### BREP & CSG

The geometric modelling technique has revolutionized the design and manufacture of products to a great extent. Although there have been various ways of representing an object, the most commonly used modelling technique is Solid Modelling. The two main ways to express solid models are Boundary Representation modelling and Constructive Solid Geometry modelling.

##### CONSTRUCTIVE SOLID GEOMETRY

Constructive solid geometry or C-REP/CREP, previously known as computational binary solid geometry, is a reliable modelling technique that allows creating of a complex object from simple primitives using Boolean operations. It is based on the fundamental that a physical object can be divided into a set of primitives or basic elements combined in a particular order by following a set of rules (Boolean operations) to create an object. Typically, they are objects of simple shapes such as cuboids, cylinders, prisms, pyramids, spheres, and cones. CSG cannot represent fillets, chamfers, and other context-based features.

The primitives themselves are regarded as valid CSG models, where each primitive is bounded by orientable surfaces (Half-spaces).

These simple primitives are in generic form and must be confirmed by the user to be used in the design. The primitive may require transformations like scaling, translation, and rotation to be assigned a coveted position.

There are two kinds of CSG schemes:

Primitive based CSG: It is a popular CSG scheme based on bounded solid primitives, R-sets.

Half-space based CSG: This CSG scheme uses unbounded Half-spaces. Bounded solid primitives and their boundaries are considered composite half-spaces and the surfaces of the component half-spaces, respectively.

Some attributes of CSG are as follows:

• CSG is fundamentally different from the BREP model, where it does not store faces, edges and vertices. Instead, it evaluates them as needed by algorithms.
• CSG database stores topology and geometry.
• The validity checking in the CSG scheme occurs indirectly. Each primitive combined using a Boolean operation (r-sets) to build the CSG model fits its validity.
• The standard data structures used in CSG are graphs and trees.
• CSG representation is of considerable importance to manufacturing.
##### BOUNDARY REPRESENTATION

In solid modelling and computer-aided design, boundary representation or B-rep / BREP—is the process of representing shapes using the limits. Here a solid is described as a collection of connected surface elements. BREP was one of the first computer-generated representations to represent three-dimensional objects.

BREP defines an object by their spatial boundaries. It details the points, edges, surfaces of a volume.

BREP can also be explained in terms of cell domain combination.

A cell is a connected limitation of the underlying geometry. There are four kinds of cells as per the spatial dimension they inhabit:

• Vertex
• Edge
• Face
• Volume

A domain is a set of connected cells grouped to define boundaries. Fields define various components inside a non-manifold object.

Boundary representation of models consists of two kinds of information:

Topology: The main topological entities are faces, edges, and vertices.

Geometry: The main geometrical entities are surfaces, curves, and points.

The topological and geometrical entities are intertwined in a way where:

• the face is a bounded portion of a character.
• An edge is an enclosed piece of a curve.
• A vertex lies at a point. Topological items allow making links between geometrical entities.

• It is appropriate for constructing solid models of unusual shapes.
• A BREP model is relatively simple to convert to the wireframe model.
• BREP uses only primitive objects and Boolean operations to combine them, unlike CSG (Constructive Solid Geometry).
• In addition to the Boolean operations, B-rep has extrusion (or sweeping), chamfer, blending, drafting, shelling, tweaking and other actions that use these.
• BREP is not suitable for applications like tool path generation.
##### DIFFERENCE BETWEEN BREP AND CSG

 Boundary Representation (BREP) Constructive Solid Geometry (CSG) BREP describes only the oriented surface of a solid as a data structure composed of vertices, edges, and faces. A solid is represented as a Boolean expression of primitive solid objects of a simpler structure. A BREP object is easily rendered on a graphic display system. A CSG object is always valid because its surface is closed and orientable and encloses a volume, provided the primitives are authentic in this We review the possible surface types, the winged-edge representation schema, and the Euler operators for B-rep. For CSG, the basic operations include classifying points, curves, surfaces concerning a solid, detecting redundancies in the representation, and approximating CSG objects systematically.

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.

### Faceted Modeling and NURBS

Modern CAD systems and CAD packages enable designers to model objects and retrieve them in their formats. Some formats are interchangeable while some enforce restrictions, upon which, it becomes difficult to transfer an object model from one form to another.

This article describes some of the most used CAD formats in the industry. But before we look into various CAD formats, it is essential to understand the concept of Faceted geometry and Analytic geometry (NURBS).

##### FACETED GEOMETRY

Faceted geometry, also known as discrete geometry, are models which consist of groups of polygons which is often triangles.

Most Computer-Aided Design (CAD) systems typically use continuous surface and edge definitions based on NURBS. CAE simulations break down this NURBS representation into facets by a process known as meshing. The faceted models are quite appealing to engineering marketing, as such simulations are less bothered with exact physical reality and tend to emphasize on creating eye-catching visuals, such as airflow over a car, which can be incorporated into a marketing brochure. File formats typically used for faceted models are: .3ds, .dxf, .obj, .stl (Stereolithography).

Almost all the faceted formats, except for STL, reflect material properties such as glass and metal by providing groupings of facets. However, such groupings are inadequate for a CAE simulation.

##### ANALYTIC GEOMETRY (NURBS)

NURBS or Non-uniform rational basis spline describes curves and surfaces with mathematical functions, and form the most common analytic geometry representations. The NURBS geometry has unlimited resolution. The NURBS definition defines the location of the boundary points and uses control points with slope definition to determine the internal shape of curves and surfaces, thereby enabling a great deal of flexibility. NURBS geometry is typically produced in CAD systems such as CATIA, Pro/Engineer, Solidworks, NX, etc. A significant drawback of NURBS geometry is that they are generally specific to the CAD packages that created them, and interchanging formats can be error-prone and inaccurate.

##### DIFFERENCE BETWEEN FACETED GEOMETRY AND ANALYTIC GEOMETRY (NURBS)

 Faceted geometry NURBS geometry Facets are always guaranteed to comply with the original definition In NURBS geometry, different levels of model detail are created without losing fidelity Faceted geometry describes a shape as a mesh, points usually connected by triangles Analytic geometry defines curves and surfaces with mathematical functions Faceted geometry has limited resolution NURBS geometry has unlimited resolution Evaluating  a faceted surface, one can get a shape defined by linear interpolation between known discrete points One can assess a NURBS surface anywhere and get coordinates lying on the surface Simple definition Includes topology

 Cons of Faceted geometry Cons of NURBS geometry Fixed resolution More computing intense No topology High data exchange

Although faceted geometry has its use, NURBS geometry is superior for design and manufacturing processes. Due to the high demands on geometric precision, NURBS geometry finds its place in CAE applications. But if the modeling requirements ask for stunning visuals, faceted models are worth giving a try.

### 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.

### Parametric and Non-parametric modelling

Up until now, we believe our readers got a clear explanation of reverse engineering. Let us give walkthrough — Reverse engineering is the process of extracting design information after studying a physical product, with the intent to reproduce the product, or to create another object that can interact with it.

In the past, designers resorted to physical measurement of the product to redraw its geometry. Today, designers use 3D scanners to capture measurements. The scanned data is then imported to CAD where the design can be analyzed, processed, manipulated and refined. Two key aspects that fall in place when focusing on reverse engineering process are:

##### Parametric Model/Modeling

A parametric model captures all its information about the data within its parameters. All you need to know for predicting a future data value from the current state of the model is just its parameters.
The parameters are usually finite in dimensions. For a parametric model to predict new data, knowing just the parameters is enough. A parametric model is one where we assume the ‘shape’ of the data, and therefore only have to estimate the coefficients of the model.

##### Non-parametric Model/Modeling

A non parametric model can capture more subtle aspects of the data. It allows more information to pass from the current set of data that is attached to the model at the current state, to be able to predict any future data.
The parameters are usually said to be infinite in dimensions. Hence, it can express the characteristics in the data much better than parametric models. For a non parametric model, predicting future data is based on not just the parameters but also in the current state of data that has been observed. A non-parametric model is one where we do not assume the ‘shape’ of the data, and we have to estimate the most suitable form of the model, along with the coefficients.

### Path to Product Development

If you are an engineering professional, most likely you are aware of how a physical product comes to life. From the early days of sketching and blueprints, manufacturing of a commodity has come a long way. The modern methodology of creating a product has not only changed drastically, but it has become way more efficient and precise in its approach. Today’s engineer lives and thrives in the world of 3-dimensional models. Whatever masterpiece a designer has in his mind, he has the tools and system to give it life. And it is not just limited to inception of a new idea being turned to a product; it has made the art of reverse engineering being implemented more than ever.

So what are the factors that have revolutionized this craft?

It is the safe to say that with the invention of new tools, techniques and computer, the road to new product development has become more smooth, accurate and flexible. Although a professional can get deep into the subject matter, this article gives a brief overview of the product development from technical perspective.

The footsteps to a new product can be summarized in the following sequence.

To put it in words, here is how the entire sequence goes:

• Scanning: Whether you have an entirely new idea on your mind, or you want to base your idea on an already existing product; you need a reference. Your reference can be either technical manuals from the manufacturer or the physical product itself. The first step is to scan the product using 3D scanners. 3D scanning technology comes in many shapes and forms. Scanners capture and store the 3D information of the product. The scanned information gets stored in the form of closely spaced data points known as Point Cloud.
• Point Cloud: A point cloud is a collection of data points defined by a given coordinates system. In a 3D coordinates system, for example, a point cloud may define the shape of some real or created physical system.
• Mesh: Point clouds are used to create 3D meshes. A mesh is a network that constitutes of cells and points. Mesh generation involves point clouds to be connected to each other by the virtue of vertices, edges and faces that meet at shared edges. There are specific softwares for carrying of meshing function.
• 3D Model: Once the meshed part is generated, it goes through required software applications to be transferred to Computer Aided Design (CAD) tools to get transformed into a proper 3D CAD model. 3D model is the stage where whole sorts of applications such as sewing, stitching, etc, are implemented to create a prototype.
• Testing: A prototype goes through numerous tests in this phase, to check for limitations and possible calibrations if necessary. This is done to determine the optimum stage where the prototype can be turned to a product.
• Product: This is where the entire process comes to an end. Once a prototype is evaluated and finalized, it is sent for production in order to introduce it to the market.

This introductory part gives you a summary of product development and the related technical terms. In the next chapters, we will dive deep and go through all the mentioned stages, one by one.

### Point Clouds

Whether working on a renovation project or making an information data about an as-built situation, it is understandable that the amount of time and energy spent on analysis of the object/project in hand can be quite debilitating. Technical literatures over the years, has come up with several methods to make a precise approach. But inarguably, the most prominent method is the application of Point Clouds.

3D scanners gather point measurements from real-world objects or photos for a point cloud that can be translated to a 3D mesh or CAD model.

But what is a Point Cloud?

A common definition of point clouds would be — A point cloud is a collection of data points defined by a given coordinates system. In a 3D coordinates system, for example, a point cloud may define the shape of some real or created physical system.

Point clouds are used to create 3D meshes and other models used in 3D modeling for various fields including medical imaging, architecture, 3D printing, manufacturing, 3D gaming and various virtual reality (VR) applications. A point is identified by three coordinates that, correlate to a precise point in space relative to a point of origin, when taken together.
There are numerous ways of scanning an object or an area, with the help of laser scanners which vary based on project requirement. However, to give a generic overview of point cloud generation process, let us go through the following steps:

1. The generation of a point cloud, and thus the visualization of the data points, is an essential step in the creation of a 3D scan. Hence, 3D laser scanners are the tools for the task. While taking a scan, the laser scanner records a huge number of data points returned from the surfaces in the area being scanned.
1. Import the point cloud that the scanner creates into the point cloud modeling software. The software enables visualizing and modeling point cloud, which transforms it into a pixelated, digital version of the project.
1. Export the point cloud from the software and import it into the CAD/BIM system, where the data points can converted to 3D objects.
##### Different 3D point cloud file formats

Scanning a space or an object and bringing it into designated software lets us to further manipulate the scans, stitch them together which can be exported to be converted into a 3D model. Now there are numerous file formats for 3D modeling. Different scanners yield raw data in different formats. One needs different processing software for such files and each & every software has its own exporting capabilities. Most software systems are designed to receive large number of file formats and have flexible export options. This section will walk you through some known and commonly used file formats. Securing the data in these common formats enables the usage of different software for processing without having to approach a third party converter.

Common point cloud file formats

OBJ: It is a simple data format that only represents 3D geometry, color and texture. And this format has been adopted by a wide range of 3D graphics applications. It is commonly ASCII (American Standard Code for Information Interchange).

PLY: The full form of PLY is the polygon file format. PLY was built to store 3D data. It uses lists of nominally flat polygons to represent objects. The aim is to store a greater number of physical elements. This makes the file format capable of representing transparency, color, texture, coordinates and data confidence values. It is found in ASCII and binary versions.

PTS, PTX & XYZ: These three formats are quite common and are compatible with most BIM software. It conveys data in lines of text. They can be easily converted and manipulated.

PCG, RCS & RCP: These three formats were developed by Autodesk to specifically meet the demands of their software suite. RCS and RCP are relatively newer.

E57: E57 is a compact and widely used vendor-neutral file format and it can also be used to store images and data produced by laser scanners and other 3D imaging systems.

##### Challenges with point cloud data

The laser scanning procedure has catapulted the technology of product design to new heights. 3D data capturing system has come a long way and we can see where it’s headed. As more and more professionals and end users are using new devices, the scanner market is rising in a quick pace. But along with a positive market change, handling and controlling the data available becomes a key issue.

Five key challenges professionals working with point cloud face are:

• Data Format: New devices out there in the market yields back data in a new form. Often, one needs to bring together data in different formats from different devices against a compatible software tool. This presents a not-so-easy situation
• Data Size: With the advent of new devices, scanning has become cheaper with greater outputs. It is possible to scan huge assets from a single scan. This has resulted in the creation of tens of thousands of data points. A huge data of points can be challenging to handle and share between project partners.
• Inter-operability: Integration between new technologies with the existing software can be quite arduous. Although, with careful investment of time and money, the goal can be achieved nonetheless.
• Access: All the professionals involved in the entire lifecycle of a product can benefit from having access to point cloud data. But multiple datasets in multiple formats usually makes it more of a hassle.
• Ownership: Who owns point cloud data? In the past, EPCs and the contractors who capture the data become custodians of the information.
• Rendering: Different formats can result in rendering problems for point clouds.

### Reverse Engineering vocabulary

3D Scanning – The process of collecting 3-Dimensional data from physical object through a variety of data acquisitions devices.

3D to CAD: The process of converting 3-Dimensional point to a dimensionally defined graphic model.

Accuracy: The extent of how close a measurement is to the recognized true value.

Annotation Models: A digital model containing specific coordinate locations verifying deviations from nominal data.

AS IS CAD: A CAD model that represents actual manufactured parts rather than a designed CAD model.

CAD (Computer-aided design): The use of computer technology to assist in the creation, analysis, or modification of a design.

CAM (Computer Aided Manufacturing): The use software that can support both machine tools and 3D CAD modeling capabilities.

Cone beam: A conical-shaped x-ray beam that produces two dimensional images of an object.

Design intent: The process of taking a manufactured part into account with inherent errors and modifying the same till it is true.

GD&T (Geometric Dimensioning and Tolerancing): System of languages and symbols used for defining and communicating engineering tolerances.

Hand held scanner: Portable camera that is used for capturing 3D imagery of objects with a laser or structured light based.

Hybrid Model: Combining two different modeling processes to accurately define 3D geometry.

Laser Scanner: A device used to capture 3D surface geometry, consisting of a laser output and a sensor to interpret the data.

LIDAR: A combination of the words: “Light” and “RADAR.” A LIDAR scanner employs RADAR’s technique of emitting a signal and measuring distances to objects based off of the signals reflection.

Long Range Scanning: Acquiring data at expansive distances from hundreds of feet away to miles away. Data can be captured through a variety of devices including LIDAR, Time of Flight and phase shift scanners.

Modeling: Digitally creating 2D or 3D object using CAD or data manipulation software, such as Polyworks, Geomagic or Solidworks.

NanoCT: Capturing images using CT (Computed Tomography), with a resolution of the images defined in nanometers.

Parametric Model: A sketch driven model that builds a design tree that can be opened in a CAD environment and allows the operator to manipulate the model.

Parametric Modeling: This process is taking 3d scan data and through the use of design tools, creating a sketch driven model with consistent relationships between features in the feature tree.

Phase Based Scanners: LIDAR Scanners that take measurements by sending laser pulses towards an object and measuring the phase shift of the pulses’ reflection off of the object.

Point Cloud: A set of points defined by X, Y, and Z coordinates that represent the external surfaces of an object.

Prismatic Modeling: Creating CAD geometry using basic geometry shapes, i.e. planes, cylinders, cones etc, to define correct shapes of the 3D geometry.

Re-Engineering: The process of modifying an existing part or assembly of parts digitally to improve its performance or use.

Repeatability: The variation in measurements taken with the same piece of equipment, under the same conditions, across multiple tests.

Reverse Engineering: The process by which a man-made object is dismantled to reveal its architecture, designs, or to extract knowledge from the object in order to know about its functioning and structural integrity.

SCAN to CAD: The process of collecting 3D data using 3D scanning hardware and converting the dimensional data to CAD format using a variety of software packages.

2D Drawings / Schematics: A 2D print that describes the physical characteristics of an object, how it should be made, assembled, handled, etc. These can be used to provide basic dimensional values to define its function.

Sectioning: The process of creating 2D profiles through sections of an object.

Short range scanning: A process used to collect dimensional data in 3D space from short ranges.

Solid Modeling: Defining an object with CAD tools such as extrudes, revolves, sweeps, etc. A solid model is enclosed and is said to have mass and volumetric values can be calculated.

Surface Model: An objects exterior skin defined by CAD features or NURBS surfaces.

Triangulation Scanner: Projecting a known pattern of light grids or fringe onto an object in order to calculate surface geometry by analyzing the distortions of the pattern.

White Light Scanner: A 3D camera projecting a known pattern of light grids or fringe onto an object in order to calculate surface geometry by analyzing the distortions of the pattern.

### 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.