BezierCurve Class

Bezier curve is a curve that is defined by positions of control points and the tangents at the control points. The curve passes through the specified control points, while the curvature is defined by the tangents.

The specified curve positions (the points the curve will pass though) and tangent points are defined in a single array of control points (Vector3[]).

The structure of the control points array is as follows:
control point index = 0: start position of the curve
control point index = 1: point that defines the tangent from the curve's start position to the next position.

control point index = 2: point that defines the tangent from the previous position to this position.
control point index = 3: the second position on the curve.
control point index = 4: point that defines the tangent from this position to the next position.

... (three control points for other positions; two for tangents and one for curve position.)
control point index = n - 2: point that defines the tangent from the previous position to the last position.
control point index = n - 1: the last position on the curve.

It is possible to fully define the Bezier curve by specifying all the required control points. But because it could be quite difficult to define all the tangent control points, it is also possible to define the Bezier curve by specifying only the curve positions and defining the curve scale, which defines how far from the curve positions the tangent control points are defined. This way, the curve scale defines the curvature.

The BezierCurve instance can be created by specifying all the control points in the BezierCurve constructor. To create a BezierCurve that goes through specified positions use the static CreateBezierCurvePositionsThroughPoints(Vector3, Int32, Single) static method. This method automatically calculates the tangent control positions based on the specified curveScale parameter.

To make the curve smooth, more points are created on a segment between two control points. The number of points generated per a segment is controlled by the positionsPerSegment parameter.

It is also possible to get the positions on the curve without creating an instance of BezierCurve class and with using static CreateBezierCurvePositions(Vector3, Int32) or CreateBezierCurvePositionsThroughPoints(Vector3, Int32, Single) methods. Both methods return Vector3[] array that defines the curve (i.e., the array of interpolated points that can be used to draw the curve).

For advanced use, it is possible to create an instance of the BezierCurve class. This enables calling GetPositionOnCurve(Single) method that returns any position on the curve as defined by the t parameter. The t parameter can have any value between 0 to 1, with 0 corresponding to the first control point and 1 corresponding to the last control point.

NOTE: To create a B-spline or NURBS curve use the BSpline class.

Reference