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3D Primer – page 2

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2.01 No NURBS here


There are lots of different types of 3D modeling with a computer these days from CAD technical drawing packages that turn flat sketches into buildings right up to virtual potters wheel apps. This Primer is about Polygon Modeling using Sub-Division surfaces. It doesn’t include any information about a different form of Modeling known as NURBS.

NURBS, short for Non Uniform Rational B-spline, is a computer graphics technique for drawing curves. A NURBS curve is defined by a set of weighted control points, the curve’s order and a knot vector. NURBS are generalizations of both B-splines and Bezier curves, with the primary difference being the weighting of the control points which makes them rational (non-rational B-splines are a special case of rational B-splines, in practice most NURBS curves are non-rational).

And guess what? We aren’t going to be discussing them here at all!


Sub-division gained mainstream popularity long after  NURBS modeling was well established. It is generally excepted that modeling in Sub-D’s is freer and more fluid than with splines. Major Film studios have adopted Subdivision surfaces with Pixar being one of the earliest to develop and fully embrace them.


2.02 What is Subdivision modeling


Subdivision modeling allows the Modeler to create a smoothed (Sub-divided) model from a lower resolution model (Known as the cage or control cage).

In the example below you can see a basic polygon cube which will act as the control cage. Some programs let you Sub-divide in stages and other programs will be set to a very high level of Sub-division as default . In this example you can still see the Cube in outline form showing you that this object, even when it looks like a Sphere is still actually a six sided object.



Too many polygons moving around a screen is bad. It’s bad for games as they slow things down and uses too much system and graphic card memory. It’s also bad for 3D Modeling/animation packages as more polygons means more complex scenes and longer render times.
As mentioned earlier, Sub-Division modeling allows you to create a polygonal model that acts as a `cage` that contains the structure of the smoother, subdivided one. Only the smoothed version is taken into account at render time. It is achieved by using sub-division algorithms (math routines that do the smoothing)


`Subdivision surfaces are used to create smooth surfaces out of arbitrary meshes. Subdivision surfaces are defined as the limit of an infinite refinement process. They were introduced simultaneously by Edwin Catmull and Jim Clark, and by Daniel Doo and Malcom Sabin in 1978. Little progress was made until 1995, when Ulrich Reif solved subdivision surfaces behavior near extraordinary vertices`. That’s what the books all say. But what does it mean to me as a new starter in this confusing world of Polygon Modeling?


Sometimes it is necessary to model with the geometry already Sub-divided. This allows you to see your mesh in its final, smoothed state as you go along. A disadvantage is that you may not focus on the layout and position of the polygons in the underlying geometry (or Cage). If you don’t switch in and out of Sub-division mode as you model you may end up with a messy mesh.


2.03 Messy meshes


By Messy mesh I am referring to a polygonal model that looks fine when Sub-divided but looks a complete mess when not. It may have vertices/points, edges or polygon faces that cross over each other in lots of places. This looks messy but more importantly it can create problems in later stages of the project.

For example:

If UV co-ordinates are created on the base mesh they may need lots of tweaking in a UV view to prevent Stretching (In most programs polygon faces need to be flattened out in a UV view and not have points crossed over each other).

When rigging a character with a bone system the usual way is to have the bones effect groups of points with differing degrees influence (usually called weighting). Therefore it follows that if the points are all messy and crossing over each other it will make the whole job much harder. Obviously this is different from software package to software package.


2.04 Catmull Clark or Doo-Sabin?


Sub-division algorithm routines (the math doing the sub-dividing behind the scenes) can come in different flavors and seem to be named after the clever guys who created them. One very common one is Catmull Clark and can be found in most of the major 3D packages available today and to be honest you don’t really need to know it’s being used unless you plan to help work on developing the software. Even ZBrush uses this type of Sub-division in its multi-resolution Sub-d features.

Source Wikipedia; Dr. Edwin Catmull (born 1945 in West Virginia) is a computer scientist who has contributed to many important developments in computer graphics. Early in life, Catmull found inspiration in Disney movies such as Peter Pan and Pinocchio and dreamed of becoming a feature film animator. However, he assessed his chances realistically and decided that his talents lay elsewhere. Instead of pursuing a career in the movie industry, he enrolled in the physics and computer science programs at the University of Utah. It was there that he made three fundamental computer graphics discoveries: Z-buffering, texture mapping and bicubic patches. While at the university, he invented algorithms for anti-aliasing and rendering subdivision surfaces and created, in 1974, his earliest contribution to the film industry, an animated version of his left hand for Futureworld, the science fiction sequel to the film Westworld and the first film to use 3D computer graphics. After leaving the university, Catmull founded the Computer Graphics Lab at the New York Institute of Technology. In 1979 he went to work for George Lucas at Lucasfilm. It was at Lucasfilm that he helped develop digital image compositing technology used to combine multiple images in a convincing way. Later, in 1986, Catmull founded Pixar with Alvy Ray Smith. At Pixar, Catmull was a key developer of the RenderMan rendering system used in films such as Toy Story and Finding Nemo. In 1993, the Academy of Motion Picture Arts and Sciences presented Catmull with his first Academy Award “for the development of Renderman software which produces images used in motion pictures from 3D computer descriptions of shape and appearance.” Again in 1996, he received an Academy Award “for pioneering inventions in Digital Image Compositing”. Finally, in 2001, he received an Oscar “for significant advancements to the field of motion picture rendering exemplified in Pixar’s RenderMan.”


2.05 Edge Loops


Edge loops and knowing how to use them is key to learning how to model with Subdivision surfaces

Essentially an edge loop is a line of polygon edges that follow a continuous path around an object. Where the edge reaches all the way around the model and comes back on itself it forms an edge loop.

They are commonly encountered in all subdivision modeling but they have become synonymous with organic character modeling For example, they are often likened to the muscles that form the ring around an eye. Good edge loops make for good animation deformation.

The edge loop doesn’t have to be in the center of an object. It can form the outer edge or an inner edge forming an open hole in the mesh.

Where an edge loop meets a junction of four edges, if it continues along the middle path it remains as an edge loop. Where it takes either of the other two branches it terminates the loop. If the edge loop meet a 3-edge junction it also has to terminate


There has been lots of discussion about where the future of sub-D modeling and therefore edge loops is going. As innovative software like Pixologics ZBrush and Voxel based modelling packages like 3DCoat allow the digital sculptor to create multi-million polygon meshes the relevance of edge loops slips away. While there is still a low polygon cage in the equation and of course animation requiring weighting then edge loops matter.



2.06 3, 4 and 5 sided polygons and poles


Polygonal models are made up of Polygon Faces. Faces are made up of Edges and Points. Most 3D modeling packages support the use of Polygons with more than 4 sides ( called N-Gons).

A Pole is a Point (vertice) that has more than 4 Edges coming into it. When ever you perform an extrude on a quad based mesh you will be creating Poles, both 3 and 5 edged Poles. These can be referred to as the N-Pole (5 edges meeting at a point) and the E-Pole (3 edges meeting at a point)

An example of the above is shown in the image below. The head on the right is made up entirely of Quads and gives a very predictable Sub-divided mesh. The head of the left is full of N-Gons and Tri’s and once Sub-divided pinching and irregularities in the mesh can be seen. Both models however do contain five-edged Poles.


So which is it then? Who is right and what are the rules? These questions abound in the forums for every Sub-division package available and here is a selection of answers I have taken from books, forums, magazines, training material and good old fashioned experience from the last few years:

Modeling with all quads is good for several reasons. Firstly when you sub-divide a quad you get a very predictable result. Second, if you model with 100% quads by default you have also modeled 100% Triangles if needed. You simply hit the button that splits the quads in half (Usually something like triple or tessellate). So a mesh with 2000 Quads can be quickly and predictably turned into 4000 Triangles.

Not all modelers agree with this and you will find articles to support both theories. SteveStahlberg for example

If you are learning to model then learn to model with all Quads. Generally speaking modeling is one step in a process: Concept Art > Modeling > UV’ing >Texturing > Rigging/Muscles > Animation. So if you are a modeler working as part of a team you will have very clear direction about how the mesh is to be created. If the instruction is ‘anything goes’ then all is well. If the requirement is a limited polygon count and all Quads but you never took the time to learn to model that way then you lose.

It is, of course, easier to just model without constraint and end up with 3, 4, 5 and more sided polygons. It can be liberating to just model away throwing caution to the wind and think about shape and form in the way a traditional sculptor may do. Some very skilled modeler do indeed model this way and create awesome looking models.
N-Gons (Polygons with more than 4 sides) don’t work in all sub-division modeling packages. So, If you want maximum cross platform compatibility use only Quads and Triangles. Even packages that can Sub-divide N-Gons can give unpredictable results when Sub-divided

A lot of modeling experts seem to stick to the mantra of  ‘All Quads except where you have to have a Tri`. Model with quads as much as possible and where you struggle to achieve this use a Triangle but try and hide them on the model in case they cause an issue at Sub-Division time. The issues I refer to are usually facets in the smoothed mesh or some sort of geometry error.

A model that looks great and Sub-divides well in the base or rest pose may not do so when animated. Try to bear this in mind as you construct your geometry.

What about modeling for games? The big challenge for game creators in recent years has been to keep the polygon count low enough so that the game play isn’t adversely affected. One way that game programmers have been able to get round this is to use maps that simulate high detail on the surface of the low detail models. One very specialized type of map is called a normal map. These maps take information from high detail models that can then be used on a low polygon version to simulate detail. The model is no more complex but the visual experience is much improved. Game engines convert the mesh to all triangles so using triangles is common place. However, making a 100% quad mesh also give you a predictable 100% Tri mesh if needed.


2.07 Which 3D program do I need?


So to the question that you will have already asked and maybe even had answered. Which program are you going to use to sculpt these polygons we keep talking about? There is no right answer here (unless you work for one of the companies that sell the software).


You will choose your software based on a number of questions and choices:


  • How much can I afford? If the answer is nothing then look to the free solutions.
  • Do I want more than just modeling? If so you need to look into the more comprehensive solutions that include texturing, bones, animation and full rendering solutions.
  • Do I want a job in a studio that specialises in only one program (3DStudio Max for example)



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