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...omputer graphics]] and [[geometric modeling]] in the context of [[implicit surface]]s and the [[function representation]]. They also appear in certain [[bound ...al-cnc.me.wisc.edu/Research/meshless/R-functions/R-functions.html Meshfree Modeling and Analysis, R-Functions (University of Wisconsin)] ...

'''Geometric modeling''' is a branch of [[applied mathematics]] and [[computational geometry]] th ...s are important in computer [[typography]] and [[technical drawing]]. [[3D modeling|Three-dimensional model]]s are central to [[computer-aided design]] and [[c ...

{{Short description|Surface in 3D space defined by an implicit function of three variables}} [[File:Torus-40-15.svg|thumb|Implicit surface torus {{math|1=(''R'' = 40, ''a'' = 15)}}.]] ...

{{short description|Surface representing points of constant value within a volume}} ...al analog of an [[Contour line|isoline]]. It is a [[Surface (mathematics)|surface]] that represents points of a constant value (e.g. [[pressure]], [[temperat ...

...expansion. The momentum equation may be used in situations where the water surface profile is rapidly varied. These situations include hydraulic jumps, hydrau ..., HEC-RAS solves the full, dynamic, [[1-D Saint Venant Equation]] using an implicit, finite difference method. The unsteady flow equation solver was adapted fr ...

{{redirect|Level surface|the application to force fields|Equipotential surface|water level surfaces|Equigeopotential}} ...vel surface''' (or ''[[isosurface]]''); so a level [[Surface (mathematics)|surface]] is the set of all real-valued roots of an equation in three variables {{m ...

...function]] of several variables (often a [[polynomial]]). For example, the implicit equation of the [[unit circle]] is <math>x^2 + y^2 - 1 = 0.</math> ...h>x^2 + y^2 - 1 = 0</math> of the [[unit circle]] defines {{mvar|y}} as an implicit function of {{mvar|x}} if {{math|−1 ≤ ''x'' ≤ 1}}, and {{mvar|y}} is restri ...

{{short description|Object modeling method}} ...[[NURBS]] surfaces, [[subdivision surface]]s, and equation-based (implicit surface) representations used in [[Ray tracing (graphics)|ray tracers]]. ...

...n two or developing holes). These characteristics make LSM effective for [[modeling]] objects that vary in time, such as an [[airbag]] inflating or a drop of o ...er is a [[bounded region]] with a well-behaved boundary. Below it, the red surface is the graph of a level set function <math>\varphi</math> determining this ...

* [[3D modeling]] * [[Bézier surface]] ...

...a positive metaball by creating an indentation in the positive metaball's surface.|200px]] ...inn |first=James Frederick |date=1982 |title=A generalization of algebraic surface drawing |url=https://dl.acm.org/doi/10.1145/357306.357310 |journal=ACM Tran ...

[[Image:Steiner's Roman Surface.gif|thumb|An animation of the Roman surface]] In [[mathematics]], the '''Roman surface''' or '''Steiner surface''' is a self-intersecting [[Map (mathematics)|mapping]] of the [[real proje ...

{{Short description|Surface area of a biomolecule accessible to a solvent}} ...e center of the probe sphere (in blue) as it rolls along the van der Waals surface. Note that the probe radius depicted here is of smaller scale than the typi ...

...for a given expiry produces a skewed "smile" instead of the expected flat surface. The pattern differs across various markets. Equity options traded in Amer ...smile and term structure of volatility in a consolidated three-dimensional surface for all options on a given underlying asset. ...

{{short description|Creating a complex 3D surface or object by combining primitive objects}} ...46-664X(82)90169-1 }}</ref><ref name="bb">{{citation|title=Introduction to Implicit Surfaces|first1=Jules|last1=Bloomenthal|first2=Chandrajit|last2=Bajaj|autho ...

...erally, a [[manifold]] or a [[algebraic variety|variety]], defined by an [[implicit equation]]. The inverse process is called [[implicitization]].<ref name="hu ...s a ''parametric curve''). One similarly gets the parametric equation of a surface by considering functions of two parameters {{math|''t''}} and {{math|''u''} ...

...a [[Constructive solid geometry|CSG]] tree, [[NURBS]] patches, a set of [[implicit function]]s, a [[triangle mesh]], or just a [[Point cloud|cloud of points]] ...operators for creating 3D models ([[polygon]]s, [[b-rep]]s, [[subdivision surface]]s). As a "shape programming language," it is a true generalization of "fla ...

{{Short description|Set of polygons to define the surface of a 3D model}} ...ace}}s''' that defines the shape of a [[polyhedron|polyhedral]] object's [[surface]]. It simplifies [[Rendering (computer graphics)|rendering]], as in a [[wir ...

{{Short description|Set of principles for modeling solid geometry}} ...n-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 an ...

...|last2=Cline |first2=Harvey E. |title=Marching cubes: A high resolution 3D surface construction algorithm |journal=ACM SIGGRAPH Computer Graphics |date=1 Augu ...ensen, William |status=granted |title=System and method for the display of surface structures contained within the interior region of a solid body |gdate=1987 ...