https://github.com/micycle1/betterbeziers
High-precision utils for 2D Cubic Bezier Curves
https://github.com/micycle1/betterbeziers
bezier bezier-curves quadrature
Last synced: about 2 months ago
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High-precision utils for 2D Cubic Bezier Curves
- Host: GitHub
- URL: https://github.com/micycle1/betterbeziers
- Owner: micycle1
- License: unlicense
- Created: 2023-01-27T10:27:36.000Z (about 2 years ago)
- Default Branch: main
- Last Pushed: 2023-03-10T15:15:04.000Z (about 2 years ago)
- Last Synced: 2025-01-18T03:28:57.398Z (3 months ago)
- Topics: bezier, bezier-curves, quadrature
- Language: Java
- Homepage:
- Size: 15.6 KB
- Stars: 2
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
[](https://jitpack.io/#micycle1/BetterBeziers)
# BetterBeziers
High-precision utils for 2D Cubic Bezier Curves.
## Overview
BetterBeziers is a Java library that provides high-precision utilities for working with 2D Cubic Bezier Curves. The library offers two main functions: computing the length of a cubic bezier curve and finding the time `t` at which a specific arc length occurs.
The length computation function uses _Legendre-Gauss quadrature_, while the function for finding time `t` for a specified arc length uses a hybrid approach of Newton’s method and bisection. Both of these algorithms are described in the paper _Moving Along a Curve with Specified Speed_ [[1]].
With these two functions, it is easy to sample the curve (find t) for a given distance (or fractional distance) along the curve, as well as subdividing the curve into equal-length segments. BetterBeziers offers methods for all of these operations.
## Usage
To use BetterBeziers in your project, you can add it as a dependency using [JitPack](https://jitpack.io/#micycle1/BetterBeziers).
To compute the length of a cubic bezier curve, you can use the `getLength()` function. For example:
```
final double[][] controlPoints = {{0, 0}, {0.2, 0.3}, {0.7, 0.8}, {1, 1}};
CubicBezier bezier = new CubicBezier(controlPoints);
double length = bezier.getLength();
```
To find the time t at which a specific arc length occurs, you can use the `getCurveParameter()` function. For example:
```
final double[][] controlPoints = {{0, 0}, {0.2, 0.3}, {0.7, 0.8}, {1, 1}};
CubicBezier bezier = new CubicBezier(controlPoints);
arcLength = bezier.getLength()/3;
double t = bezier.getCurveParameter(arcLength);
```
[1]: https://www.geometrictools.com/Documentation/MovingAlongCurveSpecifiedSpeed.pdf