curveto

Curveto is a path drawing operation used in vector graphics to render a cubic Bézier curve from the current point to a specified endpoint, guided by two control points. The curve is defined by four points: P0 (the starting point, the current point), P1 and P2 (the control points), and P3 (the endpoint). As a parameter t ranges from 0 to 1, the curve follows a cubic Bézier equation that blends the four points to produce a smooth transition from P0 to P3.

In common graphics languages, curveto appears in several forms. In PostScript and PDF, the operator curveto takes six numbers in the order x1 y1 x2 y2 x y and appends a cubic Bézier segment to the current path, using (x1, y1) and (x2, y2) as control points and (x, y) as the endpoint. In SVG path data, the equivalent commands are C for an absolute-curveto and c for a relative-curveto, each with the same six coordinates. After the command, the current point becomes the endpoint (x, y).

Mathematically, a curveto segment is one piece of a cubic Bézier curve, which provides smooth, scalable curves widely used in fonts, illustrations, and UI graphics. It can be chained with other path commands to form complex shapes. Some systems also provide shorthand or smoothing variants (such as SVG’s S or T commands) that infer control points from preceding curve segments. Curveto remains fundamental in vector graphics for precise, controllable curvature.