“3D modeling… is the process of developing a mathematical representation of any three-dimensional surface or object..” (Wikipedia). Most 3D programs “offer several types of geometry” to model with (Softimage User Guide). Namely one can use polygon meshes or sub-division surfaces, when creating polygonal models, or NURB curves or surfaces, when creating NURB models (Softimage User guide).
“Polygonal modeling is an approach (to) modeling objects by representing or approximating their surfaces using polygons” (Wikipedia). “A polygon is a closed 2D shape formed by straight edges. The edges meet at vertices. There is exactly the same number of vertex points as edges. The simplest polygon is a triangle” (Softimage User guide). A 3D object can be generated out of combining numerous polygons together to make a polygon mesh.
There are several ways to create and manipulate a polygon mesh. The most common and quickest is by selecting a primitive polygonal mesh object from the tool bar in your 3D modeling software package. Alternatively one can “build polygon meshes from curves by performing operations such as extruding, lofting and revolving” (Softimage users guide). Once you have created your polygonal mesh one can manipulate in various different ways. Such as through scaling, rotating and moving the actual edges, vertices or faces to achieve your desired shape or one can merge two or more polygon meshes together.
The geometry of a polygon meshes “is mathematically simple and quick to calculate” for this reason “they are particularly useful when modeling for games and other real time environments where speed is important… However the main draw back of polygon meshes is that they are poor at representing organic shapes – you may require a very heavy geometry (that is, many points) to obtain smoothly curved objects… Another huge advantage of polygon meshes is that “you can apply materials and textures to selected polygons instead of the whole mesh” (Softimage User guide).
Sub-Division surfaces “consist of a low-resolution polygon mesh hull that controls a higher-resolution polygon mesh object. They provide many of the benefits of polygon meshes, plus the ability to approximate smooth surfaces without the need for heavy geometry” (Softimage users guide).
There are three ways to subdivide polygon meshes:
1) By generating a new object, which entails that one creates a “new high-resolution polygon mesh from a low-resolution one. As long as there is a modeling relation between the two objects, you can modify and animate the low-resolution object to drive the high resolution one” (Softimage users guide). In simpler terms this means that the low-resolution object drives the overall shape of the high-resolution subdivided polygon. However you can still move points on the high-resolution subdivided mesh independently of the low-resolution one (Softimage users guide).
2) By modifying the geometry approximation, where you turn “the polygon mesh object into a subdivision surface by applying a geometrical approximation property… The original mesh becomes the control of cage of the new geometry… The advantage of this method is that no new geometry is actually created, so scene files can still be quite small. However the disadvantage, of this method, is that you can’t manipulate individual points etc., on the high-resolution geometry… (you can only manipulate) the components that correspond to components on the control cage” (Softimage users guide).
3) Local subdivision, allows on to “add subdivisions locally to selected polygons” in a mesh. This method adds an operator to the polygon mesh’s operator stack and modifies its topology. (However it is useful) for adding detail exactly where you want it. Although new geometry is created you control the amount and the location” (Softimage users guide).
Additionally one can “combine these methods to obtain the effect you want” (Softimage user guide).
“Non-uniform rational basis spline (NURBS) is a mathematical model commonly used in computer graphics for generating and representing curves and surfaces which offers great flexibility and precision for handling both analytic and freeform shapes” (Wikipedia).
“NURBS curves, are cubic or linear splines… Linear curves are composed of straight segments and cubic curves are composed of curved segments… You cannot render them” but you can convert them into polygonal meshes, which will render (Softimage user guide).
There are two main ways which one can create curves:
1) Drawing curves by placing control points or knots by simply clicking to place them where you want them. The four commands one can use to create a curve in this manor is either to “Draw cubic by CVs, Draw cubic by Bezier- knot points, Draw cubic by knot points or Draw Linear” (Softimage user guide).
2) “By holding the mouse button down and dragging continuously, as if you were sketching with a pen. This method creates cubic curves only” (Softimage users guide).
However one can also import curves into a 3d modeling program from Encapsulated PostScript or from Adobe Illustrator. Once these curves are in the 3D program one can convert them into a polygonal mesh to use in your model.
A second form of NURB modeling is through NURB surfaces. “Surfaces are two dimensional NURBS patches defined by intersecting curves in U and V directions. In a cubic NURBS surface, the surface is mathematically interpolated between the control points, resulting in a smooth shape with relatively few control points. The accuracy or NURBS makes them ideal for smooth, manufactured objects like cars and areoplane bodies. One limitation of surfaces is that they are always four sided. Another limitation is that they so not support different textures on different areas” (Softimage Users guide).
Finally the last type of NURBS modeling is Surface meshes, which “are quilts of NURBS surfaces acting as a single object. They overcome limitations that surfaces must be four-sided; with surface meshes, you can create complex objects and characters with holes, legs and so on” (Softimage User guide).
In conclusion it is apparent that there are numerous ways to successfully model in 3D, while each way provides individual benefits they additionally provide certain drawbacks. Therefore it is important to chose your modeling method according to the object you are modeling as that way you will assume the best results.