Model Types
There are several model types:
Polygonal mesh
Parametric surfaces
CSG - Constructive Solid Geometry
Mathematical shapes
Metaballs
The polygonal mesh object is perhaps the most common type of 3D model. The idea behind it is to approximate a surface using a mesh of planar consecutive polygons.
For a cube this is straightforward, there are six squares connected. For a generic curved surface the problem of using flat polygons will face up. In this case you can only have an approximation of the shape. So to increase the approximation you can only increase the number of polygons. This fact is a problem and can make mesh models to take a considerable amount of memory and disk space and make them slower to display in wireframe preview or in final rendering.
Fortunately a rendering trick can help us: Phong normal interpolation.
Another kind of model representation is by using parametric surfaces or surfaces that interpolates parametric curves (note that these two things are not exactly the same). A parametric curve is a curve whose shape is dependant from some parameters. These parameters can be a series of points in the 3D space. By manipulating the positions of these "control" points you can modify the shape of the curve.
A parametric surface is simply a 3D surface that is under the control of a series of parameters, for example a series of control points.
There are several types of parametric curves, but the most commonly used in 3D applications are:
Bezier spline
B-spline
NURBS
To render objects modeled this way there are different approaches.
One is rendering the surfaces directly (Real3D follows this approach); another one is to convert it to a polygonal mesh prior to render.
This second approach is usually followed by programs that started with polygonal mesh objects only and added parametric surfaces objects in later revisions of the software.
The models created using this technique presents usually smoother shapes and are indicated for modeling organic shapes or smooth aerodynamic surfaces like car coachworks or aeroplanes (you definitely won't use NURBS to model a F117 Stealth Fighter however!).
These curves usually require more processing power to compute and this is perhaps the main cause that near all 3D packages started with a polygonal approach.
This technique is suitable to create geometrically perfect objects, but the quality of the model obtained directly depends by the variety of the available primitives.
The idea behind CSG is that an object can be done with composition of simpler parts. Those simpler parts can be composed from even simpler ones. This process repeats until we reach the simplest objects named "primitives".
Some examples of primitives are:
Sphere
Box
Cylinder
Cone
Torus
You can perform boolean operations on primitives to obtain more complex object.
This technique is suitable to create geometrically perfect objects, but the quality of the model obtained directly depends from the variety of the available primitives.
Mechanical parts are usually better reproduced this way.
Organic shapes, instead, are hard to model in CSG.
Although this name can be applied to all possible shapes, I use this term to define those objects like 3D fractals and other interesting stuff that can be created with Mathematica or similar programs and then exported and converted to 3D objects.
3D fractals like the julia_fractal of POV-Ray are fine to look at, but the most useful use of fractal objects is as landscapes.
Fractal landscapes can be very impressive and right now is the best way to obtain realistic landscapes in 3D graphics. There is a whole range of programs that are nearly entirely based on this technique to create their images. The most famous of them are probably Vistapro and Bryce.
Metaballs (also known as "Blob") are a relatively recent introduction in 3D. It's not easy to explain by words the behaviour of this interesting staff.
In his basic implementation a metaball is a sphere that "feels" the proximity of another metaball. If two metaball are close enough their surfaces start to deform and stretch as there is an attraction between metaballs's surfaces. As metaballs become closer they join together like two drops of honey.
Each metaball has three parameters, radius, threshold and strength. If strength is a negative value the metaball repulse other metaballs instead of attract them.
With the aid of a good metaball editor it is possible to model extremely realistic organic models, like human bodies, animals, monsters...
With the exception of POV-Ray, I think that near all 3D packages convert the metaballs object to a polygonal mesh prior to render.
Recently POV-Ray 3.0 introduced cylindrical blobs, but the real revolution in 3D modeling is called metamuscles.
This new object is a metaball that can be shaped like a spline. It allows the creation of stunning quality organic models that could be only created using a huge number of spherical metaballs.
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