Bezier
Bezier is a single header only C++11 library for Bezier curve calculations and manipulations. Currently only supports 2D bezier curves.
General Usage
The following examples demonstrate how to use the library. In this context, t is the parametrized factor defining the Bezier curve, ranging from 0 to 1. Even though the Bezier curve is defined to be between t = 0 and t = 1, there is nothing wrong with using other values for t, the results will only be outside the normal range of the bezier curve.
// Create a cubic bezier with 4 points. Visualized at https://www.desmos.com/calculator/fivneeogmh
Bezier::Bezier<3> cubicBezier({ {120, 160}, {35, 200}, {220, 260}, {220, 40} });
// Get coordinates on the curve from a value between 0 and 1 (values outside this range are also valid because of the way bezier curves are defined).
Bezier::Point p;
p = cubicBezier.valueAt(0); // (120, 60)
p = cubicBezier.valueAt(0.5); // (138.125, 197.5)
// Get coordinate values for a single axis. Currently only supports 2D.
float value;
value = cubicBezier.valueAt(1, 0); // 220 (x-coordinate at t = 1)
value = cubicBezier.valueAt(0.75, 1); // 157.1875 (y-coordinate at t = 0.75)
value = cubicBezier.length(); // 272.85 (Arc length of the bezier curve)
// Translate and rotate Bezier curves.
Bezier::Bezier<3> copy = cubicBezier;
copy.translate(10, 15); // Translate 10 in x-direction, 15 in y-direction
copy.rotate(0.5); // Rotate 0.5 radians around the origin
copy.rotate(3.14, {-5, 20}); // Rotate 3.14 radians around (-5, 20)
// Get normals along the bezier curve.
Bezier::Normal normal = cubicBezier.normalAt(0.75); // Get normalized normal at t = 0.75. Add false as second argument to disable normalization.
float angle = normal.angle(); // Angle in radians
float angleDeg = normal.angleDeg(); // Angle in degrees
// Get tangents along the bezier curve.
Bezier::Tangent tangent = cubicBezier.tangentAt(0.25); // Get normalized tangent at t = 0.25. Add false as second argument to disable normalization.
angle = tangent.angle(); // Angle in radians
angleDeg = tangent.angleDeg(); // Angle in degrees
// Get derivatives of the Bezier curve, resulting in a Bezier curve of one order less.
Bezier::Bezier<2> db = cubicBezier.derivative(); // First derivative
Bezier::Bezier<1> ddb = db.derivative(); // Second derivative
// Get extreme values of the Bezier curves.
Bezier::ExtremeValues xVals = cubicBezier.derivativeZero(); // Contains 3 extreme value locations: t = 0.186811984, t = 1.0 and t = 0.437850952
Bezier::ExtremeValue const& xVal = xVals[0]; // Contains t value and axis for the first extreme value
Bezier::Point xValCoord = cubicBezier.valueAt(xVal.t); // Get the coordinates for the first extreme value (97.6645355, 182.55565)
Bezier::ExtremePoints xPoints = cubicBezier.extremePoints(); // Or get all the extreme points directly (includes 0 and 1)
// Get bounding boxes of the Bezier curves.
Bezier::AABB aabb = cubicBezier.aabb(); // Axis Aligned Bounding Box
aabb = cubicBezier.aabb(xPoints); // Or get from extreme points (if you already have them) to reduce calculation time
Bezier::TightBoundingBox tbb = cubicBezier.tbb(); // Tight bounding box
// Split the Bezier curve at desired points. The left and right parts are new bezier curves
// of the same order as the original curve.
auto split = cubicBezier.split(0.5f);
auto left = split.left; // Left part of the split
auto right = split.right; // Right part of the split
// Find the mid point on the curve by arch length.
float tAtMidPoint = cubicBezier.archMidPoint(); // 0.70718
Bezier::Point midPoint = cubicBezier.valueAt(tAtMidPoint); // (183.8, 168.8)