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Bezier

Bezier is a single header only C++11 library for bezier curve calculations and manipulations. Currently only supports 2D bezier curves.

Include Bezier in Your Project

If it is desirable to use the single header file directly, simply download and include it, for example curl -O https://raw.githubusercontent.com/oysteinmyrmo/bezier/master/include/bezier.h.

It is also easy using CMake's FetchContent functionality:

include(FetchContent)

FetchContent_Declare(
    bezier
    GIT_REPOSITORY https://github.com/oysteinmyrmo/bezier.git
    GIT_TAG        v0.2.1
)

set(BEZIER_TESTS OFF) # Default ON
FetchContent_MakeAvailable(bezier)

...

target_link_libraries(some_target PRIVATE bezier)

When this is done the library can be included by doing #include <bezier/bezier.h>.

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, 160)
p = cubicBezier.valueAt(0.5); // (138.125, 197.5)

// Get coordinate values for a single axis. Currently only supports 2D.
double 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.
double angle = normal.angle();       // Angle in radians
double 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(0.5);
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.
double tAtMidPoint = cubicBezier.archMidPoint();           // 0.70718
bezier::Point midPoint = cubicBezier.valueAt(tAtMidPoint); // (183.837, 168.768)