Box Blur

If you ever have heard the terms “Box Blur”, “Boxcar Function”, “Box Filter”, “Boxcar Integrator” or other various combinations of those words, you may have thought it was some advanced concept that is hard to understand and hard to implement. … Continue reading

Resizing Images With Bicubic Interpolation

In the last post we saw how to do cubic interpolation on a grid of data. Strangely enough, when that grid is a grid of pixel data, bicubic interpolation is a common method for resizing images! Bicubic interpolation can also … Continue reading

Cubic Hermite Rectangles

Time for another Frankenstein post. This time we are going to combine the following: Cubic Hermite Interpolation Rectangular Bezier Patches The end result is going to be a Cubic Hermite Rectangle Surface like the below. Note that the curve only … Continue reading

Cubic Hermite Interpolation

It’s a big wide world of curves out there and I have to say that most of the time, I consider myself a Bezier man. Well let me tell you… cubic Hermite splines are technically representable in Bezier form, but … Continue reading

Lagrange Rectangles

In this post we are going to Frankenstein ideas from two other recent posts. If you haven’t seen these yet you should probably give them a read! Ingredient 1: Lagrange interpolation Ingredient 2: Rectangular Bezier Patches Lagrange Surface Lets say … Continue reading

Finite Differences

Finite differences are numerical methods for approximating function derivatives – otherwise known as the slope of a function at a specific point on the graph. This can be helpful if it’s undesirable or impossible to calculate the actual derivative of … Continue reading

Rectangular Bezier Patches

Rectangular Bezier Patches are one way to bring Bezier curves into the 3rd dimension as a Bezier surface. Below is a rendered image of a quadratic Bezier rectangle (degree of (2,2)) and a cubic Bezier rectangle (degree of (3,3)) taken … Continue reading

Lagrange Interpolation

Lagrange interpolation is a way of crafting a function from a set of data points.. In the past I’ve seen reference to Lagrange interpolation in relation to audio programming like, for helping make a soft knee for a limiter, but … Continue reading

The De Casteljau Algorithm for Evaluating Bezier Curves

Over the past year or so I’ve been digging fairly deeply into curves, mostly into Bezier curves specifically. While digging around, I’ve found many mentions of the De Casteljau algorithm for evaluating Bezier curves, but never much in the way … Continue reading