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Subdivision Curves 





Splitting a Quadratic Uniform BSpline Curve
We can use the matrix notation of a quadratic uniform Bspline curve to generate splitting matrices that separate the curve into two segments. 





Subdivision Curves based upon the Quadratic Uniform BSpline Curve
We can develop a subdivision/refinement procedure based on quadratic uniform Bspline curves that looks exactly like Chaikin's algorithm. 





Splitting a Cubic Uniform BSpline Curve
We can use the matrix notation of a cubic uniform Bspline curve to generate splitting matrices that separate the curve into two segments. 





Subdivision Curves based upon the Cubic Uniform BSpline Curve
We can extend these methods to develop a subdivision/refinement procedure based on the cubic uniform Bspline curve. 





Vertex and Edge Points
We can classify points on the uniform cubic Bspline 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. 



