BSpline De Boor's algorithm - Dieptranivsr/DroneIVSR GitHub Wiki

B-splines cheatsheet

• degree k
• n + 1 control points
• m + 1 knots
• m = n + k + 1

B-splines

De Boor's algorithm

A cubic B-spline with 16 segments and endpoint interpolation.

ToDo

1. Implement the De Boor’s algorithm.
2. Evaluate B-spline for the simple dataset. Modify the knot vector and recompute. What changed?
3. Evaluate B-spline for the spiral dataset. Modify the knot vector to 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5. What changed?
4. Evaluate B-spline for the camel dataset. Move the front leg by changing the x-coordinate of the last control point to -1.5. Which segments of the curve have changed? Why?

NURBS

matrix[:,0] *= matrix[:,2]
matrix[:,0] /= matrix[:,2]

Resources

• B-spline and De Boor’s algorithm
• 1.4.2 B-spline curve and 1.4.3 Algorithms for B-spline curves, online chapters from the book Shape Interrogation for Computer Aided Design and Manufacturing by N. Patrikalakis, T. Maekawa & W. Cho
• NURBS on wikipedia (includes the circle example)
• homepage of Prof. de Boor