The previous sections dealt with the initial and middle stages of reverse engineering. This section highlights a stage which is undoubtedly crucial for product development. After a meshed part is aligned, it goes through either—surface modeling in tools such as Polyworks, which generates a non-parametric model (IGES or STEP format) or parametric modeling where a sketch of the meshed part is created instead of putting it through surfacing (.PRT format). The resultant is generally called, 3D computer aided model or CAD model.

CAD is the acronym for Computer Aided Design. It covers different variety of design tools used by various professionals like artists, game designers, manufacturers and design engineers.

The technology of CAD systems has tremendously helped users by performing thousands of complex geometrical calculations in the background without anyone having to drop a sweat for it. CAD has its origin in early 2D drawings where one could draw objects using basic views: top, bottom, left, right, front, back, and the angled isometric view.  3D CAD programs allow users to take 2D views and convert them into a 3D object on the screen.  In simple definition, CAD design is converting basic design data into a more perceptible and more understandable design.

Each CAD system has its own algorithm for describing geometry, both mathematically and structurally.

Everything comes with its own varieties and CAD modeling is no stranger to it. As the technology evolved, CAD modeling came up in different styles. There are many methods of classifying them, but a broad general classification can be as follows:

• 2 dimensional or 2D CAD: The early version of CAD that most of us are aware of. These are 2-dimensional drawings on flat sheet with dimensions, layouts and other information needed to manufacture the object.
• 3 dimensional or 3D CAD: The purpose of both 2D and 3D models is the same. But what sets 3D models apart is its ability to present greater details about the individual component and/or assembly by projecting it as a full-scale 3-dimensional object. 3D models can be viewed and rotated in X, Y, or Z axes. It also shows how two objects can fit and operate which is not possible with 2D CAD.

3D models can be further classified into three categories:

• 3D Wire-frame Models: These models resemble an entire object made of just wires, with the background visible through the skeletal structure.
• Surface Models: Surface models are created by joining the 3D surfaces together and look like real-life objects.
• Solid Models: They are the best representation of real physical objects in a virtual environment. Unlike other models, solid models have properties like weight, volume and density. They are the most commonly used models and serve as prototypes for engineering projects.

Different professionals use different software, owing to different reasons like cost, project requirements, features etc. Although, software comes with their own file formats, there are instances where one needs to share their project with someone else, either partners or clients, who are using different software. In such cases, it is necessary that both party software understand each other’s file formats. As a result of this situation, it is necessary to have file formats which can be accommodated in variety of software.

• Native File Formats: Such CAD file formats are intended to be used only with the software it comes with. They cannot be shared with any other software which comes with their own CAD formats.
• Neutral File Formats: These file formats are created to be shared among different software. Thereby it increases interoperability, which is necessary.

Although there are almost hundreds of file formats out there, the more popular CAD formats are as follows:

STEP: This is the most popular CAD file format of all. It is widely used and highly recommended as most software support STEP files. STEP is the acronym for Standard for the Exchange of Product Data.

IGES: IGES is the acronym for Initial Graphics Exchange Specification. It is an old CAD file format which is vendor-neutral. IGES has fallen out lately since it lacks many features which newer file formats have.

Parasolid: Parasolid was originally developed by ShapeData and is currently owned by Siemens PLM Software.

STL: STL stands for Stereolithography which is the format for 3D information created by 3D systems. STL finds its usage mostly in 3D printers. STL describes only the outer structure or surface geometry of a physical object but doesn’t give out color, texture and other attributes of an object.

VRML: VRML stands for Virtual Reality Modeling Language. Although it gives back more attributes than STL but it can be read by a handful of software.

X3D: X3D is an XML based file format for representing 3D computer graphics.

COLLADA: COLLADA stands for Collaborative Design Activity and is mostly used in gaming and 3D modeling.

DXF: DXF stands for Drawing Exchange Format which is a pure 2D file format native to Autocad.

Computer-aided design or CAD has pushed the entire engineering process to the next level. One can actually mould or fold, modify or make a new part from scratch, all with the help of CAD modeling software. The many uses of CAD are as follows:

• CAD is used to generate design and layouts, design details and calculations, 3-D models.
• CAD transfers details of information about a product in a format that can be easily interpreted by a skilled professional, which therefore facilitates manufacturing process.
• The editing process in CAD is very fast as compared to manual process.
• CAD helps in speeding up manufacturing process by facilitating accurate simulation, hence reducing time taken to design.
• CAD can be assimilated with CAM (Computer Aided Manufacturing), which eases up product development.

### FEA, CFD and Mold Flow Analysis

Over the years, the term “Design Analysis” has found a significant place for itself in the manufacturing sector. Instead of making a prototype and creating elaborate testing regimens to analyze the physical behavior of a product, engineers can evoke this information quickly and accurately on the computer.

Design analysis is a specialized computer software technology designed to simulate the physical behavior of an object.

If an object will break or deform or how it may react to heat are the sort of queries design analysis can answer. Design analysis helps in minimizing or even eliminate the need to build a physical prototype for testing. As a result, the technology has gone mainstream as a prized product development tool and found its presence in almost all sectors of engineering.

• Finite Element Analysis (FEA)
• Computational Fluid Dynamics (CFD)
• Mold Flow Analysis
##### Finite Element Analysis (FEA)

The Finite Element Analysis (FEA) is a specialized simulation of a physical entity using the numerical algorithm known as Finite Element Method (FEM). It is used to reduce the number of physical prototypes and experiments and analyze objects in their design stage to develop better products faster. The term ‘finite’ is used to denote the limited, or finite, number of degrees of freedom used to model the behavior of each element.

FEA will analyze an object in question by breaking down its entire geometry into small ‘elements,’ which are put under simulated conditions see how the elements react. It displays the results as color-coded 3D images where red denotes an area of failure, and blue indicates fields that maintain their integrity under the load applied. However, note it down that FEA gives an approximate solution to the problem.

Mathematics is used to understand and quantify a physical phenomena such as structural or fluid behavior, wave propagation, thermal transport, the growth of biological cells, etc. Most of these processes are described using Partial Differential Equations. Finite Element Analysis has proven to be on of the most prominent numerical technique for a computer to solve these PEDs.

FEA is used in:

Problems where analytical solution is not easily obtained,

And mathematical expressions required because of complex geometries, loadings and material properties.

##### Computational Fluid Dynamics (CFD)

Computational Fluid Dynamics (CFD) is a specilaized simulation used for the analysis of fluid flows through an object using numerical solution methods. CFD incorporates applied mathematics, physics and computing software to evaluate how a gas or liquid flows and how it affects an object as it flows past. CFD is based on Navier-Stokes equations which describe the way velocity, temperature, pressure, and density of a moving fluid are related.

Aerodynamics and hydrodynamics are two engineering streams where CFD analyses are often used. Physical quantities such as lift and drag or field properties as pressures and velocities are computed using CFD. Fluid dynamics is connected with physical laws in the form of partial differential equations. Engineers transform these laws into algebraical equations and can efficiently solve these equations numerically.The CFD analysis reliability depends on the whole structure of the process. The determination of proper numerical methods to develop a pathway through the solution is highly important. The software, which conducts the analysis is one of the key elements in generating a sustainable product development process, as the amount of physical prototypes can be reduced drastically.

CFD is used in almost all industrial domains, such as:

• Food processing
• Water treatment
• Marine engineering
• Automotive
• Aerodynamics
• Aerospace

With the help of CFD, fluid flow can be analyzed faster in more detail at an earlier stage, than by tesing, at a lower cost and lower risk. CFD solves the fundamental equations governing fluid flow processes, and provides information on important flow characteristics such as pressure loss, flow distribution, and mixing rates.

CFD has become an integral part of engineering and design domains of prominent companies due to its ability to predict performance of new designs and it intends to remain so.

##### Mold Flow Analysis

Moldflow, formerly known as C-mould, is one of the leading software used in processwide plastics solutions. Mold flow computes the injection molding process where plastic flows into a mold and analyzes the given mold design to check how the parts react to injection and ensure that the mold will be able to produce the strongest and uniform pieces. Two of the most popular mold flow analysis software are Moldflow and Moldex3D used exclusively by many mold makers.

There are three types of Mold flow analysis which are as follows:

• Moldflow Filling Analysis (MFA): It facilitates visualization of shear rate and shear stress plus determination of fiber orientation and venting. MFA can predict fill pattern and injection pressure while optimizing gating and runner system.
• Moldflow Cooling Analysis (MCA): MCA specializes in finding hot spots and calculating time to freeze. It helps in determining uneven cooling between core and cavity while specifying required cooling flow rates.
• Moldflow Warpage Analysis (MWA): Moldflow warpage is all about predicting, finding and determining warpage due to orientation.

We can see benefits of using different analysis procedures that correctly understand the power of the different simulation tools. During the product design, many these methods affect the cost and quality of the product, thereby ensuring the optimum productivity as aimed by the manufacturer.

### Geometric Modeling

The culture of design & manufacturing incorporates various crucial aspects for the production of a market efficient product. Computer-aided Engineering or CAE comes up as a central part of the entire manufacturing process. Over the years, the function of CAE has evolved so much that it has developed its applications depending upon the type of usage and execution.  Geometric Modeling happens to be one of the most popular CAE applications.

The computer/software generated mathematical representation of an object’s geometry is called Geometric Modeling. As curves are easy to manipulate and bend as per application, geometric modeling uses curves extensively to construct surfaces. The formation of curves can be achieved by,

A set of points,

Analytic functions, or

Other curves/functions

The mathematical representation of an object can be displayed on a computer and used for generation of drawings; which go on for analysis and eventual manufacturing of the object. In general, there are three conventional steps to create a geometric model:

• Creating key geometric elements by using commands like points, lines, and circles.
• Applying Transformations on the geometric elements using commands like rotation, achieve scaling, and other related transformations functions.
• Constructing the geometric model using various commands that integrates the elements of the geometric model to form the desired shape.
##### REPRESENTAION OF GEOMETRIC MODELS
• Two Dimensional or 2D: It projects a two-dimensional view and is used for flat objects.
• 1 2D: It projects the views beyond the 2D and enables viewing of 3D objects that have no sidewall details.
• Three Dimensional or 3D: This representation permits complete three-dimensional viewing of the model with intricate geometry. The most leading process of geometric modeling in 3D is Solid modeling.
##### TYPES OF GEOMETRIC MODELINGS

Depending upon the representations of objects, geometric modeling system can be classified into three categories, which are:

• Solid modeling

Also known as volume modeling, this is the most widely used method as it provides a complete description of solid modeling.

• Wireframe modeling

It is a simple modeling system, which is used to represent the object by the help of lines only. Hence, it is also known as Line model representation. However, wireframe modeling is not enough to express complex solids; therefore, it is used to describe only wiring systems.

• Surface modeling

This type of modeling represents the object by its surface, and it is used to describe the object with a clear view of manufacturing. By this clear point of view, surface modeling cannot be used to develop an internal surface of any model. Surface modeling uses Bezier and B-spines.

Requirements of Geometric Modeling

The various requirements of geometric modeling are as follows:

• The cross-section, hidden lines, dimensions are needed for Graphical Visualization.
• Interchangeable manufacturing tolerance analysis is required while inspection of parts.
• There should also be properties evaluation and geometrical evaluations in Area, Volume, and property evaluation in Weight, Density, etc..
• Need for Finite element analysis and Kinematic analysis.
• Parts classification, planning, etc. in manufacturing.

Geometric modeling is a vast and elaborate field of CAE and requires in-depth study. The next articles dive deep into the various types and facets of geometric modeling.

### Types of Geometric Modeling

The previous edition gave a brief introduction of Geometric Modeling and its features. Geometric modeling is the mathematical representation of an object’s geometry. It incorporates the use of curves to create models. It can be viewed either in 2D or 3D perspective.

This edition details the primary types of geometric modeling. Geometric modeling can be classified into the following:

##### SOLID MODELING

Also known as volume modeling, this is the most widely used method as it provides a complete description of solid modeling. Solid modeling defines an object by its nodes, edges, and surfaces;  therefore, it gives a perfect and explicit mathematical representation of a precisely enclosed and filled volume. Solid modeling requires the use of topology rules to guarantee that all surfaces are stitched together correctly. This geometry modeling procedure is based upon the “Half-Space” concept.

There are two prevalent ways for representing solid models –

Constructive solid geometry: Constructive solid geometry is a combination of primary solid objects (prism, cylinder, cone, sphere, etc.). These shapes are either added or deleted to form the final solid shape.

Boundary representation: In boundary representation, an object’s definition is determined by their spatial boundaries. It describes the points, edges, surfaces of a volume, and issues command to rotate, sweep a binds facets into a third dimensional solid. The union of these surfaces enables the formation of a surface that explicitly encloses a volume.

Solid Modeling is the most widely used geometric modeling in three dimensions, and it serves the following purpose:

• Solid modeling supports weight or volume calculation, centroids, moments of inertia calculation, stress analysis, heat conduction calculations, dynamic analysis, system dynamics analysis.
• Solid modeling supports the generation of codes, robotic and assembly simulation
• Solid modeling stores both geometric and topological information; can verify if the two objects occupy same space
• Solid modeling improves the quality of design, enhances visualization, and has the potential for functional automation and integration.

Different solid modeling techniques are as follows:

• Constructive Solid Geometry
• Boundary Representation
• Feature-based modeling
• Primitive Instancing
• Cell decomposition, spatial enumeration, octree
##### SURFACE MODELING

Surface modeling represents the solid appearing object. Although it is a complicated method of representation than wireframe modeling, it is not as refined as solid modeling. Although surface models and solid models look identical, the former cannot be sliced open the way solid models can be. This model makes use of B-splines and Bezier for controlling curves.

A typical surface modeling process involves the following steps:

•  Generation of a model combining the three-dimensional surfaces and solids
• Conversion of the model to surfaces, taking advantage of associative modeling
• Validation of imperfections with surface analysis tools
• Reconstructing surfaces of objects to apply smoothness to the object

Surface modeling is used to:

• To shape design and representation of complicated objects such as a car, ship, and airplane bodies as well as castings
• There are situations where models imported from another CAD system usually lack details of the features it is comprised of. If the surfaces are complex, applying changes to this type of geometry can be quite the task. In such cases, surface modeling techniques can be used to one or more faces of the model to make the desired changes.
• Surface modeling enables building one face at a time so that one can control the exact contour and direction of any face. This feature comes in handy at a time when solid modeling technique fails to create the complex shape of a feature as it builds up several sides of shape at once.
• As it is not limited to the direct construction of a model face, surfaces can also be used as a reference geometry in a transitional step towards the creation of the required model face.
• Now, there is another modeling technique which requires a combination of solid and surface modeling techniques to create a solid model. This technique generally involves starting the model as a solid and using surfaces to modify it. Or, changing the solid to surfaces to shape and contour it, then turning it back to a solid when done.
##### WIREFRAME MODELING

The wireframe model is perhaps one of the earliest ways of representing a solid model. It consists of vertices and lines and is a skeletal representation of a real-world 3D object. It was developed back in the 1960s; it is also referred to as “Stick figure” or “edge representation.”

The lines within a wireframe connect to create polygons, such as triangles and rectangles, that represent three-dimensional shapes when bound together. The outcome may range from a cube to a complex three-dimensional scene with people and objects. The number of polygons within a model is a good indicator of how detailed the wireframe 3D model is.

Wireframe modeling helps in matching a 3D drawing model to its reference. It allows the creator to match the vertex points, so they are in alignment with the desired reference and see the reference through the model as well. Although Wireframe modeling is a quick and easy way to demonstrate concepts, creating a fully detailed, precisely constructed model for an idea can be extremely time-consuming, and if it does not match what was visualized for the project, all that time and effort was wasted. In wireframe modeling, one can skip the detailed work and present a very skeletal framework that is simple to create and is apprehensible to others.