Türkçe ansiklopedi, sözlük, genel başvuru ve bilgi sitesi   
  		  Yardım
  Rastgele    

Freeform Surface Modelling

Freeform surface modelling is the art of engineering Freeform Surfaces with a CAD or CAID system.

Introduction

The technology encompasses two main fields. Either creating aesthetic (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 surfaces. The first begins with construction curves (splines) from which the 3D surface is then swept (section along guide rail) or meshed (lofted) through.

Enlarge picture
A surface being created from curves.
Animated version


The second method is direct creation of the surface with manipulation of the surface poles/control points.
Enlarge picture
Surface edit by poles


From these initially created surfaces, other surfaces are constructed using either derived methods such as offset or angled extensions from surfaces; or via bridging and blending between groups of surfaces.

Surfaces

Freeform surface, or freeform surfacing, is used in CAD and other computer graphics software to describe the skin of a 3D geometric element. Freeform surfaces do not have rigid radial dimensions, unlike regular surfaces such as planes, cylinders and conic surfaces. They are used to describe forms such as turbine blades, car bodies and boat hulls. Initially developed for the automotive and aerospace industries, freeform surfacing is now widely used in all engineering design disciplines from consumer goods products to ships. Most systems today use nonuniform rational B-spline (NURBS) mathematics to describe the surface forms; however, there are other methods such as Gorden surfaces or Coon surfaces .

The forms of freeform surfaces (and curves) are not stored or defined in CAD software in terms of polynomial equations, but by their poles, degree, and number of patches (segments with spline curves). The degree of a surface determines its mathematical properties, and can be seen as representing the shape by a polynomial with variables to the power of the degree value. For example, a surface with a degree of 1 would be a flat cross section surface. A surface with degree 2 would be curved in one direction, while a degree 3 surface could (but does not necessarily) change once from to curvature. Some CAD systems use the term order instead of degree. The order of a polynomial is one greater than the degree, and gives the number of coefficients rather than the greatest exponent.

Enlarge picture
Example surface pole map


The poles (sometimes known as control points) of a surface define its shape. The natural surface edges are defined by the positions of the first and last poles. (Note that a surface can have trimmed boundaries.) The intermediate poles act like magnets drawing the surface in their direction. The surface does not, however, go through these points. The second and third poles as well as defining shape, respectively determine the start and tangent angles and the curvature. In a single patch surface (Bézier surface), there is one more pole than the degree values of the surface. Surface patches can be merged into a single NURBS surface; at these points are knot lines. The number of knots will determine the influence of the poles on either side and how smooth the transition is. The smoothness between patches, known as continuity, is often referred to in terms of a C value: Two more important aspects are the U and V parameters. These are values on the surface ranging from 0 to 1, used in the mathematical definition of the surface and for defining paths on the surface: for example, a trimmed boundary edge. Note that they are not proportionally spaced along the surface. A curve of constant U or constant V is known as an isoperimetric curve, or U (V) line. In CAD systems, surfaces are often displayed with their poles of constant U or constant V values connected together by lines; these are known as control polygons.

Modelling

When defining a form, an important factor is the continuity between surfaces - how smoothly they connect to one another.

One example of where surfacing excels is automotive body panels. If two curved areas of the panel have different radii of curvature and are blended together, maintaining tangential continuity (meaning that the blended surface doesn't change direction suddenly, but smoothly) won't be enough. They need to have a continuous rate of curvature change between the two sections, or else their reflections will appear disconnected.

The continuity is defined using the terms To achieve a high quality NURBS or Bezier surface, degrees of 5 or greater are generally used. Depending on the product and production process, different levels of accuracy are used but tolerances usually range from 0.02 mm to .001 mm (for example, in fairing of BIW concept surfaces to production surface). Obviously for ship building this need not be so tight and for precision gears and medical devices it is much finer.

History of Terms

The term lofting originally came from the shipbuilding industry where loftsmen worked on "barn loft" type structures to create the keel and bulkhead forms out of wood. This was then passed on to the aircraft then automotive industries who also required streamline shapes.

The term spline also has nautical origins coming from East Anglian dialect word for a thin long strip of wood (probably from old English and Germanic word splint).

Freeform Surface Modelling Software

See also

Computer-aided design (CAD) is use of a wide range of computerbased tools that assist engineers, architects and other design professions in their design activities. It is the main geometry authoring tool within the Product Lifecycle Management process and involves both
..... Click the link for more information.
Computer-aided industrial design (CAID) is a subset of computer-aided design (CAD) that includes software that directly helps in product development.

Within CAID programs designers have the freedom of creativity, but typically follow a simple design methodology:
..... Click the link for more information.
Class A surfaces is a term used in automotive design to describe a set of freeform surfaces of high quality. Although, strictly, it is nothing more than saying the surfaces have curvature and tangency alignment -to near perfect aesthetical reflection quality, many people interpret
..... Click the link for more information.
Spline can refer to:
..... Click the link for more information.
CAD may refer to:
..... Click the link for more information.
Computer graphics is a sub-field of computer science and is concerned with digitally synthesizing and manipulating visual content. Although the term often refers to three-dimensional computer graphics, it also encompasses two-dimensional graphics and image processing.
..... Click the link for more information.
plane is a two-dimensional manifold or surface that is perfectly flat. Informally it can be thought of as an infinitely vast and infinitesimally thin sheet oriented in some space.
..... Click the link for more information.
cylinder is a quadric surface, with the following equation in Cartesian coordinates:



This equation is for an elliptic cylinder, a generalization of the ordinary, circular cylinder (a = b).
..... Click the link for more information.
conic section (or just conic) is a curve that can be formed by intersecting a cone (more precisely, a right circular conical surface) with a plane. The conic sections were named and studied as long ago as 200 BC, when Apollonius of Perga undertook a systematic study of their
..... Click the link for more information.
turbine is a rotary engine that extracts energy from a fluid flow. Claude Burdin (1788-1873) coined the term from the Latin turbinis, or vortex during an 1828 engineering competition.
..... Click the link for more information.
A hull is the body of a ship or boat. It is a central concept in floating vessels as it provides the buoyancy that keeps the vessel from sinking.

General features

Nearly all watercraft, from small boats to the largest ships, adhere to a general form that serve the needs of
..... Click the link for more information.
Please help [ improve this article] by expanding this section.
See talk page for details. Please remove this message once the section has been expanded. (tagged since March 2007)

..... Click the link for more information.
Engineering is the applied science of acquiring and applying knowledge to design, analysis, and/or construction of works for practical purposes. The American Engineers' Council for Professional Development, also known as ECPD,[1] (later ABET [2]
..... Click the link for more information.
non-uniform, rational B-spline (NURBS) is a mathematical model commonly used in computer graphics for generating and representing curves and surfaces.

History


..... Click the link for more information.
surface is a two-dimensional manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space, E³.
..... Click the link for more information.
Computer-aided design (CAD) is use of a wide range of computerbased tools that assist engineers, architects and other design professions in their design activities. It is the main geometry authoring tool within the Product Lifecycle Management process and involves both
..... Click the link for more information.
Algebraic geometry is a branch of mathematics which, as the name suggests, combines techniques of abstract algebra, especially commutative algebra, with the language and the problematics of geometry.
..... Click the link for more information.
degree depending on the subject.

Degree of a polynomial

See main article Degree of a polynomial


The degree of a term of a polynomial in one variable is the exponent on the variable in that term; the degree of a polynomial
..... Click the link for more information.
Spline can refer to:
..... Click the link for more information.
In geometry, a cross section is the intersection of a body in 2-dimensional space with a line, or of a body in 3-dimensional space with a plane, etc. More plainly, when cutting an object into slices one gets many parallel cross sections.
..... Click the link for more information.
coefficient is a constant multiplicative factor of a certain object. For example, the coefficient in 9x2 is 9.

The object can be such things as a variable, a vector, a function, etc.
..... Click the link for more information.
Exponentiation is a mathematical operation, written an, involving two numbers, the base a and the exponent n.
..... Click the link for more information.
spline is a special function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher
..... Click the link for more information.
tangent has two distinct but etymologically-related meanings: one in geometry and one in trigonometry.

Geometry

In plane geometry, a line is tangent to a curve, at some point, if both line and curve pass through the point with the oppsite direction.
..... Click the link for more information.
In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, but this is defined in different ways depending on the context.
..... Click the link for more information.
A Bézier surface is a parametric surface, used in computer graphics, computer-aided design, and finite element modelling. It is one of several generalizations of the Bézier curve.
..... Click the link for more information.
non-uniform, rational B-spline (NURBS) is a mathematical model commonly used in computer graphics for generating and representing curves and surfaces.

History


..... Click the link for more information.
BIW may refer to:
..... Click the link for more information.
UGS NX is the commercial CAD/CAM/CAE PLM software suite developed by Siemens UGS PLM Software. It is commonly referred to as a 3D PLM software application. All stages of product development are supported, from conceptualization (CAID), to design (CAD), to analysis (CAE), to
..... Click the link for more information.
CATIA (Computer Aided Three dimensional Interactive Application) is a multi-platform PLM/CAD/CAM/CAE commercial software suite developed by Dassault Systemes and marketed world-wide by IBM. It was used by Frank Gehry in his building of the Guggenheim Museum Bilbao.
..... Click the link for more information.


This article is copied from an article on Wikipedia.org - the free encyclopedia created and edited by online user community. The text was not checked or edited by anyone on our staff. Although the vast majority of the wikipedia encyclopedia articles provide accurate and timely information please do not assume the accuracy of any particular article. This article is distributed under the terms of GNU Free Documentation License.