epilys/bitmappers-companion

zine/book about bitmap drawing algorithms and math with code examples in Rust

A Bitmapper's Companion - zine/book about bitmap drawing algorithms and math with code examples in Rust

A small zine/book written in LaTeX. In progress. See Building section below for how to build.

View current PDF build here

Click to show planned contents

1. Introduction

• Data representation
• Displaying pixels to your screen
• Bits to byte pixels
• Loading graphics files in Rust
• Including xbm files in Rust

2. Points And Lines

• Distance between two points
• Equations of a line
  • Line through a point 𝑃 = (𝑥𝑝, 𝑦𝑝) and a slope 𝑚
  • Line through two points
• Distance from a point to a line
  • Using the implicit equation form
  • Using an 𝐿 defined by two points 𝑃1, 𝑃2
  • Using an 𝐿 defined by a point 𝑃𝑙 and angle ̂𝜃
  • Find perpendicular to line that passes through given point
• Angle between two lines
  • Intersection of two lines
  • Line equidistant from two points
  • Normal to a line through a point

3. Points And Line Segments

• Drawing a line segment from its two endpoints
• Drawing line segments with width
• Intersection of two line segments
  • Fast intersection of two line segments
• Points, Lines and Circles
• Equations of a circle
• Bounding circle

4. Curves other than circles

• Parametric elliptical arcs
• Bézier curves

5. Points, Lines and Shapes

• Union, intersection and difference of polygons
• Centroid of polygon
• Polygon clipping
• Triangle filling
• Flood filling

6. Vectors, matrices and transformations

• Rotation of a bitmap
  • Fast 2D Rotation
• 90° Rotation of a bitmap by parallel recursive subdivision
• Magnification/Scaling
  • Smoothing enlarged bitmaps
  • Stretching lines of bitmaps
• Mirroring
• Shearing
  • The relationship between shearing factor and angle
• Projections

7. Addendum

• Faster Drawing a line segment from its two endpoints using Sym- metry
• Joining the ends of two wide line segments together
• Composing monochrome bitmaps with separate alpha channel data
• Orthogonal connection of two points
• Join segments with round corners
• Faster line clipping
• Space-filling Curves
  • Hilbert curve
  • Sierpiński curve
  • Peano curve
  • Z-order curve
  • flowsnake curve
• Dithering
  • Floyd-Steinberg
  • Atkinson dithering
• Marching squares

Samples

Cover	Thumb index overview
Frontmatter	contents
Page spread	Bezier interactive demo

Building

Run make (might need to run it twice), output will be in the ./build directory.

To run the rust example binaries, first you can inspect them with ls ./src/bin/, for example:

$ ls ./src/bin
atkinsondither.rs
beams.rs
bezierglyph.rs
bezier.rs
boundingcircle.rs
bresenham.rs
distance_between_two_points.rs
floyddither.rs
fonts.rs
hilbert.rs
introduction.rs
rotation.rs
scale.rs
shearing.rs
smooth_scale.rs
xbmtors.rs
zcurve.rs

Then execute one with cargo run --bin for example cargo run --bin atkinsondither.