bezier-curve

Below is the first paper of my son, Mete Yazar. It is about a mathematical and geometric exercise of calculating the surface area of an arbitrary shape (a classical guitar’s body panel). He did a good job in utilizing Bezier/de Casteljau curves and generating the…

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…

In this short tutorial, I am going to show you how to locate a parametric point on a Bezier curve. This will be a third-degree cubic Bezier curve. So, I start by placing four control points. I name these points from P0 to P3. Then,…

De Boor’s algorithm, a maestro of basis spline refinement, meticulously navigates through knots, unraveling the intricacies of B-splines with mathematical precision. Meanwhile, De Casteljau, the geometric orchestrator, takes center stage in the Bezier ballet, elegantly guiding control points through a recursive dance. Together, these algorithms…

Today’s curve is the beautiful Bezier curve. A series of linear interpolations between the coordinates of control points describe a Bezier curve. So, I created a simple tool in Grasshopper called Bezier Function Extractor to experiment with this elegant construction. In the linear form (degree…

This is a new paper published in Nexus Network Journal. I tried to implement euclidean constructions by compass in the approximation of famous parametric curves; Bézier curves, and B-Splines. Then, I created the algorithms to calculate the number of steps on a compass-only construction of…

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…

Below is the Python code you can run in Rhino, that draws a cubic Bézier curve (degree 3). As you can see, the Rhino Python code is very slow and inefficient because we calculate every point with lots of computations. Instead, we can use the…

It has been nearly 2 years since we designed and produced this garden. Similar to the first version, Common-action Gardens #2 is injected in formal park layouts. We build it for recreation as garden structures with an aim to support the “preserve, sustain, and share”…

I developed this code 13 years ago while learning the fundamentals of Visual Programming in Grasshopper. I was studying the ways of NURBS curve geometry. The animation shows the construction process of several Bezier Curves. In 2024, I optimized the code and added the thickness….