High-precision utils for 2D Cubic Bezier Curves.
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.
To use BetterBeziers in your project, you can add it as a dependency using JitPack.
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);