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Everything about Parametric surface
Surface specified with parameters
A parametric surface is a surface in the Euclidean space which is defined by a parametric equation with two parameters . 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. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Parametric surfaceA 5-minute orientation
- Skim a recent paper: New Artificial Tangential Motions for Parametric Finite Element Approximation of Surface EvolutionInfluential work since 2022
- Pick up a classic book: CalculusThe most-reprinted book on the subject
- Read the landmark paper: On the Assessment of Surface Heat Flux and Evaporation Using Large-Scale ParametersCited 4,848 times
- Go sideways: CurvatureA closely related topic
- Go sideways: Second fundamental formA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
On the Assessment of Surface Heat Flux and Evaporation Using Large-Scale Parameters
A marching method for parametric surface/surface intersection
Two-frequency parametric excitation of surface waves
The characterization of parametric surface sections
Parametric design of surface textures on journal bearing
Parametric description of one-process surface texture
Reconfigurable Parametric Amplifications of Spoof Surface Plasmons
Smooth parametric surface approximations to discrete data
🆕 Influential since 2022
New Artificial Tangential Motions for Parametric Finite Element Approximation of Surface Evolution
Parametric optimization of surface dielectric barrier discharge actuators for ice sensing application
Parametric optimization of novel solar chimney power plant using response surface methodology
Parametric investigation of continuous beams strengthened with near surface mounted FRP bars
Parametric Excitation and Instabilities of Spin Waves Driven by Surface Acoustic Waves
📚 Books worth reading
CalculusRobert T. Smith · 2012- 📕Hilbert Schemes of Points and Infinite Dimensional Lie AlgebrasZhenbo Qin · 2018
- 📕Commutative algebra and its connections to geometryPan-American Advanced Studies Institute (2009 Universidade Federal de Pernambuco) · 2011
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Curvature In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being…
- Second fundamental form In differential geometry, the second fundamental form (or shape tensor) is a quadratic form on the tangent plane of a smooth surface in the three-dimensional…
- Gaussian curvature In differential geometry, the Gaussian curvature or Gauss curvature (symbol Κ, named after Carl Friedrich Gauss) of a smooth surface in three-dimensional…
- Differentiable curve Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential…
- Mean curvature In mathematics, the mean curvature H of a surface S is an extrinsic measure of curvature that comes from differential geometry and that locally describes…
- Differential geometry of surfaces In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most…
- Surface (mathematics) In mathematics, a surface is a mathematical model of the common concept of a surface. It is a generalization of a plane, but, unlike a plane, it may be…
- Parallel curve A parallel curve of a given (progenitor) curve is the envelope of a family of congruent (equal-radius) circles centered on the curve. It generalises the…