### 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.

### Neutral 3D CAD File Formats

Every CAD design/model, upon completion, is stored in a respective file format. A 3D file format stores information about 3D models in plain text or binary data. The 3D formats encode a model’s

geometry, which describes its shape,

scene, which includes position of light and peripheral objects;

appearance, which means colors and textures;

and animations, which defines how a 3D model moves.

Not every 3D format stores all such data. Each software comes with its 3D file formats. However, every software has a different file format due to many reasons such as cost, feature, etc. It is necessary for any two software to enable interchangeability/interoperability to make things work. Some of the popular 3D file formats are STL, OBJ, FBX, COLLADA, etc. Each industry comes with its version of 3D file formats. This article gives a brief description of 3D file formats.

##### SALIENT FEATURES OF 3D FILE FORMATS

Considering there are different file types, it is essential to understand the various properties. Different file types allow CAD model viewing in different ways. Some CAD files are limited to only 2D viewing to show the end customer. Following are the main features of 3D file formats:

Proprietary or neutral

The two main types of file format are – proprietary and neutral. All CAD design software uses a proprietary file type. This file type is specific to that particular software. Generally, such file types can only be viewed using the same software it was created with. However, it won’t open in a completely different design program. Proprietary files could be used in intercompany tasks.

Neutral files, on the other hand, are designed to be interoperable. Hence they can be viewed on a multitude of programs. Neutral data come in handy if the document is being distributed to end-users who don’t use CAD software.

Precise or tessellated

CAD designs are displayed in two different ways, namely, precise or tessellated. The difference lies in the fact that the product that is viewed while designing looks quite different from the actual product in real life. It is particularly noticeable in the case of lines and edges that form the product shape. This differentiates between precise drawings versus tessellated drawings.

To create a product, CAD software uses precise lines and angles to complete complex manufacturing processes. Such specific instructions have to be included in a file format to edit the actual drawing or change its design. While displaying a CAD drawing for visual purposes, the lines and edges are tessellated.

Type of assembly

Multi-part designs present a complicated situation while choosing a file format. Depending on the type of file format, multi-part product design may be limited to one single file for the whole assembly. Alternatively, designers also opt for separate files for each component. Awareness of how a particular software will display a multi-part product or if it will display a multi-part product is essential.

Parts Listings

CAD designs accompany models with a list of parts. Different 3D file formats come up with different ways of showing parts list. Two main types of parts list displays are Bill of Material (BOM) and flat list. A bill of material showcases a single part and all its positions in a drawing. A flat list shows all parts individually.

Now that the different features of 3D CAD file formats have been explained, let us walk through some of the popular and most used file formats out there.

##### NEUTRAL FILE FORMATS

To counter interoperability, neutral file formats, also called open source formats, are used as intermediate formats for converting between two proprietary formats. Naturally, these formats are widely used nowadays. Two known examples of neutral formats are STL (with a .STL extension) and COLLADA (with a .DAE extension).  They are used to share models across CAD software.

3D CAD file formats generally fall into two categories: Native or Neutral file formats.

• Native file formats are exclusive to particular CAD software, which can be used with the respective software only.
• Neutral or Standards were explicitly created to enable interoperability, which helps the exchange of files between different CAD software. Neutral file formats allow easier transfer of files with someone who uses different CAD software.
##### DIFFERENT 3D FILE FORMATS
• STEP: STEP is the most recommended and widely used of 3D file Formats. It is an ISO 10303-21 certified standard. Most of the software support STEP importing and exporting.
• IGES: IGES is the abbreviation for Initial Graphics Exchange Specification. It is a vendor-neutral file format. Using IGES, a CAD user can exchange 3D models in the form of circuit diagrams, wireframe, or solid models. Applications backed by IGES include traditional engineering drawings, analysis models, and other manufacturing functions
• Parasolid: Parasolid, initially developed by ShapeData, is now owned by Siemens PLM Software. It is licensed to other companies for use in their 3D computer graphics software products.
• STL: STL, which stands for stereolithography, is the universal format for pure 3D information. It is used in 3D printers and somewhat loved by CAM. STL denotes only the surface geometry of a 3D object without any representation of color, texture, or other common CAD model attributes.
• VRML: VRML stands for Virtual Reality Modeling Language. It is a standard file format for representing 3D interactive vector graphics.
• X3D: X3D is an ISO standard XML-based file format for representing 3D computer graphics. X3D features extensions to VRML (e.g., CAD, Geospatial, NURBS, etc.).
• DXF: DXF stands for Drawing Interchange Format, or Drawing Exchange Format. It is a simple 2D format and technically should be viewed as a Native format. It is Autocad’s native 2D format.

### The Reverse Engineering process

Sometimes, situations arise where you don’t have access to a part’s original design documentation from its original production. This might be due to the absence of the original manufacturer altogether or stoppage on the production itself.

Reverse engineering empowers us to analyze a physical part and explore how it was originally built to replicate, create variations, or improve on the design. The goal is to ultimately create a new CAD model for use in manufacturing.

Let us take a look at the steps involved in reverse engineering. Commonly, it involves careful executions of the following steps:

• ##### Scanning

The first step involves using a 3D scanner for collecting the geometric measurements and dimensions of the existing part quickly and accurately using projected light patterns and camera system. Generally, the types of scanners used for such execution are blue light scanner, white light scanner, CT scanner and /or laser scanner. The former two captures the outward dimension and measurements while the latter two is capable of scanning the entire inside out.

• ##### Point Cloud

Once a certain part is scanned, the data gets transformed in the form of point clouds. Point cloud is a 3D visualization consisting of thousands or even millions of points. Point clouds define the shape of a physical system.

• ##### Meshing/Triangulation

This stage serves involves conversion of point clouds to mesh (STL or Stereolithographic format). Mesh generation is the practice of converting the given set of points into a consistent polygonal model that generates vertices, edges and faces that only meet at shared edges. Common software tools used to merge point clouds are Polyworks, Geomagic, ImageWare, MeshLab. The meshed part is then run for alignment in the mentioned software tools.

• ##### Parametric/Non-parametric Modeling

After the meshed part is aligned, it goes through either of two stages. The first option involves applying surface modeling on meshed part in tools such as Polyworks. It results in the generation of non-parametric model (IGES or STEP format). An alternate option is creating a sketch of the meshed part instead of putting it through surfacing. This work-process is known as parametric modeling (.PRT format). 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. For a parametric model to predict new data, knowing just the parameters is enough.

The next stage consists of transferring the data through CAD software tools such as NX, Catia, Solidworks, Creo etc, for applying functions such as ‘stitch’, ‘sew’, ‘knit’, ‘trim’, ‘extrude’, ‘revolve’ etc for creation of 3D CAD model.

• ##### Inspection

This stage includes visual computer model inspections and alignment of the merged models against actual scanned parts (STL) for any discrepancies in the geometry as well as dimensions. Generally, inspection is carried out by using tools such as Polyworks or Geomagic. Reverse engineering inspection provides sufficient information to check tolerances, dimensions and other information relevant to the project.

• ##### Documentation

Documentation of 3D stage model depends solely on one’s technical/business requirements. This step is about converting 3D model to 2D sketch, usually with the help of tools such as inventor or Isodraw/Coraldraw, citing measurements which can be used for reference in the future.

### 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.

### What are BREP and CSG | Difference between BREP and 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.

### What are Parametric and Non-parametric Modeling

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.

### What is 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.