Different types of geometry
When we look at the geometry that's most used in programs that create 3D objects, there are 3 types of geometry we see a lot. Each of those types has it's own advantages and disadvantages. The three types are:
- Polygon geometry
- NURBS geometry
These three are not the only types, some other geometry types are: Bezier patches, Nurms and subdivision surfaces. The three main types mentioned above do have properties that can be found in other geometry types.
Knowledge of the properties of the 3D geometry is essential because they influence the way the geometry can be created and the way in which it can be modified. Both are of great influence on designer's freedom of shape.
At this point the use of 3D digital geometry does not differ a lot from traditional modeling material like cardboard, wood and clay. With each of these materials almost every shape can be generated, however, some materials are more suited for specific shapes than others. It is possible to make double curved shapes with cardboard, but the material has it's limitations; clay would be better suited for it.
The three different types of materials have very different properties, for instance: just like with clay, NURBS geometry is more suited for double curved surfaces than polygons. A quick comparison between NURBS and polygons is made below, more specific information about every type of geometry can be found in the modeling with polygons and in the modeling with nurbs section.
Comparison between NURBS and polygons
Unlike a Polygon a single NURBS surface can never define a closed object. NURBS surfaces always have a "rectangular" topology. This can be illustrated with the analogy of the two sets of curves which define the geometry. The organization of vertices and the parameterization of the geometry are basically crosswise organized to each other to create basically a surface with four edges.
Forms like spheres and tubes are basically deformed rectangular surfaces. By welding (closing) the connection of one of the directions of the isoparms the surface can be closed in one direction creating a tube like structure.. However the other direction can’s be welded or closed. The surface remains open.
Another difference between NURBS and polygon geometry is that polygon geometry is based on points (vertices) that are connected with straight lines. Which means a (perfect) smooth shape is never possible with polygons, even tough it may look very smooth from a distance.