Geometric modeling

Geometric modeling is a branch of <a href="/facts/Applied_mathematics/qyqklXXm">applied mathematics</a> and <a href="/facts/Computational_geometry/eeaotQtl">computational geometry</a> that studies methods and <a href="/facts/Algorithms/fnl5NmRt">algorithms</a> for the mathematical description of <a href="/facts/Shape_(mathematics)/nww0x85d">shapes</a>.
The shapes studied in geometric modeling are mostly two- or three-<a href="/facts/Dimension/0ktmUyac">dimensional</a> (<a href="/facts/Solid_figure/tHH3JFoq">solid figures</a>), 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. <a href="/facts/2D_geometric_model/Azdx2M1y">Two-dimensional models</a> are important in computer <a href="/facts/Typography/byx4sANl">typography</a> and <a href="/facts/Technical_drawing/WtTmaUwL">technical drawing</a>. <a href="/facts/3D_modeling/6V3Ry9AJ">Three-dimensional models</a> are central to <a href="/facts/Computer-aided_design/5gSXrmmN">computer-aided design</a> and <a href="/facts/Computer-aided_manufacturing/gqYHXcK9">manufacturing</a> (CAD/CAM), and widely used in many applied technical fields such as <a href="/facts/Civil_engineering/avh5kEq2">civil</a> and <a href="/facts/Mechanical_engineering/cbId4fye">mechanical engineering</a>, <a href="/facts/Architecture/FccThs8G">architecture</a>, <a href="/facts/Geologic_modeling/Em1YUS35">geology</a> and <a href="/facts/Medical_image_processing/pL6JyJEp">medical image processing</a>.
Geometric models are usually distinguished from <a href="/facts/Procedural_modeling/0DC1epAX">procedural</a> and <a href="/facts/Object-oriented_modeling/JucpfFVa">object-oriented models</a>, which define the shape implicitly by an opaque <a href="/facts/Algorithm/fnl5NmRt">algorithm</a> that generates its appearance. They are also contrasted with <a href="/facts/Digital_image/3TNT47Mv">digital images</a> and <a href="/facts/Volumetric_model/4Y171FIK">volumetric models</a> which represent the shape as a subset of a fine regular partition of space; and with <a href="/facts/Fractal/sXj38JeN">fractal</a> models that give an infinitely recursive definition of the shape. However, these distinctions are often blurred: for instance, a <a href="/facts/Digital_image/3TNT47Mv">digital image</a> can be interpreted as a collection of <a href="/facts/Color/XDvW7ESP">colored</a> <a href="/facts/Square_(geometry)/JHJeMvmL">squares</a>; and geometric shapes such as <a href="/facts/Circle/9fy5ggKn">circles</a> are defined by implicit mathematical equations. Also, a <a href="/facts/Fractal/sXj38JeN">fractal</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.

Geometric modeling open-in-new

Geometric modeling