Since I already had the binary search and interpolation code, it was just a matter of writing different samplers for ellipses and Bézier curves. ;; make a sampler function for a bezier curve (defun make-bezier-sampler (p0 p1 p2 p3) (lambda (k) (decasteljau p0 p1 p2 p3 k))) ;; make a…
Category: Maths
More on ellipses
I think I will use the same method as I do for Bézier curves to step along the circumference. Another generalisation I had to make from the circle code is with respect to the normal. For a circle of radius r, centred on the origin, and parameterised by angle θ,…
On ellipses
Having conquered equidistant spacing along a Bézier curve, my thoughts now turn to the same problem for an ellipse. I have solved the problem for a circle of course, which is a special case of an ellipse. One would think that going from a circle to an ellipse would be…
Experimenting with (cubic) Bézier subdivision
As you know, a Bézier curve (here meaning specifically a cubic Bézier) is often used for drawing all kinds of things in vector graphics. It has the nice property that the endpoints and control points form a bounding box, and deCasteljau’s algorithm is a nice numerically stable way of evaluating…
Exploring Pascal’s Triangle
Pascal’s Triangle (henceforth known as PT). You know – that thing you learned in maths. The Wikipedia entry, like most mathematical Wikipedia entries, reads (if your mathematical background is anything like mine) like “here’s a few things you might vaguely remember from school, oh and of course gleep = glorp”….