A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of

sight Visual perception is the ability to interpret the surrounding environment through photopic vision (daytime vision), color vision, scotopic vision (night vision), and mesopic vision (twilight vision), using light in the visible spectrum reflecte ...

and

touch In physiology, the somatosensory system is the network of neural structures in the brain and body that produce the perception of touch ( haptic perception), as well as temperature ( thermoception), body position (proprioception), and pain. It ...

, and is the portion with which other materials first interact. The surface of an object is more than "a mere geometric solid", but is "filled with, spread over by, or suffused with perceivable qualities such as color and warmth". The concept of surface has been abstracted and formalized in mathematics, specifically in

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

. Depending on the properties on which the emphasis is given, there are several non equivalent such formalizations, that are all called ''surface'', sometimes with some qualifier, such as algebraic surface,

smooth surface In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspective ...

fractal surface A fractal landscape is a surface that is generated using a stochastic algorithm designed to produce fractal behavior that mimics the appearance of natural terrain. In other words, the result of the procedure is not a deterministic fractal surfac ...

. The concept of surface and its mathematical abstraction are both widely used in

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...

computer graphics Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great de ...

, and many other disciplines, primarily in representing the surfaces of physical objects. For example, in analyzing the

aerodynamic Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dyn ...

properties of an

airplane An airplane or aeroplane (informally plane) is a fixed-wing aircraft that is propelled forward by thrust from a jet engine, Propeller (aircraft), propeller, or rocket engine. Airplanes come in a variety of sizes, shapes, and wing configurat ...

, the central consideration is the flow of air along its surface. The concept also raises certain philosophical questions—for example, how thick is the layer of atoms or molecules that can be considered part of the surface of an object (i.e., where does the "surface" end and the "interior" begin), and do objects really have a surface at all if, at the subatomic level, they never actually come in contact with other objects.

Perception of surfaces

The surface of an object is the part of the object that is primarily perceived. Humans equate seeing the surface of an object with seeing an object. For example, in looking at an automobile, it is normally not possible to see the engine, electronics, and other internal structures, but the object is still recognized as an automobile because the surface identifies it as one. Conceptually, the "surface" of an object can be defined as the topmost layer of atoms. Many objects and organisms have a surface that is in some way distinct from their interior. For example, the peel of an apple has very different qualities from the interior of the apple,. and the exterior surface of a radio may have very different components from the interior. Peeling the apple constitutes removal of the surface, ultimately leaving a different surface with a different texture and appearance, identifiable as a peeled apple. Removing the exterior surface of an electronic device may render its purpose unrecognizable. By contrast, removing the outermost layer of a rock or the topmost layer of liquid contained in a glass would leave a substance or material with the same composition, only slightly reduced in volume.

In mathematics

In the physical sciences

Many surfaces considered in

and chemistry (

physical sciences Physical science is a branch of natural science that studies non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together called the "physical sciences". Definition Phy ...

in general) are interface (matter), interfaces. For example, a surface may be the idealized limit between two fluids (the surface of the sea) or the idealized boundary of a solid (the surface of a ball). In fluid dynamics, the shape of a surface may be defined by surface tension. However, they are surfaces only at macroscopic scale. At microscopic scale, they may have some thickness. At atomic scale, they do not look at all as a surface, because of holes formed by spaces between atoms or molecules. Other surfaces considered in physics are wavefronts. One of these, discovered by Augustin-Jean Fresnel, Fresnel, is called wave surface by mathematicians. The surface of the reflector of a telescope is a paraboloid of revolution. Other occurrences: * Soap bubbles, which are physical examples of minimal surfaces * Equipotential surface in, e.g., gravity fields * Earth's surface * Surface science, the study of physical and chemical phenomena that occur at the interface of two phases * Surface metrology * Surface wave, a mechanical wave * :Atmospheric boundaries, Atmospheric boundaries (tropopause, edge of space, plasmapause, etc.)

In computer graphics

One of the main challenges in computer graphics is creating realistic simulations of surfaces. In technical applications of 3D computer graphics (CAx) such as computer-aided design and computer-aided manufacturing, surfaces are one way of representing objects. The other ways are wireframe (lines and curves) and solids. Point clouds are also sometimes used as temporary ways to represent an object, with the goal of using the points to create one or more of the three permanent representations.

References

{{Authority control Surfaces, Geometric shapes Broad-concept articles