COTA 751 Form Visualization: Handout 1

What is a model?
A model is a representation of a planned or existing object. In the fields of science, education, engineering, and architecture, a model is constructed so that the object's essential information stands out in the model and we can analyze important aspects of the object by observing the model. In order to be concise and analytic, a model may be different from the object which the model represents in its scale, complexity, and appearance. A model of a building may be built on a scale of 1:1000 so that the model can be placed on a desk and examined by architects from any angle.

A mathematical model of a complex natural phenomenon may be built by choosing only the parameters which play important roles in the phenomenon of interest in order for us to explain or predict nature. Mathematical models have been expressed as equations. In recent years a mathematical model formulated on the computer is visualized as graphical image which we can understand intuitively. In the process of modeling and visualizing an object (or a natural phenomenon), insignificant parameters of the object may be discarded. Shapes and colors may be given to the components of the object which are invisible to us in nature. An object is simplified and given a new appearance to become a model which is conceivable to us.

In the fields of art, advertisement, and communications, a model on the computer can operate in two ways. First, a computer model may be a representation of an object which is produced in the process of analyzing and/or designing the object. In this case, a computer model is similar to the ones in used in science and technology, and it is a tool or a process to achieve a goal.

Secondly, a computer model can be an object itself. In this second case, the model is neither a process or a tool but it is an end product. For instance, an abstract 3D sculpture created on the computer using an interactive tool represents nothing else but itself. This second nature of a computer model is reflected in the fact that the words "model" and "object" are used interchangeably in computer graphics. Following this convention, in this class, the word "object" is used to mean a model -- especially a geometric model -- existing in a virtual world on the computer without real entity. When a model represents an existing object or an object which will be produced in the real world, the object is called a physical object in order to avoid confusion.

Geometric modeling studies shapes of objects. It is concerned only with the geometric and topological information of an object. Other characteristics of an object, such as color, surface texture, density, material, temperature, and pressure are not in the scope of geometric modeling.

A representation method is a set of rules used to describe the shape of an object. A physical object can be measured and its shape can be represented as a geometric model on the computer. The shape of a non-existing object can be created directly on the computer and represented as a geometric model as well. There are a group of representation methods used in the field of computer graphics. You may choose one method over others, depending on your goal. All the same, all the representation methods describe object shapes using coordinate systems.


Surface models, solid models, and volume models
Why do we need different types of 3D models (i.e., representation methods)? It's because each type has advantages and disadvantages. You need to select the most appropriate model type, depending on your purposes and applications. Different models require different modeling, manipulation, and rendering techniques.

Type of 3D models Example of applications
Surface models Computer animation
Solid models Engineering, manufacturing, computer aided design (CAD)
Volume models Scientific visualization, medical visualization

When an architect previsualizes the exterior of a building under consideration for a customer, surface models may be appropriate to use. When an architect wants to predict the stress on a structure constructed with a new material, solid models may be used. When an architect simulates the effect of dust of varying density on lighting in a room, a volume model is probably the most appropriate. Intuitively, while a volume model represents the contents and shell of an egg, a solid model represents the complete egg shell and the enclosed space, and a surface model represents a fraction of the egg shell or the complete shell.

Solid models vs volume models
A solid model always has a crisp surface which can divide the entire universe into two regions, i.e., the inside of the model and the outside of the model. vs A volume model may have a crisp or ambiguous surface or no surface at all.

Volume models can represent fuzzy things, such as clouds. vs Solid or surface models cannot.

The interior of a volume model is non-homogeneous. vs The interior of a solid model is homogeneous.

Volume model consists of volume data of a physical characteristics (e.g, electric charge and temperature) measured at various locations in the space of interest or the space containing an object of interest, or a field defined by a set of mathematical equations. When surfaces are extracted from volume models, the volume models are called "implicit surfaces," "blobby models," "meta-balls," and "soft objects."

Notes: Volume models vs surface models/solid models
Both surface models and solid models (excluding octree models) represent the surface shapes of objects explicitly. vs Volume models can represent fuzzy things. Solid or surface models cannot.