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.
  • 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.

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.