Freeform Surface Modelling
Freeform surface modelling is a technique for engineering freeform surfaces with a Computeraided design, CAD or Computeraided industrial design, CAID system. The technology has encompassed two main fields. Either creating aesthetic surfaces (class A surfaces) that also perform a function; for example, car bodies and consumer product outer forms, or technical surfaces for components such as gas turbine blades and other fluid dynamic engineering components. CAD software packages use two basic methods for the creation of computer representation of surfaces, surfaces. The first begins with construction curves (Spline (mathematics), splines) from which the 3D surface is then swept (section along guide rail) or meshed (lofted) through. The second method is direct creation of the surface with manipulation of the surface poles/control points. From these initially created surfaces, other surfaces are constructed using either derived methods such as offset or angled extensions from su ... [...More Info...] [...Related Items...] 

Computeraided Design
Computeraided design (CAD) is the use of computers (or ) to aid in the creation, modification, analysis, or optimization of a design. This software is used to increase the productivity of the designer, improve the quality of design, improve communications through documentation, and to create a database for manufacturing. Designs made through CAD software are helpful in protecting products and inventions when used in patent applications. CAD output is often in the form of electronic files for print, machining, or other manufacturing operations. The term CADD (for c''omputer aided design and drafting'') is also used. Its use in designing electronic systems is known as electronic design automation (EDA). In mechanical design it is known as mechanical design automation (MDA) or computeraided drafting (CAD), which includes the process of creating a technical drawing with the use of computer software. CAD software for mechanical design uses either vectorbased graphics to depict th ... [...More Info...] [...Related Items...] 

Gordon Surface
Gordon may refer to: People * Gordon (given name), a masculine given name, including list of persons and fictional characters * Gordon (surname), the surname * Gordon (slave), escaped to a Union Army camp during the U.S. Civil War * Clan Gordon, aka the House of Gordon, a Scottish clan Education * Gordon State College, a public college in Barnesville, Georgia * Gordon College (Massachusetts), a Christian college in Wenham, Massachusetts * Gordon College (Pakistan), a Christian college in Rawalpindi, Pakistan * Gordon College (Philippines), a public university in Subic, Zambales * Gordon College of Education, a public college in Haifa, Israel Places Australia *Gordon, Australian Capital Territory *Gordon, New South Wales *Gordon, South Australia *Gordon, Victoria *Gordon River, Tasmania *Gordon River (Western Australia) Canada *Gordon Parish, New Brunswick *Gordon, Ontario, Gordon/Barrie Island, municipality in Ontario *Gordon River (Chochocouane River), a List of rivers of Qu ... [...More Info...] [...Related Items...] 

Bézier Surface
Bézier surfaces are a species of spline (mathematics), mathematical spline used in computer graphics, computeraided design, and finite element modeling. As with the Bézier curve, a Bézier surface is defined by a set of control points. Similar to interpolation in many respects, a key difference is that the surface does not, in general, pass through the central control points; rather, it is "stretched" toward them as though each were an attractive force. They are visually intuitive, and for many applications, mathematically convenient. History Bézier surfaces were first described in 1962 by the France, French engineer Pierre Bézier who used them to design automobile bodies. Bézier surfaces can be of any degree, but bicubic Bézier surfaces generally provide enough degrees of freedom (physics and chemistry), degrees of freedom for most applications. Equation A given Bézier surface of degree (''n'', ''m'') is defined by a set of (''n'' + 1)(''m'' +&nbs ... [...More Info...] [...Related Items...] 

Curvature
In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ..., curvature is any of several strongly related concepts in geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. A mat .... Intuitively, the curvature is the amount by which a curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line (geometry), line, but that does not have to be Linearity, straight. Intuitively, a curve may be thought of as the trace left by a moving point (geo ... deviates from being a straight line 290px, A representation of one line segment. In g ... [...More Info...] [...Related Items...] 

Tangent
In geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. A mat ..., the tangent line (or simply tangent) to a plane curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line (geometry), line, but that does not have to be Linearity, straight. Intuitively, a curve may be thought of as the trace left by a moving point (geo ... at a given point Point or points may refer to: Places * Point, LewisImage:Point Western Isles NASA World Wind.png, Satellite image of Point Point ( gd, An Rubha), also known as the Eye Peninsula, is a peninsula some 11 km long in the Outer Hebrides (or Western I ... is the straight line 290px, A representation of one line segment. In geometry, the notion of line or straight line was introduced by ancient ... [...More Info...] [...Related Items...] 

Control Point (mathematics)
In computeraided geometric design a control point is a member of a set of Point (geometry), points used to determine the shape of a spline curve or, more generally, a computer representation of surfaces, surface or higherdimensional object. For Bézier curves, it has become customary to refer to the dvectors p_i in a parametric representation \sum_i p_i \phi_i of a curve or surface in dspace as control points, while the scalarvalued functions \phi_i, defined over the relevant parameter domain, are the corresponding weight function , ''weight'' or blending function , ''blending functions''. Some would reasonably insist, in order to give intuitive geometric meaning to the word "control", that the blending functions form a partition of unity, i.e., that the \phi_i are nonnegative and sum to one. This property implies that the curve lies within the convex hull of its control points.. This is the case for Bézier's representation of a polynomial curve as well as for the Bsplin ... [...More Info...] [...Related Items...] 

Surface Modelling
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 Visual perception, sight and Somatosensory system, touch, 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. 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 or fractal surface. The concept of surface and its mathematical abstraction are both widely used in physics, engineering, computer graphics, and many other discipline ... [...More Info...] [...Related Items...] 

Exponent
Exponentiation is a mathematical Mathematics (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximately 10.7 ... operation, written as , involving two numbers, the ''base Base or BASE may refer to: Brands and enterprises * Base (mobile telephony provider), a Belgian mobile telecommunications operator *Base CRM Base CRM (originally Future Simple or PipeJump) is an enterprise software company based in Mountain Vie ...'' and the ''exponent'' or ''power'' , and pronounced as " raised to the power of ". When is a positive integer An integer (from the Latin Latin (, or , ) is a classical language belonging to the Italic branch of the IndoEuropean languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the Roman Re ..., exponentiation correspond ... [...More Info...] [...Related Items...] 

Coefficient
In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ..., a coefficient is a multiplicative factor in some term of a polynomial In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ..., a series Series may refer to: People with the name * Caroline Series (born 1951), English mathematician, daughter of George Series * George Series (1920–1995), English physicist Arts, entertainment, and media Music * Series, the ordered sets used i ..., or any expression; it is usually a number, but may be any expression (including variables such as , and ). When the coefficients are ... [...More Info...] [...Related Items...] 

Convex
Convex means curving outwards like a sphere, and is the opposite of concave. Convex or convexity may refer to: Science and technology * Convex lens A lens is a transmissive optics, optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a #Compound lenses, compound lens consists of several simpl ..., in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytope, a polytope with a convex set of points ** Convex metric space, a generalization of the convexity notion in abstract metric spaces * Convex function, when the line segment between any two points on the graph of the function lies above or on the graph * Convex conjugate, of a function Economics and finance * Convexity (finance), second derivatives in financial modeling generally * Convexity in economics * Bond conve ... [...More Info...] [...Related Items...] 

Concave
Concave means curving in or hollowed inward, as opposed to convex. Concave may refer to: * Concave function In , a concave function is the of a . A concave function is also ously called concave downwards, concave down, convex upwards, convex cap, or upper convex. Definition A realvalued f on an (or, more generally, a in ) is said to be ''concave' ..., the negative of a convex function * Concave lens A lens is a transmissive optics, optical device that focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a #Compound lenses, compound lens consists of several simple ... * Concave mirror A curved mirror is a mirror with a curved reflecting surface. The surface may be either ''convex'' (bulging outward) or ''concave'' (recessed inward). Most curved mirrors have surfaces that are shaped like part of a sphere of a sphere A spher ... * Concave polygon A simple polygon that is not convex polyg ... [...More Info...] [...Related Items...] 

Cross Section (geometry)
In geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. A mat ... and science Science () is a systematic enterprise that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe."... modern science is a discovery as well as an invention. ..., a cross section is the nonempty intersection The line (purple) in two points (red). The disk (yellow) intersects the line in the line segment between the two red points. In mathematics, the intersection of two or more objects is another, usually "smaller" object. Intuitively, the inter ... of a solid body in threedimensional space Threedimensional space (also: 3space or, rarely, tridimensional space) is a geometric setting in which three v ... [...More Info...] [...Related Items...] 