What is Geometric Modeling

The culture of design & manufacturing incorporates various crucial aspects for producing a market- efficient product. Computer-aided Engineering or CAE is 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.

Geometric Modeling is the computer/software-generated mathematical representation of an object’s geometry. It includes both graphical and non-graphical information. This information is stored in a database and displayed as a picture. It is then possible to edit and analyze the model in different ways.

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 the generation of drawings, which go on for analysis and eventual manufacturing of the object. In general, there are three conventional steps to creating a geometric model:
  • They create key geometric elements using commands like points, lines, and circles.
  • Applying Transformations on the geometric elements using commands like rotation, achieve scaling, and other related transformations functions.
  • Construct the geometric model using various commands that integrate the geometric model's elements to form the desired shape.

Representation of Geometric Models

There are two basic types of geometric models: a two-dimensional model, which is used for technical drawing, and a three-dimensional model, which is used for computer-aided design and manufacturing.
  • Two-Dimensional or 2D: It projects a two-dimensional view and is used for flat objects.
  • Three-Dimensional or 3D: This representation permits complete three-dimensional viewing of the model with intricate geometry. The leading process of geometric modeling in 3D is Solid modeling.
Constructing a geometric model in CAD involves using a 3D computer program to describe geometric relationships and the physical extent of a component. The models may also contain material properties and other attributes of the element, such as the mass of the component. Many CAD programs can calculate a component's mass properties and evaluate its other physical properties. These capabilities may be crucial for flexible and adaptive manufacturing lines.

There are two main types of representations in geometric modeling. The classical presentation of geometric objects consists of geometric pointsets defined by boundaries. On the other hand, modern geometric modeling uses parametric families of pointsets. Parametric families are defined using geometric operation graphs, features, and constraints. In both cases, a user interacts with an example object from the family. It may also be a surface, a volume, or a solid. In addition to these models, geometric modeling can incorporate other design and manufacturing aspects. Computer- aided engineering, or CAE, is the central component of the manufacturing process. With the help of geometric modeling applications, key elements can be created, transformed, and integrated into the desired shape. In addition to this, CAD applications can also incorporate complex mathematical operations.

Types of Geometric Modelings

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

Solid modeling
Solid modeling also known as volume modeling, this is the most widely used method, providing a complete description of solid modeling. Solid modeling tools allow you to build many sides of an object at once. Solid models make multiple sides at once, reducing the ambiguity in surface modeling.

Surface modeling
Surface modeling is another popular method. This type of modeling represents the object by its surface and is used to describe the object with a clear view of manufacturing. This method uses surface geometry to create objects with complex forms. From 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. Surface modeling is better for design engineers as it organizes the edges that define polygonal surfaces.

Wireframe modeling
It is a simple modeling system used to represent the object with 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. Wireframe geometric modeling is a good option for small-scale companies, where intricate surface details are essential for product design.

Requirements for Geometric Modeling

The various requirements of geometric modeling are as follows:
  • The cross-section, hidden lines, and dimensions are needed for Graphical Visualization.
  • Interchangeable manufacturing tolerance analysis is required while inspecting parts.
  • There should also be properties 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 models are beneficial in applications where the algorithm aims to predict a set of variables in a complex environment.
Geometric modeling is a vast and elaborate field of CAE and requires in-depth study. The following articles dive deep into the various types and facets of geometric modeling.