https://github.com/bubner/bezier

171-point dynamic Bezier curve generator in Unity 2D
https://github.com/bubner/bezier

bezier-curve computer-graphics cs math unity unity-webgl unity2d webgl

Last synced: 5 months ago
JSON representation

171-point dynamic Bezier curve generator in Unity 2D

• Host: GitHub
• URL: https://github.com/bubner/bezier
• Owner: bubner
• Created: 2024-05-20T06:12:56.000Z (about 2 years ago)
• Default Branch: master
• Last Pushed: 2024-07-15T10:44:51.000Z (almost 2 years ago)
• Last Synced: 2025-03-29T11:34:32.113Z (about 1 year ago)
• Topics: bezier-curve, computer-graphics, cs, math, unity, unity-webgl, unity2d, webgl
• Language: ShaderLab
• Homepage: https://serve.bubner.me/unity/bezier
• Size: 1.21 MB
• Stars: 3
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

Awesome Lists containing this project

README

          
# Bézier Curves

###### https://serve.bubner.me/unity/bezier

$$\text{Bézier curve general formula}$$


$$B(t) = \sum_{i=0}^{n} \binom{n}{i} (1-t)^{n-i} t^i P_i$$


$$\therefore B(t) = \sum_{i=0}^{n} \frac{n!}{i!(n-i)!} (1-t)^{n-i} t^i P_i$$


$$\because \binom{n}{k} = \frac{n!}{k!(n-k)!}$$




This small Unity app generates Bézier curves using the explicit definition of summated binomial coefficients and linear interpolation. Created as a proof-of-concept and for fun to learn more about the math involved in computer graphics.

## Features

- Add up to 171 points (`double` datatype precision)

- Remove individual or all points

- Edit points and reflect changes dynamically and instantly (like Desmos)

- Scrub along a vector by interpolation ratio `t` with a slider or animation

  - Draw-point scrubbing `t` shows construction lines as a set of linear interpolations

- Adjust resolution (delta t) of rendered curve

- Real-time curve rendering

[![bezier](https://github.com/bubner/Bezier/assets/81782264/2981d643-439e-44e1-8bf8-8032ffb1025a)](https://serve.bubner.me/unity/bezier)