parametric surface

Surface in the Euclidean space

EntityQ1071743

Also known as parametrized surface

Subclass of: surface

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

A parametric surface is a surface in the Euclidean space which is defined by a parametric equation with two parameters ⁠ :\mathbb {R} ^{2}\to \mathbb {R} ^{3}} ⁠. Parametric representation is a very general way to specify a surface, as well as implicit representation. Surfaces that occur in two of the main theorems of vector calculus, Stokes' theorem, and the divergence theorem, are frequently given in a parametric form. The curvature and arc length of curves on the surface, surface area, differential geometric invariants such as the first and second fundamental forms, Gaussian, mean, and principal curvatures can all be computed from a given parametrization.

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12 statements · 17% with external sources · numbers in brackets are citations

Defining formula: \boldsymbol{\Phi}(u, v) = (x(u, v), y(u, v), z(u, v))
In defining formula: \boldsymbol{\Phi} symbol represents: surface parameterization
x symbol represents: Cartesian coordinate x
y symbol represents: Cartesian coordinate y
z symbol represents: Cartesian coordinate z

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7 identifiers linking parametric surface across the web's reference databases

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statements

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Source last edited September 18, 2026. AIDB refreshes this page daily.

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AIDB. (2026). parametric surface (Q1071743). Retrieved from https://aidb.si/e/parametric-surface-Q1071743