BREP & CSG

The geometric modelling technique has revolutionised 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 prominent ways to express solid models are Boundary Representation modelling and Constructive Solid Geometry modelling.

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, and sends commands to rotate, sweep a binds facets into a three dimensional solid. The union, thus, enables the formation of a surface that notably encloses a volume

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 surface;

an edge is an enclosed piece of a curve and;

A vertex lies at a point. Topological items allow making links between geometrical entities.

BREP comes with its share of advantages and disadvantages, which are:

  • 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).
  • BREP is more flexible with a more rich operation set.
  • In addition to the Boolean operations, B-rep has extrusion (or sweeping), chamfer, blending, drafting, shelling, tweaking and other actions which make use of these.
  • The BREP library does not store geometric or other information associated with topological entities.
  • BREP is not suitable for applications like tool path generation.
CONSTRUCTIVE SOLID GEOMETRY

Constructive solid geometry or C-REP/CREP, previously known as computational binary solid geometry, is a solid modelling technique that allows creating 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 that can be 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.

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

These simple primitives are in some 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 which is based on bounded solid primitives, R-sets.

Half-space based CSG: This CSG scheme uses unbounded Half-spaces. Bounded solid primitives and its 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 CSG scheme occurs indirectly. Each primitive that is combined using a Boolean operation (r-sets) to build the CSG model is checked for its validity.
  • The standard data structures used in CSG are graphs and trees.
  • CSG representation is of considerable importance to manufacturing.
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 set of 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 in the sense that its surface is closed and orientable and encloses a volume, provided the primitives are authentic in this sense.
For B-rep, we review the possible surface types, the winged-edge representation schema, and the Euler operators. For CSG, The basic operations include classifying points, curves, and surfaces concerning a solid; detecting redundancies in the representation; and approximating CSG objects systematically.

 

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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.

 

 

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Geometric Dimensioning and Tolerancing (GD&T)

The design model is a depiction of a part design. However, the design model can never be an accurate representation of the product itself. Due to shortcomings in manufacturing and inspection processes, physical parts never match the design model exactly. An essential aspect of a design is to specify the lengths the part features may deviate from their theoretically accurate geometry. It is vital that the design intent and functionality of the part be communicated between the design engineers and the manufacturing unit. It is where the approach of GD&T comes into play.

Geometric dimensioning and tolerancing or GD&T is a language of symbols and standards used on engineering drawings and models to determine the allowable deviation of feature geometry. 

GD&T consists of dimensions, tolerances, definitions, symbols, and rules that enable the design engineers to convey the design models appropriately. The manufacturing unit uses the language to understand the design intent.

To master GD&T, one needs to understand the crucial concepts, which includes:

  • Machining tolerances: Tolerances mean the allowable amount of deviation from the proposed drawing. Machined parts look flat and straight through the naked eye, but if viewed with calipers, one can find imperfections all over. These imperfections or variations are allowed within the tolerance constraints placed on the parts. Tolerances should be kept as large while preserving the functions of the part.
  • The Datum Reference Frame: DRF is the most important aspect of GD&T. It is a three-dimensional cartesian coordinate system. It’s a skeletal reference to which all referenced geometric specifications are related.
  • GD&T Symbols: It is essential to be familiar with numerous symbols and types of applied tolerance in GD&T. The language of symbols makes it easier to interpret designs and improve communications from the designer to the shop. By using GD&T standard, the design intent is fully understood by suppliers all over the world.

  • Feature Control Frame: The feature control frame describes the requirements or instructions for the feature to which it is attached. A feature control frame contains only one message. If a feature needs two messages, the feature would need the corresponding amount of feature control frames for every message required.
  • Basic Dimensions: Basic dimensions are exact numerical values in theory, which defines the size, orientation, form, or location of a part or feature. 
  • Material Condition Modifiers: It is often necessary to state that a tolerance applies to a feature at a particular feature size. The Maximum Material Condition (MMC) allows an engineer to communicate that intent.

GD&T is an efficient way to describe the dimensions and tolerances compared to traditional approximation tolerancing. The engineer might design a part with perfect geometry in CAD, but the produced part, more often than not, turns out to be not accurate. Proper use of GD&T improves quality and reduce time and cost of delivery by providing a common language for expressing design intent.

 

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The New Product Development Process

You might be a seasoned design professional thinking “What do my bosses sit around and do all day while I do the real design work".

This section outlines and explores the various early stages of the industrial design process that a product goes through. It does serve as a reasonable account of the overall and general product design process.

  • Ideating or initial ideas

Before any design work can begin on a product, there must first be a definition of what the product or product line might be. The idea’s genesis can be many factors such as:

Consumer demand – Reviews & feedbacks from the customers or even their ideas can help companies generate new product ideas.

Internal sources – Companies provide incentives and perks to employees who come up with new product ideas

Market research – Companies constantly review the changing needs, requirements and trends of the market by conducting plethora of market research analysis.

Competition – Competitors SWOT analysis helps companies to generate ideas.

  • Idea screening

An idea can be excellent, good, moderate or very bad. Once a suitable product opportunity has been identified, a specification document or design brief is created to define the product. It is usually created by the higher management of a company who’ll have access to information, such as budgeting and buyer/seller feedback. This step involves filtering out the good and feasible ideas which maintains the technical integrity while staying within realistic cost expectations.

Features such as a mechanical specification or a reference to an existing invention the product might be based upon, are outlined. Expectations, uses, and underlying intelligence associated to the product are included as well. Electronics, including sounds, lights, sensors, and any other specific inputs, such as colors and new materials may also be mentioned. Finally, a few reference sketches or photo images can be added to convey a possible direction.

  • Concept design & development

All ideas that pass through the screening stage are turned into concepts for testing purpose. A concept is a detailed strategy or blueprint version of the idea. In most companies, designers work up a design brief or product specification that guides their designs. It’s the designer’s role to make these ideas a reality. A professional designer has the ability to provide a large variety of designs in a quick and efficient manner. Many people can draw one or two ideas, but when asked to elaborate they often fall short. What separates the true design professional is depth and breadth of their presented ideas and vision in a clear and concise manner. Concept design generally means the use of hand-drawn or digital sketches to convey what’s in a designer’s mind onto paper or a screen.

  • Business analysis

A detailed business analysis is required to determine the feasibility of the product. This stage determines whether the product is commercially profitable or not, whether it will have a regular or seasonal demand and the possibilities of it being in the market for the long run.

  • Modeling

With the help of 3D modeling software (CAD – Computer Aided Design), the ideas/concept is rendered a shape, thereby creating a 3D model. The technical and engineering team has the biggest workload during this phase. These 3D models will often show up problematic areas where the theoretical stresses and strains on the product to be developed will be exposed. If any problem persists, it is a best phase of product development to handle the design errors and come up with modifications to address the same.

  • Prototyping & pilot runs (preliminary design stage)

In this stage, prototypes are built and tested after several iterations and pilot run of the manufacturing process is conducted. This stage involves creating rapid prototypes for a concept that has been deemed to have business relevance and value. Prototype means a ‘quick and dirty’ model rather than a refined one that will be tested and marketed later on. Adjustments are carried out as required before finalizing the design.

  • Test marketing

Apart from continuously testing the product for performance, market testing is also carried out to check the acceptability of the product in the defined market and customer group. It is usually performed by introducing the new product on a very small scale, to check if there are any shortcomings. This helps to know in advance, whether customer will accept and buy this product on launching in the market. Test marketing is a powerful tool indeed.

  • New product launch

This is the final stage in which the product is introduced to the target market. Production starts at a relatively low level of volume as the company develops confidence in its abilities to execute production consistently and marketing abilities to sell the product. Product manufacturing expenses depend on the density of the product, if there are numerous parts, material selection etc. The organization must equip its sales and customer service entities to address and handle queries. Product advertisements, website pages, press releases, and e-mail communications are kept on standby on the launching day.

Product development is an ever evolving fluid process and cannot be summed up in a few steps. The entire procedure sees insertion of additional stages or even eviction of a crucial part, depending on the nature of the project. Each group of professionals, whether designers, engineers or marketing, sales; has their role to play in this methodology. It is the company’s responsibility to continuously monitor the performance of the new product.

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