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In computer graphics, the centripetal Catmull–Rom spline is a variant form of the Catmull–Rom spline, originally formulated by Edwin Catmull and Raphael Rom, [1] which can be evaluated using a recursive algorithm proposed by Barry and Goldman. [2]
A smooth curve that is not closed is often referred to as a smooth arc. [6] The parametrization of a curve provides a natural ordering of points on the curve: () comes before () if <. This leads to the notion of a directed smooth curve. It is most useful to consider curves independent of the specific parametrization.
A simple tessellation pipeline rendering a smooth sphere from a crude cubic vertex set using a subdivision method. In computer graphics, tessellation is the dividing of datasets of polygons (sometimes called vertex sets) presenting objects in a scene into suitable structures for rendering.
An arc diagram is a style of graph drawing, in which the vertices of a graph are placed along a line in the Euclidean plane, with edges being drawn as semicircles in one or both of the two halfplanes bounded by the line, or as smooth curves formed by sequences of semicircles. In some cases, line segments of the line itself are also allowed as ...
A B-spline function is a combination of flexible bands that is controlled by a number of points that are called control points, creating smooth curves. These functions are used to create and manage complex shapes and surfaces using a number of points. B-spline function and Bézier functions are applied extensively in shape optimization methods. [5]
It is an example of a hedgehog, a type of curve determined as the envelope of a system of lines with a continuous support function. The hedgehogs also include non-convex curves, such as the astroid, and even self-crossing curves, but the smooth strictly convex curves are the only hedgehogs that have no singular points. [33]
For example, if X and Y are smooth over a scheme S and if i is an S-morphism, then i is a regular embedding. In particular, every section of a smooth morphism is a regular embedding. [ 1 ] If Spec B {\displaystyle \operatorname {Spec} B} is regularly embedded into a regular scheme , then B is a complete intersection ring .
A NURBS curve. (See also: the animated creation of a NURBS spline.) A NURBS surface. Non-uniform rational basis spline (NURBS) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing curves and surfaces.