Circles are too flat. What if we want to make a cylindrical Earth? We can take the same sort of approach, but we need a couple more parameters. Let’s say we have a cap radius and height , then we can make this: With the sphere radius , by matching the surface areas, the possible […]

## Variable-Radius Flat Earth

No, not the conspiracy theory. For example, here is an Earth-splat: And here is an Earth-square: And both are equal-area projections! How did I do this? Math. Math math math. We’ll use spherical coordinates, with polar angle and azimuthal angle . This means that latitude is, in radians, , and longitude is . We’ll say […]

## Stochastic Halftoning

Fancy patterns aren’t totally necessary. A field of random numbers can also provide a pattern with the right properties needed for local partitionless thresholding. Even simple white noise can work, as the header image shows. But that’s not so pretty. What about other colors of noise? Or minimum wavelengths? The following image shows different colors […]

## Thresholding with a Pattern

Last time, I used the Cumulative Distribution Function of an image’s intensity to make a black and white image. This time, I’ll use a different pattern as the basis for halftoning the image. For example, I’ll use the following pattern of circles on a regular grid: This time, instead of finding a threshold from the […]

## Partitionless Halftoning

We’ve looked at two halftoning methods using thresholding: either directly on the image, or using a pattern. These require making subdivisions of the image to get any decent spatial resolution. Instead, we can specify properties of the pattern such that the pattern itself acts as a threshold. The black and white image can then be […]

## Intro to Halftoning

The general idea behind halftoning is to render an image using a very limited number of colors. On this blog, I’ll focus particularly on rendering black and white images. The following image is the Lena test image, and its grayscale version (converted in MATLAB). I’ll be using these for most of the approaches that I […]

## Earth as a Disc

I wanted an equal-area projection of the earth onto a disk. This is a simple one. We’ll use spherical coordinates, with polar angle and azimuthal angle . This means that latitude is, in radians, , and longitude is . We’ll say that the sphere has a radius of . We’ll have the North pole at […]