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Clipping (computer graphics) Clipping path; Collision detection; Color depth; Color gradient; Color space; Colour banding; Color bleeding (computer graphics) Color cycling; Composite Bézier curve; Compositing; Computational geometry; Compute kernel; Computer animation; Computer art; Computer graphics; Computer graphics (computer science ...
The mathematical basis for Bézier curves—the Bernstein polynomials—was established in 1912, but the polynomials were not applied to graphics until some 50 years later when mathematician Paul de Casteljau in 1959 developed de Casteljau's algorithm, a numerically stable method for evaluating the curves, and became the first to apply them to computer-aided design at French automaker Citroën ...
Special properties of implicit curves make them essential tools in geometry and computer graphics. An implicit curve with an equation F ( x , y ) = 0 {\displaystyle F(x,y)=0} can be considered as the level curve of level 0 of the surface z = F ( x , y ) {\displaystyle z=F(x,y)} (see third diagram).
PDE surfaces are used in geometric modelling and computer graphics for creating smooth surfaces conforming to a given boundary configuration. PDE surfaces use partial differential equations to generate a surface which usually satisfy a mathematical boundary value problem.
The curves remain widely used in computer graphics to model smooth curves. Bézier developed the notation, consisting of nodes with attached control handles, with which the curves are represented in computer software. The control handles define the shape of the curve on either side of the common node, and can be manipulated by the user, via the ...
Expander graphs have many applications to computer science, number theory, and group theory, see e.g Lubotzky's survey on applications to pure and applied math and Hoory, Linial, and Wigderson's survey which focuses on computer science. Ramanujan graphs are in some sense the best expanders, and so they are especially useful in applications ...
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]
In technical applications of 3D computer graphics such as computer-aided design and computer-aided manufacturing, surfaces are one way of representing objects. The other ways are wireframe (lines and curves) and solids.