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Geometric Modelling is the field that discusses the mathematical methods behind the modelling of realistic objects for computer graphics and computer aided design.

The three principal classifications of the geometric modelling systems are:

1) Wireframe modelling

2) Surface modelling

3) Solid modelling

**Wireframe Modelling**

A wireframe model represents the shape of a solid object with its characteristic lines and points. The word “wireframe” is related to the fact that one may imagine a wire that is bent to follow the object edges to generate a model.

In other words, a wire frame model is an edge or skeletal representation of a real-world 3D object using lines and curves.

Model consists entirely of points, lines, arcs and circles, conics, and curves. In 3D wireframe model, an object is not recorded as a solid. Instead the vertices that define the boundary of the object or the intersections of the edges of the object boundary are recorded as a collection of points and their connectivity.

One can use a wire frame model to

1) View the model from any vantage point

2) Generate standard orthographic and auxiliary views automatically

3) Generate exploded and perspective views easily

4) Analyse spatial relationships, including the shortest distance between corners and edges, and checking for interferences

5) Reduce the number of prototypes required

**Merits**

- Simple to construct for 2D and simple and symmetric 3D objects.
- Designer needs little training
- System needs little memory
- Take less manipulation time
- Retrieving and editing can be done easy
- Consumes less time
- Best suitable for manipulations as orthographic isometric and perspective views.

**Demerits**

- Image causes confusion
- Cannot get required information from this model
- Hidden line removal features not available
- Not possible for volume and mass calculation, NC programming cross sectioning etc.
- Not suitable to represent complex solids

**Surface Modelling**

A surface model is a set of faces. A surface model consists of wireframe entities that form the basis to create surface entities the basis to create surface entities.

A Surface modelling is a model with minimized ambiguous representation than the wireframe modelling but not as good as solid modelling. The construction of surface modelling is done with the use of geometric entities like surfaces and curves. Surface Modelling uses B - Splines and Bezier mathematical techniques for controlling curves.

It is used to make technical surfaces (e.g. air plane wing) or aesthetic surfaces (e.g. car’s hood). It was developed for the aerospace and automotive industries in the late 70s.

Overall on the basis of performance, the surface modelling stays in between wireframe modelling and solid modelling for representing a realism object.

**Merits**

- It is less ambiguous.
- Complex surfaces can be easily identified.
- It removes hidden line and adds realism.

**Demerits**

- Difficult to construct.
- Difficult to calculate mass property.
- More time is required for creation.
- Requires high storage space as compared to wire frame modelling.
- Also requires more time for manipulation.

**Solid Modelling**

Solid Modelling is a modelling that provides a complete representation of an object than a wire frame modelling and surface modelling. In this model, the appearance of an object is displayed in solid design. A solid modelling is defining an object with geometric mass.

Solid modelling programs usually create models by creating a base solid and adding or subtracting from it with subsequent features. It was originally developed for machine design, and is used heavily for engineering with large part assemblies, digital testing and rapid prototyping.

**Merits**

- Complete modelling.
- Unambiguous.
- Best suitable for calculating mass properties.
- Very much suitable for automated applications.
- Fast creation.
- Gives huge information.

**Demerits**

- Requires large memory.
- Slow manipulation.
- Some manipulations can be complex and require tedious procedure