Extra Polynymous
I want to approximate images using constant-color shapes. Given a shape, how do we choose where to put it? We have the original image, , and the approximate image, . I want to place a shape, , with area on such that it improves the approximation. First, define the average color under the shape (which […]
Line integral convolution, or LIC, is a nice way to get a sense of the directions of a flow field. By averaging a noisy image along sections of streamlines, you get some nice streaks. Look at this example, applied to the flow around a spinning cylinder: There are a couple main parameters to tweak: the […]
There’s a whole body of literature out there for illustrating vector fields. One topic is ‘evenly spaced streamlines’: lines that follow a direction field, and don’t get too close to each other. How do we do this? From a starting point, use the midpoint method to figure out the position of the next point. If […]
I’ve refined image approximations with rectangles and triangles. Let’s try with splitting regions into two with a straight line, and filling each part with the average color that they’re covering. This is the same basic idea as the rectangles, except that now the line can be at any angle, rather than just vertical or horizontal. […]
The easiest way to make a reaction-diffusion pattern involves two blurs and a comparison. It doesn’t give the full fancy dynamics of other approaches, but it works well for halftoning. This simple method avoids differential equations, and works with just image filtering. At each step, the activation chemical spreads with radius , and the inhibition […]
Voronoi diagrams are great, so let’s use them to stylize images. First, let’s just throw a bunch of points on an image, and compute the Voronoi diagram. Then for each cell, we fill it with the average or median color within: Hmm. That’s not great. It doesn’t pay attention to the edges at all, and […]
Previously, I split an image into a bunch of rectangles. What about using triangles? This requires more thought, as it’s a little trickier to divide up the plane using triangles. The natural solution is to keep track of a set of vertices, then use a Delaunay triangulation to split up the image. First, let’s do […]
I want to represent an image with a bunch of rectangles. Let’s say that each shape has constant color, as a start. First, fill a rectangle with the average color that it covers. That’s the initial approximation. Wherever the error in a rectangle (between the original image and the approximation) is too big, subdivide that […]
Check out this art style! They dip a string in ink, lay it on a page, fold the page over, and pull the string out of the bottom. It leaves nice floral patterns with the ink, and is pleasantly complex and organic. I wanted to mimic this style algorithmically, so the first thing that I […]
Tic Tac Toe (TTT) is a minimally complicated game, so it is relatively easy to find all possible moves and see which will lead you to a victory, tie, or loss. I’ve never solved TTT before, so I threw together some code to do that! Solving Tic Tac Toe Without removing boards that are effectively […]