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class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Outermost or uppermost layer of a physical object or space</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For the computer, see <a href="/wiki/Microsoft_Surface" title="Microsoft Surface">Microsoft Surface</a>. For other uses, see <a href="/wiki/Surface_(disambiguation)" class="mw-disambig" title="Surface (disambiguation)">Surface (disambiguation)</a>.</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Red_Apple.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Red_Apple.jpg/220px-Red_Apple.jpg" decoding="async" width="220" height="199" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Red_Apple.jpg/330px-Red_Apple.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/15/Red_Apple.jpg/440px-Red_Apple.jpg 2x" data-file-width="2418" data-file-height="2192" /></a><figcaption>The surface of an apple has various perceptible characteristics, such as curvature, smoothness, texture, color, and shininess; observing these characteristics by sight or touch allows the object to be identified.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Water_droplet_lying_on_a_damask.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Water_droplet_lying_on_a_damask.jpg/250px-Water_droplet_lying_on_a_damask.jpg" decoding="async" width="220" height="169" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Water_droplet_lying_on_a_damask.jpg/330px-Water_droplet_lying_on_a_damask.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/Water_droplet_lying_on_a_damask.jpg/500px-Water_droplet_lying_on_a_damask.jpg 2x" data-file-width="4310" data-file-height="3312" /></a><figcaption><a href="/wiki/Water" title="Water">Water</a> droplet lying on a <a href="/wiki/Damask" title="Damask">damask</a>. <a href="/wiki/Surface_tension" title="Surface tension">Surface tension</a> is high enough to prevent floating below the textile.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:171879main_LimbFlareJan12_lg.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/171879main_LimbFlareJan12_lg.jpg/250px-171879main_LimbFlareJan12_lg.jpg" decoding="async" width="220" height="154" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/171879main_LimbFlareJan12_lg.jpg/330px-171879main_LimbFlareJan12_lg.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/da/171879main_LimbFlareJan12_lg.jpg/500px-171879main_LimbFlareJan12_lg.jpg 2x" data-file-width="1014" data-file-height="712" /></a><figcaption>The <a href="/wiki/Sun" title="Sun">Sun</a>, like all stars, appears from a distance to have a distinct surface, but on closer approach has no set surface.</figcaption></figure> <p>A <b>surface</b>, as the term is most generally used, is the outermost or uppermost layer of a <a href="/wiki/Physical_object" title="Physical object">physical object</a> or space.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Sorensen_2-0" class="reference"><a href="#cite_note-Sorensen-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> It is the portion or region of the object that can first be perceived by an observer using the senses of <a href="/wiki/Visual_perception" title="Visual perception">sight</a> and <a href="/wiki/Somatosensory_system" title="Somatosensory system">touch</a>, 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".<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>The concept of surface has been abstracted and formalized in <a href="/wiki/Mathematics" title="Mathematics">mathematics</a>, specifically in <a href="/wiki/Geometry" title="Geometry">geometry</a>. Depending on the properties on which the emphasis is given, there are several non equivalent such formalizations, that are all called <i>surface</i>, sometimes with some qualifier, such as <a href="/wiki/Algebraic_surface" title="Algebraic surface">algebraic surface</a>, <a href="/wiki/Smooth_surface" class="mw-redirect" title="Smooth surface">smooth surface</a> or <a href="/wiki/Fractal_surface" class="mw-redirect" title="Fractal surface">fractal surface</a>. </p><p>The concept of surface and its mathematical abstraction are both widely used in <a href="/wiki/Physics" title="Physics">physics</a>, <a href="/wiki/Engineering" title="Engineering">engineering</a>, <a href="/wiki/Computer_graphics" title="Computer graphics">computer graphics</a>, and many other disciplines, primarily in representing the surfaces of physical objects. For example, in analyzing the <a href="/wiki/Aerodynamics" title="Aerodynamics">aerodynamic</a> properties of an <a href="/wiki/Airplane" title="Airplane">airplane</a>, 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),<sup id="cite_ref-Sorensen_2-1" class="reference"><a href="#cite_note-Sorensen-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> and do objects really have a surface at all if, at the subatomic level, they never actually come in contact with other objects.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Perception_of_surfaces">Perception of surfaces</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Surface&action=edit&section=1" title="Edit section: Perception of surfaces"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>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.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Conceptually, the "surface" of an object can be defined as the topmost layer of atoms.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> 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,<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> 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.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="In_mathematics">In mathematics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Surface&action=edit&section=2" title="Edit section: In mathematics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="excerpt-block"><style data-mw-deduplicate="TemplateStyles:r1066933788">.mw-parser-output .excerpt-hat .mw-editsection-like{font-style:normal}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable dablink excerpt-hat selfref">This section is an excerpt from <a href="/wiki/Surface_(mathematics)" title="Surface (mathematics)">Surface (mathematics)</a>.<span class="mw-editsection-like plainlinks"><span class="mw-editsection-bracket">[</span><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Surface_(mathematics)&action=edit">edit</a><span class="mw-editsection-bracket">]</span></span></div><div class="excerpt"> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Sphere_and_Ball.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Sphere_and_Ball.png/220px-Sphere_and_Ball.png" decoding="async" width="220" height="218" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Sphere_and_Ball.png/330px-Sphere_and_Ball.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/07/Sphere_and_Ball.png/440px-Sphere_and_Ball.png 2x" data-file-width="1548" data-file-height="1536" /></a><figcaption>A <a href="/wiki/Sphere" title="Sphere">sphere</a> is the surface of a solid <a href="/wiki/Ball_(mathematics)" title="Ball (mathematics)">ball</a>, here having <a href="/wiki/Radius" title="Radius">radius</a> <i>r</i></figcaption></figure> <p>In <a href="/wiki/Mathematics" title="Mathematics">mathematics</a>, a <a href="/wiki/Surface_(mathematics)" title="Surface (mathematics)">surface</a> is a <a href="/wiki/Mathematical_model" title="Mathematical model">mathematical model</a> of the common concept of a surface. It is a generalization of a <a href="/wiki/Plane_(mathematics)" title="Plane (mathematics)">plane</a>, but, unlike a plane, it may be <a href="/wiki/Curvature" title="Curvature">curved</a>; this is analogous to a <a href="/wiki/Curve" title="Curve">curve</a> generalizing a <a href="/wiki/Straight_line" class="mw-redirect" title="Straight line">straight line</a>. </p><p>There are several more precise definitions, depending on the context and the mathematical tools that are used for the study. The simplest mathematical surfaces are planes and <a href="/wiki/Sphere" title="Sphere">spheres</a> in the <a href="/wiki/Euclidean_3-space" class="mw-redirect" title="Euclidean 3-space">Euclidean 3-space</a>. The exact definition of a surface may depend on the context. Typically, in <a href="/wiki/Algebraic_geometry" title="Algebraic geometry">algebraic geometry</a>, a surface may cross itself (and may have other <a href="/wiki/Singular_point_of_an_algebraic_variety" title="Singular point of an algebraic variety">singularities</a>), while, in <a href="/wiki/Topology" title="Topology">topology</a> and <a href="/wiki/Differential_geometry" title="Differential geometry">differential geometry</a>, it may not. </p> A surface is a <a href="/wiki/Topological_space" title="Topological space">topological space</a> of <a href="/wiki/Dimension" title="Dimension">dimension</a> two; this means that a moving point on a surface may move in two directions (it has two <a href="/wiki/Degrees_of_freedom" title="Degrees of freedom">degrees of freedom</a>). In other words, around almost every point, there is a <i><a href="/wiki/Coordinate_patch" class="mw-redirect" title="Coordinate patch">coordinate patch</a></i> on which a <a href="/wiki/Two-dimensional_space" title="Two-dimensional space">two-dimensional</a> <a href="/wiki/Coordinate_system" title="Coordinate system">coordinate system</a> is defined. For example, the surface of the Earth resembles (ideally) a sphere, and <a href="/wiki/Latitude" title="Latitude">latitude</a> and <a href="/wiki/Longitude" title="Longitude">longitude</a> provide two-dimensional coordinates on it (except at the poles and along the <a href="/wiki/180th_meridian" title="180th meridian">180th meridian</a>).</div></div> <div class="mw-heading mw-heading2"><h2 id="In_the_physical_sciences">In the physical sciences<span class="anchor" id="In_physics"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Surface&action=edit&section=3" title="Edit section: In the physical sciences"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Euclidean_planes_in_three-dimensional_space#Occurrence_in_nature" title="Euclidean planes in three-dimensional space">Euclidean planes in three-dimensional space § Occurrence in nature</a></div> <p>The concept of a surface in the physical sciences encompasses the structures and dynamics of and occurring at surfaces. The field underlies many practical disciplines such as semiconductor physics and applied nanotechnology but is also of fundamental interest. </p><p>Synchrotron x-ray and neutron scattering measurements are used to provide experimental data on the structure and motion of molecular adsorbates adsorbed on surfaces. The aim of such methods is to provide the data needed to benchmark the latest developments in the modelling of surface systems, their electronic and physical structures and the energetics and friction associated with surface motion. </p><p>Current projects focus on the surface adsorption of polyaromatic hydrocarbons (PAHs), a class of molecules key to the refinement of the modelling of dispersive forces through approaches such as density functional theory, and build on our complementary work applying helium atom scattering and scanning tunnelling microscopy to small molecules with aromatic functionality.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>Many surfaces considered in <a href="/wiki/Physics" title="Physics">physics</a> and <a href="/wiki/Chemistry" title="Chemistry">chemistry</a> (<a href="/wiki/Physical_sciences" class="mw-redirect" title="Physical sciences">physical sciences</a> in general) are <a href="/wiki/Interface_(matter)" title="Interface (matter)">interfaces</a>. For example, a surface may be the idealized limit between two <a href="/wiki/Fluid" title="Fluid">fluids</a>, liquid and gas (the surface of the sea in air) or the idealized boundary of a solid (the surface of a ball). In <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">fluid dynamics</a>, the shape of a <a href="/wiki/Free_surface" title="Free surface">free surface</a> may be defined by <a href="/wiki/Surface_tension" title="Surface tension">surface tension</a>. However, they are surfaces only at <a href="/wiki/Macroscopic_scale" title="Macroscopic scale">macroscopic scale</a>. At <a href="/wiki/Microscopic_scale" title="Microscopic scale">microscopic scale</a>, they may have some thickness. At <a href="/wiki/Atomic_scale" class="mw-redirect" title="Atomic scale">atomic scale</a>, they do not look at all as a surface, because of holes formed by spaces between <a href="/wiki/Atom" title="Atom">atoms</a> or <a href="/wiki/Molecule" title="Molecule">molecules</a>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>Other surfaces considered in physics are <a href="/wiki/Wavefront" title="Wavefront">wavefronts</a>. One of these, discovered by <a href="/wiki/Augustin-Jean_Fresnel" title="Augustin-Jean Fresnel">Fresnel</a>, is called <a href="/wiki/Wave_surface" title="Wave surface">wave surface</a> by mathematicians. </p><p>The surface of the reflector of a <a href="/wiki/Telescope" title="Telescope">telescope</a> is a <a href="/wiki/Paraboloid_of_revolution" class="mw-redirect" title="Paraboloid of revolution">paraboloid of revolution</a>. </p><p>Other occurrences: </p> <ul><li><a href="/wiki/Soap_bubble" title="Soap bubble">Soap bubbles</a>, which are physical examples of <a href="/wiki/Minimal_surface" title="Minimal surface">minimal surfaces</a></li> <li><a href="/wiki/Equipotential_surface" class="mw-redirect" title="Equipotential surface">Equipotential surface</a> in, e.g., <a href="/wiki/Gravity" title="Gravity">gravity</a> fields</li> <li><a href="/wiki/Earth%27s_surface" class="mw-redirect" title="Earth's surface">Earth's surface</a></li> <li><a href="/wiki/Surface_science" title="Surface science">Surface science</a>, the study of physical and chemical phenomena that occur at the interface of two phases</li> <li><a href="/wiki/Surface_metrology" title="Surface metrology">Surface metrology</a></li> <li><a href="/wiki/Surface_wave" title="Surface wave">Surface wave</a>, a mechanical wave</li> <li><a href="/wiki/Category:Atmospheric_boundaries" title="Category:Atmospheric boundaries">Atmospheric boundaries</a> (<a href="/wiki/Tropopause" title="Tropopause">tropopause</a>, <a href="/wiki/Edge_of_space" class="mw-redirect" title="Edge of space">edge of space</a>, <a href="/wiki/Plasmapause" class="mw-redirect" title="Plasmapause">plasmapause</a>, etc.)</li></ul> <div class="mw-heading mw-heading2"><h2 id="In_computer_graphics">In computer graphics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Surface&action=edit&section=4" title="Edit section: In computer graphics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Computer_representation_of_surfaces" title="Computer representation of surfaces">Computer representation of surfaces</a></div><p>In computer graphics, a surface is a mathematical representation of a 3D object or shape. Surfaces are used to model and render the outer layer of an object, giving it form, texture, and color in a virtual space. A surface is essentially a collection of points in 3D space that are mathematically defined and visualized to form the shape of an object. Surfaces are crucial for creating realistic 3D models, as they define the "skin" or "outer boundary" of an object. </p><p>Surfaces can be categorized based on how they are defined or represented: </p> <ul><li>Polygonal surfaces are made up of polygons, which are typically triangles or quadrilaterals. They are approximate and sometimes visibly faceted. They are common in games and other real-time rendering because they are computationally efficient.</li> <li>Parametric surfaces are defined using equations that depend on parameters. They include Bézier surfaces and <a href="/wiki/NURBS" class="mw-redirect" title="NURBS">NURBS</a>. They are smooth and exact. They are used in CAD and animation.</li> <li>Implicit surfaces are the solution sets of equations of the form <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x,y,z)=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x,y,z)=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d9dc9c0f7052aaefb6f7194bb0d9e419086a4bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.99ex; height:2.843ex;" alt="{\displaystyle f(x,y,z)=0}" /></span>. They capture some complex shapes well.</li></ul> <p>Surfaces in computer graphics have several important attributes that define their behavior and appearance. Geometry is a key attribute that determines the shape, size, and position of the surface in 3D space, forming the foundational structure of the model. Material properties, such as texture, color, shininess, and transparency, influence how the surface interacts with light and contribute to its visual appeal. Additionally, normals, which are perpendicular vectors to the surface at each point, are essential for accurate lighting and shading calculations, ensuring that the surface responds realistically to light sources. Surfaces in computer graphics have a wide range of applications. They are extensively used in modeling objects, such as designing characters, cars, and buildings, where the surface defines the shape and structure of the model. In rendering, surfaces play a critical role in determining how objects appear in a scene by influencing their shading, reflections, and textures, which contribute to the overall realism. Additionally, surfaces are vital in simulations, where they help replicate physical properties such as the movement of water waves or the dynamics of fabrics, enhancing the accuracy of visual and interactive experiences. </p><p>One of the main challenges in computer graphics is creating realistic simulations of surfaces. In technical applications of <a href="/wiki/3D_computer_graphics" title="3D computer graphics">3D computer graphics</a> (<a href="/wiki/CAx" class="mw-redirect" title="CAx">CAx</a>) such as <a href="/wiki/Computer-aided_design" title="Computer-aided design">computer-aided design</a> and <a href="/wiki/Computer-aided_manufacturing" title="Computer-aided manufacturing">computer-aided manufacturing</a>, 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. </p><p>One technique used for enhancing surface realism in computer graphics is the use of <a href="/wiki/Physically_based_rendering" title="Physically based rendering">physically-based rendering</a> (PBR) algorithms which simulate the interaction of <a href="/wiki/Light" title="Light">light</a> with surfaces based on their physical properties, such as <a href="/wiki/Reflectance" title="Reflectance">reflectance</a>, roughness, and <a href="/wiki/Transparency_and_translucency" title="Transparency and translucency">transparency</a>. By incorporating mathematical models and algorithms, PBR can generate highly realistic renderings that resemble the behavior of real-world materials. PBR has found practical applications beyond entertainment, extending its impact to <a href="/wiki/Architectural_design" class="mw-redirect" title="Architectural design">architectural design</a>, product <a href="/wiki/Prototype" title="Prototype">prototyping</a>, and scientific simulations. </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Surface&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFSparkeFisher2016" class="citation book cs1">Sparke, Penny & Fisher, Fiona (2016). <i>The Routledge Companion to Design Studies</i>. New York: <a href="/wiki/Routledge" title="Routledge">Routledge</a>. p. 124. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781317203285" title="Special:BookSources/9781317203285"><bdi>9781317203285</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/952155029">952155029</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Routledge+Companion+to+Design+Studies&rft.place=New+York&rft.pages=124&rft.pub=Routledge&rft.date=2016&rft_id=info%3Aoclcnum%2F952155029&rft.isbn=9781317203285&rft.aulast=Sparke&rft.aufirst=Penny&rft.au=Fisher%2C+Fiona&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASurface" class="Z3988"></span></span> </li> <li id="cite_note-Sorensen-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-Sorensen_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Sorensen_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSorensen2011" class="citation book cs1">Sorensen, Roy (2011). <i>Seeing Dark Things: The Philosophy of Shadows</i>. Oxford: <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>. p. 45. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780199797134" title="Special:BookSources/9780199797134"><bdi>9780199797134</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/955163137">955163137</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Seeing+Dark+Things%3A+The+Philosophy+of+Shadows&rft.place=Oxford&rft.pages=45&rft.pub=Oxford+University+Press&rft.date=2011&rft_id=info%3Aoclcnum%2F955163137&rft.isbn=9780199797134&rft.aulast=Sorensen&rft.aufirst=Roy&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASurface" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFButchvarov1970" class="citation book cs1">Butchvarov, Panayot (1970). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/conceptofknowled0000butc"><i>The Concept of Knowledge</i></a></span>. Evanston: <a href="/wiki/Northwestern_University_Press" title="Northwestern University Press">Northwestern University Press</a>. p. <a rel="nofollow" class="external text" href="https://archive.org/details/conceptofknowled0000butc/page/249">249</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780810103191" title="Special:BookSources/9780810103191"><bdi>9780810103191</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/925168650">925168650</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Concept+of+Knowledge&rft.place=Evanston&rft.pages=249&rft.pub=Northwestern+University+Press&rft.date=1970&rft_id=info%3Aoclcnum%2F925168650&rft.isbn=9780810103191&rft.aulast=Butchvarov&rft.aufirst=Panayot&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fconceptofknowled0000butc&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASurface" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFStroll1988" class="citation book cs1">Stroll, Avrum (1988). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/surfaces00stro"><i>Surfaces</i></a></span>. Minneapolis: <a href="/wiki/University_of_Minnesota_Press" title="University of Minnesota Press">University of Minnesota Press</a>. p. <a rel="nofollow" class="external text" href="https://archive.org/details/surfaces00stro/page/n217">205</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780816616947" title="Special:BookSources/9780816616947"><bdi>9780816616947</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/925290683">925290683</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Surfaces&rft.place=Minneapolis&rft.pages=205&rft.pub=University+of+Minnesota+Press&rft.date=1988&rft_id=info%3Aoclcnum%2F925290683&rft.isbn=9780816616947&rft.aulast=Stroll&rft.aufirst=Avrum&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsurfaces00stro&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASurface" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPleshaGrayCostanzo2012" class="citation book cs1">Plesha, Michael; Gray, Gary & Costanzo, Francesco (2012). <i>Engineering Mechanics: Statics and Dynamics</i> (2nd ed.). New York: <a href="/wiki/McGraw-Hill_Higher_Education" class="mw-redirect" title="McGraw-Hill Higher Education">McGraw-Hill Higher Education</a>. p. 8. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780073380315" title="Special:BookSources/9780073380315"><bdi>9780073380315</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/801035627">801035627</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Engineering+Mechanics%3A+Statics+and+Dynamics&rft.place=New+York&rft.pages=8&rft.edition=2nd&rft.pub=McGraw-Hill+Higher+Education&rft.date=2012&rft_id=info%3Aoclcnum%2F801035627&rft.isbn=9780073380315&rft.aulast=Plesha&rft.aufirst=Michael&rft.au=Gray%2C+Gary&rft.au=Costanzo%2C+Francesco&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASurface" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><a href="#CITEREFButchvarov1970">Butchvarov (1970)</a>, p. 253.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><a href="#CITEREFStroll1988">Stroll (1988)</a>, p. 54.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><a href="#CITEREFStroll1988">Stroll (1988)</a>, p. 81.</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFGibson1950" class="citation journal cs1">Gibson, James J. (1950). <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/1418003">"The Perception of Visual Surfaces"</a>. <i>The American Journal of Psychology</i>. <b>63</b> (3): <span class="nowrap">367–</span>384. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F1418003">10.2307/1418003</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0002-9556">0002-9556</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/1418003">1418003</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/15432778">15432778</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+American+Journal+of+Psychology&rft.atitle=The+Perception+of+Visual+Surfaces&rft.volume=63&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E367-%3C%2Fspan%3E384&rft.date=1950&rft_id=info%3Apmid%2F15432778&rft.issn=0002-9556&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1418003%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.2307%2F1418003&rft.aulast=Gibson&rft.aufirst=James+J.&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1418003&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASurface" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www5.open.ac.uk/science/physical-science/research/physics/surface-physics">"Surface Physics"</a>. <i>School of Physical Sciences</i>. 2019-03-28<span class="reference-accessdate">. Retrieved <span class="nowrap">2024-09-23</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=School+of+Physical+Sciences&rft.atitle=Surface+Physics&rft.date=2019-03-28&rft_id=https%3A%2F%2Fwww5.open.ac.uk%2Fscience%2Fphysical-science%2Fresearch%2Fphysics%2Fsurface-physics&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASurface" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.britannica.com/science/surface-chemistry-and-physics">"Surface | Definition & Facts | Britannica"</a>. <i>www.britannica.com</i><span class="reference-accessdate">. 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class="vector-sticky-header-end" aria-hidden="true"> <div class="vector-sticky-header-icons"> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-talk-sticky-header" tabindex="-1" data-event-name="talk-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbles mw-ui-icon-wikimedia-speechBubbles"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-subject-sticky-header" tabindex="-1" data-event-name="subject-sticky-header"><span class="vector-icon mw-ui-icon-article mw-ui-icon-wikimedia-article"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-history-sticky-header" tabindex="-1" data-event-name="history-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-history mw-ui-icon-wikimedia-wikimedia-history"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only mw-watchlink" id="ca-watchstar-sticky-header" tabindex="-1" data-event-name="watch-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-star mw-ui-icon-wikimedia-wikimedia-star"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-edit-sticky-header" tabindex="-1" data-event-name="wikitext-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-wikiText mw-ui-icon-wikimedia-wikimedia-wikiText"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-ve-edit-sticky-header" tabindex="-1" data-event-name="ve-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-edit mw-ui-icon-wikimedia-wikimedia-edit"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>5 languages</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbleAdd-progressive mw-ui-icon-wikimedia-speechBubbleAdd-progressive"></span> <span>Add topic</span> </a> </div> <div class="vector-sticky-header-icon-end"> <div class="vector-user-links"> </div> </div> </div> </div> </div> <div class="mw-portlet mw-portlet-dock-bottom emptyPortlet" id="p-dock-bottom"> <ul> </ul> </div> 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