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# Geometric modeling

Geometric modeling involves the use of a CAD system to develop a mathematical description of the geometry of an object.

Geometric modeling

Geometric modeling involves the use of a CAD system to develop a mathematical description of the geometry of an object. The mathematical description, called a geometric model is contained in computer memory. These operations include creating new geometric models from basic building blocks available in the system. Geometric modeling is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description of shapes.

The shapes studied in geometric modeling are mostly two- or three-dimensional, although many of its tools and principles can be applied to sets of any finite dimension. Today most geometric modeling is done with computers and for computer-based applications. Two-dimensional models are important in computer typography and technical drawing. Three-dimensional models are central to computer-aided design and manufacturing (CAD/CAM), and widely used in many applied technical fields such as civil and mechanical engineering, architecture, geology and medical image processing.

Geometric models are usually distinguished from procedural and object-oriented models, which define the shape implicitly by an opaque algorithm that generates its appearance. They are also contrasted with digital images and volumetric models which represent the shape as a subset of a fine regular partition of space; and with fractal models that give an infinitely recursive definition of the shape.

However, these distinctions are often blurred: for instance, a digital image can be interpreted as a collection of colored squares; and geometric shapes such as circles are defined by implicit mathematical equations. Also, a fractal model yields a parametric or implicit model when its recursive definition is truncated to a finite depth.

Geometric modeling techniques;

These are various types of geometric models used in CAD,

·        Based on the dimensioning, - Two dimensional modeling, - Three dimensional modeling.

·        Based on the modeling,

-         Wire frame modeling,

-         Surface modeling,

-         Solid modeling.

2D Vs 3D;

2D models are best utilized for design problems, such as flat objects and layouts of building.

3D models are capable of modeling an object in three dimensional according to user instructions.

This is helpful in conceptualizing the object since in true 3D models can be displayed in various views and form different angles.

1. Wire-frame modeling technique in CAD

A wire-frame model is a visual presentation of a three-dimensional (3D) or physical object used in 3D computer graphics. It is created by specifying each edge of the physical object where two mathematically continuous smooth surfaces meet, or by connecting an object's constituent vertices using straight lines or curves. The object is projected onto a display screen by drawing lines at the location of each edge. The term wire frame comes from designers using metal wire to represent the three-dimensional shape of solid objects. 3D wire frame allows to construct and manipulate solids and solid surfaces. The 3D solid modeling technique efficiently draws higher quality representations of solids than the conventional line drawing.

Using a wire-frame model allows visualization of the underlying design structure of a 3D model. Traditional two-dimensional views and drawings can be created by appropriate rotation of the object and selection of hidden line removal via cutting planes. Since wire-frame renderings are relatively simple and fast to calculate, they are often used in cases where a high screen frame rate is needed (for instance, when working with a particularly complex 3D model, or in real-time systems that model exterior phenomena). When greater graphical detail is desired, surface textures can be added automatically after completion of the initial rendering of the wire frame. This allows the designer to quickly review Chan solids or rotate the object to new desired views without long delays associated with more realistic rendering.

The wire frame format is also well suited and widely used in programming tool paths for direct numerical control (DNC) machine tools. Hand-drawn wire-frame-like illustrations date back as far as the Italian Renaissance.[1] Wire-frame models were also used extensively in video games to represent 3D objects during the 1980s and early 1990s when properly filled 3D objects would have been too complex to calculate and draw with the computers of the time. Wire-frame models are also used as the input for computer-aided manufacturing (CAM). There are mainly three types of 3D CAD models. Wire frame is one of them and it is the most abstract and least realistic. Other types of 3D CAD models are surface and solid. This method of modeling consists of only lines, points and curves defining the edges of an object.

·        Simple to construct,

·        Designer needs little training.

·        It needs less memory space,

·        It takes less manipulation time,

·        It is best suitable for manipulation as orthographic, isometric and perspective views.

B-rep Boundry representation;

B-rep construction consists of entering all boundary edge for all surfaces. This is similar or copying an engineering drawing into the computer, line by line,

surface by surface, with one important qualification. The lines must be entered and surfaces oriented in such a way that they create valid volumes.

CSG Constructive Solid Geometry;

CSG technique uses Boolean combinations or primitives solids to build a part. The Boolean operations are addition (+), subtraction (-), as illustrated in three dimensions.

2. Surface modeling

Surface modeling is defining an object’s exterior with an infinitesimally thin skin.

This skin is created by lofts, sweeps, and NURBS curves - i.e. sculptured surfaces with lots of curvature. The surfaces are either defined by poles or guide curves. A surface is

considered a solid only when it is completely enclosed. It is used to make technical surfaces

(e.g. air plane wing) or aesthetic surfaces (e.g. car’s hood).

It was developed for the aerospace and automotive industries in the late 70s. Rhinoceros 3D and Alias Studio Tools are examples of a surface modeling programs. It is generally considered more difficult than solids modeling, but the models are more robust because the programs aren’t generally feature based. Later changes have to modify the existing geometry as opposed to just editing the original feature, which is more difficult but keeps the model from collapsing when one feature interferes with another.

3. Solid modeling technique in CAD

Solid modeling (or modelling) is a consistent set of principles for mathematical and computer modeling of three-dimensional solids. Solid modeling is distinguished from related areas of geometric modeling and computer graphics by its emphasis on physical fidelity.[1] Together, the principles of geometric and solid modeling form the foundation of computer-aided design and in general support the creation, exchange, visualization, animation, interrogation, and annotation of digital models of physical objects.

The use of solid modeling techniques allows for the automation of several difficult engineering calculations that are carried out as a part of the design process. Simulation, planning, and verification of processes such as machining and assembly were one of the main catalysts for the development of solid modeling. More recently, the range of supported manufacturing applications has been greatly expanded to include sheet metal manufacturing, injection molding, welding, pipe routing etc.

Beyond traditional manufacturing, solid modeling techniques serve as the foundation for rapid prototyping, digital data archival and reverse engineering by reconstructing solids from sampled points on physical objects, mechanical analysis using finite elements, motion planning and NC path verification, kinematic and dynamic analysis of mechanisms, and so on.

A central problem in all these applications is the ability to effectively represent and manipulate three-dimensional geometry in a fashion that is consistent with the physical behavior of real artifacts. Solid modeling research and development has effectively addressed many of these issues, and continues to be a central focus of computer-aided engineering.

·        It is complete and unambiguous.

·        Suitable for automated applications like creating part program without much human involvement.

4.Solids vs. Surface Modeling;

Computer aided design (CAD) isn’t like a car in that you can use it pretty well even if you don’t know how it works. It pays to know what happening ‘under the hood’ when

using CAD. It is important to know about surface and solids modeling because it does affect the way you model, and it is important to know if you are switching platforms. It is also very important to know about for rapid prototyping.

Surfaces and solids are the underlying math that defines the geometry of the forms

you create. There are three ways to define 3D geometry: solids, surfaces and wireframes.

Wireframes don’t play much of a role in CAD, but primarily in digital content creation

(DCC) and gaming. The easiest way to understand the difference between surface and solids modeling is to think of a water balloon; the water in the balloon would be solids modeling, while the latex skin would be surface modeling. Need more of an explanation? No problem.

Solids modeling;

Solids modeling is defining an object with geometric mass. Solids modeling programs usually create models by creating a base solid and adding or subtracting from it with subsequent features. Features such as extrudes, extrude cuts, revolves, radii, chamfers, etc. Examples of solids modeling programs are Solid works, CATIA, and Pro Engineer. It was originally developed for machine design, and is used heavily for engineering with large part assemblies, digital testing and rapid prototyping.

Surface modeling;

Surface modeling is defining an object’s exterior with an infinitesimally thin skin.

This skin is created by lofts, sweeps, and NURBS curves - i.e. sculptured surfaces with lots of curvature. The surfaces are either defined by poles or guide curves. A surface is considered a solid only when it is completely enclosed. It is used to make technical surfaces

(e.g. air plane wing) or aesthetic surfaces (e.g. car’s hood).

It was developed for the aerospace and automotive industries in the late 70s. Rhinoceros 3D and Alias Studio Tools are examples of a surface modeling programs. It is generally considered more difficult than solids modeling, but the models are more robust because the programs aren’t generally feature based. Later changes have to modify the existing geometry as opposed to just editing the original feature, which is more difficult but keeps the model from collapsing when one feature interferes with another.

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