List of numerical computational geometry topics enumerates the topics of computational geometry

Computational geometry

Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational...

 that deals with geometric objects as continuous entities and applies methods and algorithms of nature characteristic to numerical analysis

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....

. 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 mathematics

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not...

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

Algorithm

In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

s of combinatorial

Combinatorics

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...

 character.

Curves

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

• Parametric curve
  • Bézier curve
    Bézier curve
    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....
    
    
  • Spline
    Spline (mathematics)
    In mathematics, a spline is a sufficiently smooth piecewise-polynomial function. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low-degree polynomials, while avoiding Runge's phenomenon for higher...
    
    
    • Hermite spline
      Hermite spline
      In the mathematical subfield of numerical analysis, a Hermite spline is a spline curve where each polynomial of the spline is in Hermite form.-See also:*Cubic Hermite spline*Hermite polynomials*Hermite interpolation...
      
      
      • Beta spline
        • B-spline
          B-spline
          In the mathematical subfield of numerical analysis, a B-spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. B-splines were investigated as early as the nineteenth century by Nikolai Lobachevsky...
          
          
    • Higher-order spline
    • NURBS
• Contour line
  Contour line
  A contour line of a function of two variables is a curve along which the function has a constant value. In cartography, a contour line joins points of equal elevation above a given level, such as mean sea level...