A Bézier curve is a parametric curve frequently used in computer graphics and related fields. Generalizations of Bézier curves to higher dimensions are called Bézier surfaces, of which the Bézier triangle is a special case.
A Bézier curve is a parametric curve frequently used in computer graphics and related fields. Generalizations of Bézier curves to higher dimensions are called Bézier surfaces, of which the Bézier triangle is a special case.
In vector graphics, Bézier curves are used to model smooth curves that can be scaled indefinitely. "Paths," as they are commonly referred to in image manipulation programs, are combinations of linked Bézier curves. Paths are not bound by the limits of rasterized images and are intuitive to modify. Bézier curves are also used in animation as a tool to control motion.
Bézier curves are widely used in computer graphics to model smooth curves. As the curve is completely contained within the convex hull of its control points, the points can be graphically displayed and used to manipulate the curve intuitively. Affine transformations such as translation, and rotation can be applied on the curve by applying the respective transform on the control points of the curve. Furthermore, the convex hull of the control points acts as a bounding region for quick visibility tests; if the convex hull is not visible, then the Bézier curve is also not.
Quadratic and cubic Bézier curves are most common; higher degree curves are more expensive to evaluate. When more complex shapes are needed, low order Bézier curves are connected together. This is commonly referred to as a "path" in vector graphics standards (like SVG) and vector graphics programs (like Adobe Illustrator and Inkscape). To guarantee smoothness, the control point at which two curves meet must be on the line between the two control points on either side.
Bézier curves can be Linear (order 1), Quadratic (order 2), Cubic (order 3, the most common form in drawing and graphics software), and of higher order (more than 3).
