Solid modeling: Difference between revisions

Revision as of 22:54, 23 July 2024

Revision as of 04:12, 27 August 2024

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{{MOS|article|[[MOS:BBB]]|date=May 2024}}

{{Use dmy dates|date=February 2020}}

[[File:Jack-in-cube solid model, light background.gif|thumb|right|The geometry in solid modeling is fully described in 3{{nbhyph}}D space; objects can be viewed from any angle.]]

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===Implicit representation===

{{Main|Function representation}}

A very general method of defining a set of points ''X'' is to specify a [[Predicate (mathematical logic)|predicate]] that can be evaluated at any point in space. In other words, ''X'' is defined ''implicitly'' to consist of all the points that satisfy the condition specified by the predicate. The simplest form of a predicate is the condition on the sign of a real valued function resulting in the familiar representation of sets by equalities and inequalities. For example, if <math>f= ax + by + cz + d</math> the conditions <math>f(p) =0</math>, <math> f(p) > 0</math>, and <math>f(p) < 0</math> represent, respectively, a plane and two open linear [[Half-space (geometry)|halfspaces]]. More complex functional primitives may be defined by booleanBoolean combinations of simpler predicates. Furthermore, the theory of [[Rvachev function|R-functions]] allow conversions of such representations into a single function inequality for any closed semi analytic set. Such a representation can be converted to a boundary representation using polygonization algorithms, for example, the [[marching cubes]] algorithm.

===Parametric and feature-based modeling===