CubicCurve2D

CubicCurve2D refers to a mathematical concept used in computer graphics and geometry to represent a smooth curve in two-dimensional space. It is defined by four points: a start point, an end point, and two control points. These control points influence the shape and curvature of the line connecting the start and end points without necessarily lying on the curve itself. The most common type of CubicCurve2D is the Bézier curve, specifically the cubic Bézier curve.

The mathematical representation of a cubic Bézier curve is typically expressed as a parametric equation. This equation uses a parameter, often denoted by 't', which varies from 0 to 1. As 't' changes from 0 to 1, the point on the curve moves from the start point (when t=0) to the end point (when t=1). The positions of the two control points dictate how the curve bends and forms its overall shape.

Cubic curves are widely used in vector graphics software, font design, animation, and user interface elements due to their ability to create smooth, flowing lines and complex shapes. They offer a good balance between simplicity of definition and the flexibility to create a wide range of curves. The mathematical formulation allows for precise control over the curve's tangents at its endpoints.