Add Pattern-based Distortion Generator

[jboarman]

Printed documents often include artifacts that may come from the paper textures, printing presses, etc.

The geopatterns python port offers a potential avenue for generating such patterns that could be processed a bit and merged into the paper layer. Brandon Mills offers a web-based demo of geopatterns.

Below is an illustrative example that comes from the Tai Le Historical Document Image Binarization Dataset 2021:

[jboarman]

Voronoi and Delaunay tessellation offer another method to generate patterns that could be sampled and applied for generating distortions. This is particularly appealing since there are readily available python implementations that could be more quickly leveraged:

• https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.Delaunay.html
• https://github.com/Stochastic13/Voronoi-Tessellations

Voronoi Tessellation

Delaunay Tessellation

Voronoi vs Delaunay Tessellation

Additionally, colorized implementations can be generated based on a source image where the color of each shape is determined by the average color of each corner and the center of the polygon^1. Further, this may serve as a potential shortcut for implementing wrinkled paper.

[jboarman]

Related concept, using aperiodic tiling

An aperiodic monotile David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss, 2023

An aperiodic monotile, sometimes called an "einstein", is a shape that tiles the plane, but never periodically. In this paper we present the first true aperiodic monotile, a shape that forces aperiodicity through geometry alone, with no additional constraints applied via matching conditions. We prove that this shape, a polykite that we call "the hat", must assemble into tilings based on a substitution system. The drawing above shows a patch of hats produced using a few rounds of substitution.

This page collects the resources associated with this work. We invite you to look at all of the following. https://cs.uwaterloo.ca/~csk/hat/

[jboarman]

Organic Patterns

This "pattern" is more organic and random-looking, but still consistent enough to think of it as a pattern. In this case, the pattern would be combined with a deboss function (see #164) when rendered to the paper layer.

Use of Skeletonize Function

These organic patterns show the use of the skeletonize function which might be useful when applied to noise to generate organic-looking patterns:

Perlin Noise as Probability Function

Using Perlin noise (see background of this image) could also be used as a probability function for placement of shapes on a layer:

[jboarman]

While subconsciously searching for what a "pattern" even means, I noticed this paper from a mailed envelope containing tax information intended to obscure its contents.

Wikepedia has some notes on patterns from nature that also reflect on these ideas.

So far, I think patterns have the following characteristics:

• repetition
• structure, generally involving repeating shapes
• mostly regular, but could also be locally stochastic while globally averaging towards an overall regular shape or family of shapes
• interactions of shapes (whether same or dissimilar shapes)
• types of shapes may be infinite, but include all the standard geometries, including dots, lines, circles, polygons (triangles, rectangles, etc), waves

[jboarman]

Errors in Perlin Noise Makes Interesting Patterns

https://stackoverflow.com/questions/26611906/strange-result-from-perlin-noise-generator

[jboarman]

This repo some experiments with "plane-filling curves" and Fourier transforms that are interesting for considering future types of patterns.

There's more details on a number of space-filling curve techniques on wikipedia.

• Dragon curve
• Gosper curve
• Hilbert curve
• Koch curve
• Moore curve
• Murray polygon
• Sierpiński curve