Section 
Description 
Video 
Notes 
Exercises 
The BSpline Curve 

The Geometric Definition of the Bspline Curve:
We define the geometric definition of the Bspline curve. This is clearly an extension of the geometric definition for the Bézier curve. 




A Bézier Curve is a BSpline Curve:
What would be the knots for a Bézier curve?. 




The Analytic Definition of the Bspline Curve:
We can specify the blending functions in a recursive way, similar to the Bernstein polynomials for Bézier curves. Unfortunately, since Bsplines are piecewise Bézier curves, these functions are somewhat messy. 




Thinking in Pyramids
It is useful to use a pyramid structure to visualize the Bspline algorithms. 




The DeBoorCox Calculation
We use the DeBoorCox calculation to show that the geometric and analytic definitions of Bspline curves are equivalent. This is an interesting computation, as the technique usually doesn't work in general. This time it does. 




Properties of BSpline Curves:
Lots of properties for Bspline curves. They are similar to those for Bézier curves, but more complex because we are piecing things together. 




On Knots
Knots are slippery things. 




The CatmullRom Spline
A look at an interpolating spline for comparison. 



BSpline Curves and OpenGL 

How do we define BSpline Curves in OpenGL? 







