinement process.

### Calculating Tangent Vectors to Subdivision Curves

By modifying the procedure to directly generate points, we can directly calculate tangent vectors on the surfaces.