On Geometric Modeling

Geometric Modeling focuses on the categories that have represented data structures over the past forty years. The categories are made up of wire frame models, surface models, and solid models.

Wire frame models which are the oldest are representative of the shapes edge, which only allows the viewer to see outlines instead of the volume of the shape. Surface models give a representation of a limited edge or face of an object. Although surface modeling is easier to read than wireframe, the surface areas of a combined shape cannot be determined since it is not known where these surfaces are connected. Overall solid modeling is the best method to represent forms, all the information about a shape including edges, faces, and volume, can be determined.

Within solid modeling methods have been developed for creating shapes, spatial occupancy enumeration model (“voxel” model), structive solid geometry, and boundary representation model (B-rep). Spatial occupancy enumeration sees solids as sets of matter within a three-dimensional space. A grid (spatial array) is then placed within this space that is occupied by cubes or cells (voxels) that are representative of the form. Two of its shortcomings consist of the calculation of the relationship of parts and the expense of computing recourses. Constructive solid geometry creates the construction of solids through the union of different forms. CSG records operations that are then the end result of the unions of multiple shapes which is then processed through another operator which later determines what shapes are visible but the drawback of using CSG is the difficulty of using the end representation. Boundary representation determines the likelihood of points in space which makes up the edges and faces of a shape. This method, although more exact than the others, provides a more difficult model to construct and manipulate.

The author of this article refers to these types of modeling as advanced, methods that are only used and understood by the seasoned architect or engineer. But each type is broken down to explain its usefulness to the designer in creative situations. When speaking about surface modeling the author says: “its usability for design purposes, in architecture and in mechanical engineering, is limited to the visualization of finished products” (pg. 3). This can be helpful in identifying what modeling program will be best suited for different design circumstances, when visualizing surface modeling should be used, when needing a “geometrically complete” model, solid modeling should be used (pg. 3).

The usefulness for some of this information is relevant but also seems to use it in the context of creating designs using one method, instead of using them to build upon each other. Wireframe modeling, for example, is usually only used for creating the basis for a form. The author states: “representations are very familiar to architects and engineer, who are used to representing building and machines through their contours along, and are trained to “see” in their minds eye the surfaces and volumes they represent” (pg. 1). Without the wireframe there is no structure for which to build a surface or solid model, not having these forms gives the architects/engineers a base for the structure. Wireframing is the basis for which most models are built upon. Until programming is available that can identify the shape that the user intends to create, this method of modeling cannot be deemed obsolete.


“On Geometric Modeling”. Excerpt from “Modeling”, Architecture’s New Media by Yehuda Kalay, The MIT Press, 2004, pp 141-147.