surface (redirected from Surface (geometry))

surface

In geometry, a two-dimensional collection of points (flat surface), a three-dimensional collection of points whose cross section is a curve (curved surface), or the boundary of any three-dimensional solid. In general, a surface is a continuous boundary dividing a three-dimensional space into two regions. For example, the surface of a sphere separates the interior from the exterior; a horizontal plane separates the half-plane above it from the half-plane below. Surfaces are often called by the names of the regions they enclose, but a surface is essentially two-dimensional and has an area, while the region it encloses is three-dimensional and has a volume. The attributes of surfaces, and in particular the idea of curvature, are investigated in differential geometry.

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surface

Outermost layer of a material or substance. Because the particles (atoms or molecules) on the surface have nearest neighbours beside and below but not above, the physical and chemical properties of a surface differ from those of the bulk material; surface chemistry is thus a branch of physical chemistry. The growth of crystals, the actions of catalysts and detergents, and the phenomena of adsorption, surface tension, and capillarity are aspects of behaviour at surfaces. The appearance of the surface, whether achieved with electroplating, paint, oxidation-reduction, bleaching (see bleach), or another means, is aesthetically important.

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surface

(1) See Surface computer.

(2) In CAD, the external geometry of an object. Surfaces are generally required for NC (numerical control) modeling rather than wireframe or solids.

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surface

1. Geometry

a. the complete boundary of a solid figure

b. a continuous two-dimensional configuration

2. 

a. the uppermost level of the land or sea

b. (as modifier): surface transportation

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surface [′sər·fəs]

(engineering)

The outer part (skin with a thickness of zero) of a body; can apply to structures, to micrometer-sized particles, or to extended-surface zeolites.

(mathematics)

A subset of three-space consisting of those points whose cartesian coordinatesx,y, andzsatisfy equations of the formx= ƒ(u,v),y=g(u,v),z=h(u,v), where ƒ,g, andhare differentiable real-valued functions of two parametersuandvwhich take real values and vary freely in some domain.