__NOTOC__ Geometric modeling is a branch of

applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathemat ...

and computational geometry that studies methods and

algorithms In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

for the mathematical description of shapes. The shapes studied in geometric modeling are mostly two- or three-

dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coor ...

al, although many of its tools and principles can be applied to sets of any finite dimension. Today most geometric modeling is done with computers and for computer-based applications. Two-dimensional models are important in computer

typography Typography is the art and technique of arranging type to make written language legible, readable and appealing when displayed. The arrangement of type involves selecting typefaces, point sizes, line lengths, line-spacing ( leading), an ...

and

technical drawing Technical drawing, drafting or drawing, is the act and Academic discipline, discipline of composing Plan (drawing), drawings that Visual communication, visually communicate how something functions or is constructed. Technical drawing is essent ...

. Three-dimensional models are central to computer-aided design and

manufacturing Manufacturing is the creation or production of goods with the help of equipment, labor, machines, tools, and chemical or biological processing or formulation. It is the essence of secondary sector of the economy. The term may refer to a ...

(CAD/CAM), and widely used in many applied technical fields such as

civil Civil may refer to: *Civic virtue, or civility *Civil action, or lawsuit * Civil affairs *Civil and political rights *Civil disobedience *Civil engineering *Civil (journalism), a platform for independent journalism *Civilian, someone not a membe ...

and

mechanical engineering Mechanical engineering is the study of physical machines that may involve force and movement. It is an engineering branch that combines engineering physics and mathematics principles with materials science, to design, analyze, manufacture, ...

architecture Architecture is the art and technique of designing and building, as distinguished from the skills associated with construction. It is both the process and the product of sketching, conceiving, planning, designing, and constructing buildings ...

geology Geology () is a branch of natural science concerned with Earth and other astronomical objects, the features or rocks of which it is composed, and the processes by which they change over time. Modern geology significantly overlaps all other Ea ...

and medical image processing. Geometric models are usually distinguished from

procedural Procedural may refer to: * Procedural generation, a term used in computer graphics applications *Procedural knowledge, the knowledge exercised in the performance of some task * Procedural law, a legal concept *Procedural memory, a cognitive scienc ...

and

object-oriented model Object-oriented programming (OOP) is a programming paradigm based on the concept of "objects", which can contain data and code. The data is in the form of fields (often known as attributes or ''properties''), and the code is in the form of pr ...

s, which define the shape implicitly by an opaque

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

that generates its appearance. They are also contrasted with

digital image A digital image is an image composed of picture elements, also known as ''pixels'', each with '' finite'', '' discrete quantities'' of numeric representation for its intensity or gray level that is an output from its two-dimensional functions f ...

s and volumetric models which represent the shape as a subset of a fine regular partition of space; and with

fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as il ...

models that give an infinitely recursive definition of the shape. However, these distinctions are often blurred: for instance, a

can be interpreted as a collection of

color Color (American English) or colour (British English) is the visual perceptual property deriving from the spectrum of light interacting with the photoreceptor cells of the eyes. Color categories and physical specifications of color are assoc ...

square In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length a ...

s; and geometric shapes such as

circle A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is const ...

s are defined by implicit mathematical equations. Also, a

model yields a parametric or implicit model when its recursive definition is truncated to a finite depth. Notable awards of the area are the John A. Gregory Memorial Award and the Bézier award.

References

External links

Geometry and Algorithms for CAD
(Lecture Note, TU Darmstadt) Geometric algorithms Computer-aided design {{applied-math-stub

See also

References

Further reading

External links