#b-spline

This is a short video tutorial on the B-Spline decomposition I studied earlier here. This tutorial demonstrates how to decompose a B-Spline curve into Bezier curves using Rhino. Despite the original Bezier-de Casteljau algorithm requiring degree+1 control points, Rhino allows drawing a degree-3 curve with any number of control points. By examining knot points and dividing segments appropriately, the B-Spline curve can be manually subdivided into Bezier curves. This involves placing control points, dividing segments, and connecting points in a…

I have been studying the Bezier-De Casteljau algorithm for several years. Last week, I finally managed to understand and implement B-Spline Construction in Rhino and Grasshopper Python code, using the Cox-De Boor algorithm. This algorithm calculates the effect of control points on a B-Spline with many control points. After this, I am not limited to the degree+1 control points. This animation shows both algorithms working together. This Rhino Python code in a Grasshopper definition can handle three tasks. The first…

I realized this method of constructing basis splines from given control points while searching for a way to teach students about basis splines. I couldn’t find an easy and visual method to create clamped basis splines by connecting simple cubic Bézier spans. It is a tough job and requires lots of complex equations. However, I suddenly realized that there is a special way of doing that. So I decided to share this with the people searching for an easy way…