Tag: bezier

Jun

Smooth Bezier splines

Apparently, having mathematically defined curves that pass through a set of desired points is a thing. And (cubic) Bezier splines are popular for this. Professor Dagan (mentioned previously) sent me a link. Smooth Bézier Spline Through Prescribed Points The article outlines a method that given a set of points you want your Bezier curve to […]

Dec

Bezier curves prefer tea

My maths professor was hammering on the fact that Citroen used Bezier curves to make sure their cars have aesthetically pleasing curves. Again. (This is not a sponsored post from the automaker). While I appreciate his effort in trying to make what I’m learning relevant to the real world, I kinda got the idea that […]

Jul

3D Bézier curve editor

Timo Suoranta created a 3D Bézier curve editor. As of this writing, the program runs on Windows and requires OpenGL version 3 or later (shaders are involved). Here’s a screenshot: [click for larger image] It looks awesome. What, no? Then you have to understand picking. In 2D, any point you click on the screen is […]

Jul

Help! Getting a “nice” reverse engineered Bézier curve

Commenter Timo wants to know how to get a nice shape for a reverse engineered Bézier curve. The question started from calculating the control points of a cubic Bézier curve if you’re given 4 points that lie on the curve, assuming the first and last given points were also the first and last control points. […]

May

Reverse engineering quadratic Bézier curves

I wrote an article on cubic Bézier curves almost 3 years ago. And there had been emails and comments sporadically during that period. The latest one was from a lady, so I decided to write something about it (yes, I’m biased). The recurring (if you count 2 or 3 as recurring) question is about quadratic […]

Sep

Linear and cubic interpolation

Interpolation is a method of calculating a value from a set of given values. We’ll be looking at interpolation with a bias towards image processing, but the theory can be generalised for other purposes. You’ve probably already solved some interpolation problems without knowing it. Let me give you an example. A distance problem Suppose there […]

Jun

Reverse engineering Bezier curves

My initial contact with Bezier curves came when I was studying 3 dimensional computer graphics. The professor introduced the standard cubic Bezier curve equation, which looks something like this B(t) = (1-t)3p0 + 3(1-t)2tp1 + 3(1-t)t2p2 + t3p3 where p0, p1, p2, p3 are the control points. WARNING: you might find this an intensive discussion […]