List of numerical computational geometry topics enumerates the topics of computational geometry that deals with geometric objects as continuous entities and applies methods and algorithms of nature characteristic to

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

. This area is also called "machine geometry", computer-aided geometric design, and geometric modelling. See List of combinatorial computational geometry topics for another flavor of computational geometry that states problems in terms of geometric objects as

discrete Discrete may refer to: *Discrete particle or quantum in physics, for example in quantum theory * Discrete device, an electronic component with just one circuit element, either passive or active, other than an integrated circuit * Discrete group, ...

entities and hence the methods of their solution are mostly theories and

algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...

s of

combinatorial Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

character.

Curves

In the list of curves topics, the following ones are fundamental to geometric modelling. *

Parametric curve In mathematics, a parametric equation expresses several quantities, such as the coordinates of a point (mathematics), point, as Function (mathematics), functions of one or several variable (mathematics), variables called parameters. In the case ...

Bézier curve A Bézier curve ( , ) is a parametric equation, parametric curve used in computer graphics and related fields. A set of discrete "control points" defines a smooth, continuous curve by means of a formula. Usually the curve is intended to approxima ...

** Spline ***

Hermite spline In the mathematics, mathematical subfield of numerical analysis, a Hermite spline is a spline curve where each polynomial of the spline is in Hermite polynomials, Hermite form. See also *Cubic Hermite spline *Hermite polynomials *Hermite interpola ...

**** Beta spline *****

B-spline In numerical analysis, a B-spline (short for basis spline) is a type of Spline (mathematics), spline function designed to have minimal Support (mathematics), support (overlap) for a given Degree of a polynomial, degree, smoothness, and set of bre ...

*** Higher-order spline ***

NURBS 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. It offers great flexibility and precision for handling both analy ...

Contour line A contour line (also isoline, isopleth, isoquant or isarithm) of a Function of several real variables, function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a ...

Surfaces

Bézier surface Bézier surfaces are a type of mathematical spline used in computer graphics, computer-aided design, and finite element modeling. As with Bézier curves, a Bézier surface is defined by a set of control points. Similar to interpolation in many ...

Isosurface An isosurface is a three-dimensional analog of an isoline. It is a surface that represents points of a constant value (e.g. pressure, temperature, velocity, density) within a volume of space; in other words, it is a level set of a continuous f ...

Parametric surface A parametric surface is a surface in the Euclidean space \R^3 which is defined by a parametric equation with two parameters Parametric representation is a very general way to specify a surface, as well as implicit representation. Surfaces that oc ...

Other

* Level-set method *

Computational topology Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity theory. A primary concern of algorithmic topology, as its ...

{{DEFAULTSORT:Numerical computational geometry topics Mathematics-related lists Geometric algorithms

Geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...