Short Course in Computer Modeling:

Introduction

The purpose of this document is to give the reader a solid understanding of basic modeling techniques and terms. This tutorial will not instantly make you a professional modeler. Modeling is an art form, and like any art-related skill, requires a lot of practice and dedication before it is mastered. This tutorial will, however, hopefully demystify the technicalities of the modeling process so that you may focus on the artistic side of modeling.

As this document will illustrate, there is no one way to model, but there are a general set of guidelines to follow as well as a few things to avoid. The techniques and ideas in this tutorial are a culmination of ideas derived from my own professional experience and the experience of other industry professionals.

Because subdivision surfaces have quickly become the industry standard in the entertainment world (the method of choice for PIXAR and many other professional studios), the techniques in this document will be focused on polygons – which are the basis for a subdivision surface and are also used extensively in the game industry. Other types of geometry will be briefly discussed for the sake of completeness and to familiarize you with other techniques. Further, most of the techniques will be discussed in the context of organic modeling (i.e. things that deform such as an animated character). A non-organic model would be something that remains stiff, such as an inanimate table or chair. Nonetheless, many of these methods apply to both organic and non-organic modeling. If what I just said sounds like Chinese to you, than read on, this tutorial is definitely for you! Oh, and one more thing…the techniques in this tutorial are non-software specific; meaning that the techniques and methods apply to which ever software you choose to use. I will, however, make recommendations as to which software I prefer with the reasons why. Every program has its strengths and weaknesses depending on what you want to achieve. If you are curious, check out the software section at the end of the document.

Who is This Document For?

This document is for the beginner interested in furthering their knowledge of computer modeling techniques – especially as it pertains to computer animation in the entertainment industry – and has asked themselves any of the following questions:

What in the world are NURBS?
Should I use NURBS or Polygons?
What do I start with? A cube? A sphere?
Why is there weird pinching in my model?
How detailed do I make my model?
What are edge loops?
What is non-manifold geometry?

These are just a few of the questions you may have wondered when attempting to model. This document will venture to answer these questions and more.

Using This Document

This document is meant to be read in electronic form. I chose to go this route to keep the information interactive and fresh. Throughout the body of the text you will notice text in blue. Clicking on these will either link you to the glossary of terms at the end of the document or to an external web page. Footnotes in blue will link to the original reference or additional information on the statement. You will also notice that many of the illustrations are animated. These illustrations make difficult-to-explain techniques easier to visualize and are obviously not possible in a printed form. If you are extremely new to computer modeling I highly recommend skipping to the end of the document and reading through the glossary of terms first. Most of the definitions have accompanying pictures, but if the idea of reading through a dictionary still bores you than feel free to learn the terms as you go. Lastly, this document is most useful when you are connected to the internet as external links will obviously not work otherwise. I recommend viewing this document with the Mozilla Firefox web browser or Internet Explorer version 7 on at least a 19 inch monitor. With these browsers, you can middle mouse click on links to open them in a new tab without loosing your spot (middle click the tab to close it).

Fun Facts will appear randomly throughout the document and are there purely for their “interesting” factor.

Tips will also appear randomly and are simply useful tidbits of information that are somewhat related to the topic being discussed, but don’t really fit into any particular section of this document.

With no further adue, let’s get started!

We will begin with the basics and some terminology.

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Types of Geometry: The building blocks of any model

First of all, what is geometry? Traditionally, geometry is defined as “the pure mathematics of points and lines and curves and surfaces”[1]. In computer graphics there are essentially four types of geometric surfaces which are the building blocks of any computer model. They are:

Polygonal
NURBS Surfaces
Subdivision surfaces
Spline Patches

Each of these is made of subcomponents. What makes them different are the components they are made of and the way they are computed mathematically. Just as their real-world sculpting counterparts such as clay, polyurethane, silicone, etc…each has its own strengths and weaknesses depending on the type of model you are building. First, let’s introduce the subcomponents.

Subcomponents: The building blocks of geometric surfaces

Vertex

A vertex is a single point in space. It has one dimension and no definable size or volume.

Edge

An edge is a straight line between two points in space and has two dimensions.

Polygon

A polygon is a shape that is made by connecting three or more vertices in space with edges. Polygons can occupy two or three dimensions. Polygons have a surface area, but no volume.

Spline/curve

A spline is essentially a curve that consists of its own little set of components:

Control Vertex

Referring to the image directly below, a control vertex would be one of the green dots that is attached by a straight line and controls the shape of the curve with a rubber band-like connection.

Knot

On the image below, a knot would be one of the green dots that lie directly on the spline. A curve can be drawn by plotting either control vertices (CVs) or knot points.

Segment

The section of a curve between two knot points.

spline
Author: Freeformer

Image courtesy of NX Shape Studio

Splines are a good thing to get a grasp on because they can be used to generate all surface types (discussed next). [2]

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Geometric Surfaces

Here are the types of geometrical surfaces described in more detail

Polygonal

Sub components:

Points, Edges, & Polygons

Advantages:

Allow for arbitrary topology; high degree of control over edge loop direction; can be used with displacement sculpting software.

Disadvantages:

Have most potential for non-manifold geometry; not resolution independent i.e. because polygons are connected by straight lines, the profile of a polygonal mesh can appear angular if there are not enough polygons.

Polygons are arguably the most versatile geometry type. You can literally build just about any shape you can imagine out of polygons and still have it deform properly. That cannot be said for the other surface types (except subdivision surfaces which are essentially polygons). Polygons however, do not provide the accuracy required for manufacturing a machined part that must fit precisely into a car for example. An analogy that helps to explain this concept can be drawn from 2d graphics.


Fig. 1	Fig. 2
The first image is a typical image shot with a digital camera. When viewed at normal distance the image appears smooth and continuous, but upon closer inspection it is obvious that the image is made up of thousands of tiny colored squares called pixels (fig. 1). In the second image (fig. 2) we see a vector curve. Vector curves are mathematical formulas and will always be smooth no matter how close you get to it because a mathematical formula is telling the line where to be drawn between two given points. In this example, a polygon would be analogous to a pixel. A NURBS curve would be analogous to the vector curve. You can get as close as you want to a NURBS surface (discussed next) and it will always be smooth – not so with a polygonal model.

Apply this to the image below

Here are two spheres with the same amount of vertices. Notice that the polygonal sphere has an angular profile while the NURBS sphere has a smooth continuous profile because it is made of curves as opposed to points connected by straight lines.

NURBS Surfaces

Sub components:

Control Vertices, Knots, Segments, and Curves

Advantages:

Allow for arbitrary subdivision because they are based off of curves; are always smooth (resolution independent); are capable of making very complex and accurate shapes; UV maps are inherent in a NURBS surface and do not need to be generated manually; and are more friendly towards Boolean-like operations than polygons.

Disadvantages:

Do not allow for box modeling techniques; To achieve complex topology and change edge loop direction separate NURBS surfaces must be “stitched” together – when animated, stitched surfaces can sometimes tear apart creating visual seams in the mesh. NURBS were designed to be used for mechanical, hard-surface modeling (things that don’t deform); NURBS are more difficult to transfer from one modeling software program to the next.

NURBS stands for Non Uniform Rational Basis Spline. They are different than polygons in that they are entirely made up of mathematical curves as opposed to straight edges. NURBS are unique in that you can blend different meshes or cut holes in them with curves. The unique part is that these blends and holes are “virtual”. When you cut a whole in a NURBS mesh you aren’t physically cutting the geomtrey – you are merely telling the geometry to be hidden behind a selected curve (see example below). This type of geometry lends itself well to creating very precise surfaces, but can be a bit unstable when animated.


Here we see a NURBS surface being trimmed by a floating curve. Whatever modifications are made to the trim curve are reflected in the NURBS surface.	Here we see to separate NURBS cylinders being blended together at their intersection by a fillet curve.

Subdivision Surface

Sub components:

Points, Edges, & Polygons

Advantages:

Have the benefits of both NURBS (in the sense that they are resolution independent) and polygons.

Disadvantages:

Shrink away from the cage object (the original polygonal object that it is based off of); actual control vertices do not lie directly on the surface (although some programs alleviate this problem by putting pseudo points on the surface for selection sake).

Subdivision surfaces attempt to bring the advantages of NURBS to a polygonal model. They do this by applying a subdividing/smoothing algorithm to the polygonal mesh that mimics the way NURBS interpolate a curve between two points. In this way, you model with polygons, but get the smoothness of NURBS. It is this combination of flexibility and quality that have made subdivision surfaces an industry standard in the film industry. Even though subdivision surfaces are smooth, the algorithm isn’t as precise as NURBS and are, therefore, not useful for industrial manufacturing applications.

Here we see a cube being converted to a subdivision surface which becomes spherical and shrinks away from the cube due to the subdivision/smoothing algorithm. You’ll notice that the subdivision surface consists of many more polygons (indicated by the thinner, more transparent lines). Each subdivision quadruples the polygon count, but the only editable polygons are those of the original cube. The original polygon mesh that controls the subdivision surface is called a “hull” or “cage” (seen surrounding the subdivision surface.

The more detail you add, the less the subdivision surface shrinks away from the cage. Note that the closer you create new edges to existing edges the tighter the crease you will get in the subdivision. Because of this, subdivision surfaces are capable of making both smooth and sharp surfaces.

Good software programs allow you to hide the cage object and work directly on the subdivision surface which is often more intuitive as well as less messy. This can be seen at the end of the clip briefly.

I would argue that subdivision surfaces have the best combination of versatility and quality. If you plan to work in the entertainment industry, you WILL use subdivision surfaces at some point and should be very familiar with them.

Spline Patch

Sub components:	Control Vertices, Bezier (Bias) handles, Curves, and Patches
Advantages:	Are capable of producing a lot of detail with relatively little geometry; are based off of Bezier curves – allowing for control over creasing and continuity without adding extra geometry; maintain a smooth surface without shrinking like subdivision surfaces; the only smooth surface type whose control points physically lie on the surface instead of “float” above with a rubber band-like connection.
Disadvantages:	Don’t allow for box modeling techniques; spline patches cannot be extruded like polygons; are not good for producing really complex shapes; there are not very many programs capable of modeling with spline patches.

Here we see three profile splines. As you will notice, spline patches require the least amount of geometry to define a given shape.

Image courtesy of Luxology

It should be mentioned that spline patches are the rarest of the geometric surfaces but are, nonetheless, useful and intriguing. I think there is more to be seen from this surface type in the future although it has existed for years without much development. Hash’s Animation Master has the most usable spline modeling.

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Modeling Methods

Here is a list of what I believe are the most basic forms of modeling. It is not a question of which one is better, but more a question of which best suits the way your brain thinks and which will get the job done fastest. The answer to these questions depends on what kind of model you are building and how much experience you have. The best modelers likely use all methods of modeling. Rarely do you use any one singular method to build an entire model.

Volume Modeling

(Also known as “Box Modeling”)

This method really only applies to polygonal modeling. The volume modeling method always involves beginning with a “closed” polygonal primitive such as a cube or sphere. Faces are extruded and edges are split to form the various shapes and edge loops. Nearly all polygonal models are at least partially modeled using this method. Volume modeling is most like traditional sculpting in the sense that you are refining very basic forms into more specific shapes by pushing, pulling, subtracting, and adding geometry.

“Blocking in” is especially important when volume modeling. In the examples below, notice how detail is added to a primitive shape by slicing it. The new detail is sculpted before adding more detail. It is a refinement process, but care should be taken to not add too much detail too fast.

Here are a few videos done by Bay Rait (the modeler responsible for making the digital model of “Gollum” in the movie trilogy Lord of the Rings). Observe and learn.

Head

Ear

Turtle

Images Courtesy of Subdivision Modeling Resource Page [3]

Go here (http://www.arildwiro.com/tutorials/modelling/head/head.html) to see an example tutorial on box modeling technique. Not a great model, but it should give you an idea of the process.

Displacement Sculpting

The displacement sculpting method is a type of volume modeling because it involves beginning with a closed volume and deforming it from there. There are currently only three software programs available for doing this kind of modeling. They are:

ZBrush

Mudbox 3d

Silo 3d

& Blender 3d

Image Courtesy of “Pixolator” of Pixologic

Here we see Zbrush in action. Notice the minute details that are easily “painted” onto the surface. Achieving this with traditional modeling methods would be near impossible.

These programs generally work by importing a low poly model (model with relatively few polygons) built in another program, subdividing it into sometimes millions of polygons, and pushing and pulling the dense mesh as if it were clay. Displacement sculpting allows you to model immense amounts of detail that would otherwise be impossible to achieve in typical modeling software. These programs are made to push and pull millions of polygons interactively. Since animating with such a dense mesh would be impractical, these programs measure the distance between the original imported mesh’s surface and the sculpted surface and then generate a black and white texture map that is essentially a height field (called a displacement map). Black represents areas that have been pushed below the original surface and white represents areas that have been pulled above the original surface. Grey represents no displacement at all. This map can then be used in conjunction with the original low poly model and animation software to regenerate the displacement details at render time.

The ability of software to sculpt this much detail interactively is relatively new technology and largely made possible by faster computers. The idea of a displacement map is not so new however. In the “good ol’ days” models (like the computer generated dinosaurs in Jurassic Park) were sculpted in clay with all of the nitty-gritty details and scanned into the computer with lasers. These hi-tech lasers also measured the distance of fine details in relation to the “averaged” base mesh and generated a grayscale displacement map. This process is effective, but extremely expensive and not friendly to quick changes made by the director. Displacement sculpting software is by comparison much cheaper and friendly towards rapid changes and experimentation. Laser scanners are still used quite heavily in Hollywood (to make a “digital double” of an actor’s face for example) and offer a good starting point for a model or displacement map.

Images Courtesy of Universal Studios

The development of Mudbox 3d was spearheaded by two modelers at Weta Digital (the studio responsible for the digital special effects in Peter Jackson’s The Lord of the Rings and King Kong). Mudbox 3d was used to create all of those realistic details on the surface of King Kong’s skin. The resolution of the displacement map for King Kong’s thumb alone was 4,000 X 4,000 pixels. For comparison, the resolution of an entire frame of film projected on the big screen at the theatre is 2,000 pixels wide. This means that just half of King Kong’s thumb could have filled the entire movie screen and maintained its realism. [4]

Modeling these sorts of details with conventional methods would be extremely difficult and time consuming.

Image Courtesy of Universal Studios Image Courtesy of Universal Studios and Ubisoft

Displacement sculpting software works best on meshes that have a relatively even distribution of detail in the base mesh. This means that every polygon in the mesh is close to the same size. This doesn’t mean that each polygon has to be exactly the same size, it just means that you shouldn’t have extreme variations in size. These programs work by subdividing the model so if you want to sculpt some tiny details and you have one really big polygon and an area with a hundred tiny polygons the model will subdivide unevenly. In order to subdivide the big polygon enough to paint small details into it you will also have to subdivide the area with a hundred tiny polygons which will in turn create thousands and thousands of more polygons which is simply wasteful and inefficient. These programs also do not like triangles and N-gons. Try to keep your triangles and N-gons to an absolute minimum. I would say that in a character that deforms and is animated, that the triangle-to-quad ratio should be around .001%. That means that if you had a character that was 11,000 polygons, only 12 of those would be triangles. And those triangles would be tucked away in hard-to-see places or places that don’t deform a lot. Of course, there is no hard and fast rule; the point is to have very few. Having none at all is a good goal.

Need All Quads? – If you’re having trouble eliminating all triangles and N-gons from your mesh, subdividing your model by it’s very nature will convert everything to quads. You can than import this model into a program like Zbrush and paint a displacement map and apply that map to the original un-subdivided mesh. Mudbox will automatically subdivide your model once if it detects non-quad polygons.

Displacement sculpting software has really raised the bar for high-quality digital modeling and is undoubtedly the “wave of the future.” I foresee the day when all models will be at least partially made using this process. Fast computers will only make it more prominent in the industry and even more accessible to hobbyists.

Some more examples of what displacement sculpting is capable of.

Image by Chris Perna [5]

Image by Scott Wells (Ibid)

Image by Florian Fernandez (Ibid)

Image by Tibor Madjar (Ibid)

Image by PSTCHOART [6]

Surface Modeling

While volume modeling only applies to polygonal geometry, the surface modeling method applies to all geometry types. This is often a preferred method for creating humanoid faces or areas of the mesh that require very specific topology and edge loop direction. Rarely is this method use to create an entire model by itself; although, in the case of a spline patch model, this is essentially the only way to model. When you are surface modeling it is extra important to have good reference and rotoscopes. This is because you are not intuitively refining basic shapes into more complex ones. You are literally starting with the details and moving outward. A good analogy would be a drawing. If volume modeling was like drawing a figure out of cylinders, spheres, and boxes, surface modeling would be like drawing a detailed eye first, then an ear, then drawing a head around that and so on.

An example of surface modeling technique can be found at http://www.3dtotal.com/ffa/tutorials/max/joanofarc/head1.asp. Compare this with the box modeling tutorial listed above to see how two totally different techniques can be used to arrive at a similar result. Which method is better depends completely on preference. I prefer surface modeling for human faces.

Edge loop drawing

Edge loop drawing encompasses several different methods depending on what type of geometry you are using. In the case of polygonal modeling, edge loop drawing involves starting with a box or profile polygon and drawing the edge loops (main direction of muscles and orifices such as eyes and mouth) and then pulling that detail out into three dimensions. It would be impossible to model a decent animatable character using box modeling alone. Edge loops would have to be drawn on the surface at some point to direct the flow of polygons. In the case of NURBS modeling it would involve drawing profile curves and using them to loft, trim, extrude, and fillet surfaces. NURBS and spline patches can really only be made using the edge loop drawing technique because they are, by their very nature, based off of curved lines. Of course, you can also start with a primitive NURBS or patch model and go from there. It should also be noted that several software programs let you create polygonal geometry from spline. This let’s you model as you would with NURBS or Patches but you generate polygons between the curves rather than patches.

Illustrated below is a condensed version for one method of edge loop drawing with polygons. Again, this document won’t go as far as to explain the process with NURBS or spline patches – although the technique below heavily applies to spline patch modeling.

Example:

Images Courtesy of Dave Komorowski

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General Guidelines

Things to think about before starting your model

Here is a small checklist of questions you should ask yourself before you even begin to model. Being able to answer these questions will greatly affect how you approach building your model and ultimately save you immense amounts of time.

Will my model have to deform in any way?
What is the closest distance my model will be seen from?
What will be the final format that the model is seen in – film, video, print (how big)?
If it’s a character does it have clothing? Will the clothing be a separate simulated model or part of the character (no simulation)?
Will the model need texture maps? If so, what kind of texture – painted or shader based? In other words, will the model need a UV map?
Will the model be animated or rendered in a different application than I am modeling it in?
Do I have adequate reference images and rotoscopes to work from?
Is my model more mechanical or organic?
Does it move in a cartoony or realistic fashion? (i.e. how much will it deform?)
Do I have constraints on my render time?
Should details be modeled or painted in a texture/displacement map?

These questions will help you determine how detailed your model should be, what kind of geometry it should be built out of (NURBS, polygons, etc…), and how critical the topology will be.

Block-In

Just as in other art forms such as drawing, painting, and sculpting, you should start with very general forms and nail down their size, shape and proportion before adding more detail. Edge loops and general topology should be fairly well defined in a simplified state before you go crazy with details.

The rule of thumb is to not add more geometry until you have squeezed every last drop out of the geometry you already have. In other words, if you were making a head, you would start with a cube and with that cube’s eight vertices you would make it resemble the head as much as possible before adding more geometry. When adding geometry, you should only add one or two edge loops at a time, sculpt the newly added geometry, and repeat. Ideally, the majority of your “block-in” should be done with a drawing on paper. This drawing should then be scanned and used as a rotoscope in your modeling application. The most useful rotoscopes have a front and side drawing that are perfectly aligned. If you are modeling with either the surface modeling or edge loop drawing methods than it is extra important to block your model in with front and side view drawings that are perfectly aligned and imported as rotoscopes. The more reference the better.

Modeling Mouths - When modeling a head that will require its mouth to be opened during animation I usually model it with the mouth in closed position and then open it later and model the inside of the mouth with teeth and all. The best way I have found is to make a selection set and open the jaw using a static object as reference to rotate from (this object’s position would be the future location of the jaw bone. This way, when I’m done modeling the inside of the mouth I can easily select the newly created geometry along with the selection set that I saved and rotate the jaw back into position using the static object as a reference point to rotate from. Of course, if your teeth are a separate model, than this process isn’t really necessary – you would just wait until you put bones in the character and then open the jaw with an actual bone and stick the teeth in there like dentures.

Build in Sections - Even though it’s important to think of the big picture when blocking in your model, it is often helpful to break your model up into various parts. For example, you could block in your entire model but keep each body part a separate object. That way when you add new detail to an area you don’t have to worry about how it affects the other areas. In the example below, the inside of the mouth is built separately and inserted into the head afterwards. If you try to build everything in one solid piece at once you’ll go crazy. Common things to build as separate models are heads, ears, hands, feet, clothing, and other accessories. Things like ears would obviously be merged in later as seen below.

Image Courtesy of Bay Rait

Creases and Subdivision Surfaces

Creases are both good and bad depending on how they were made and whether or not they were meant to be there. “Pinching” is a slightly different phenomenon and is usually undesirable. You can read more about “pinching” here. Creases are phenomena that occur when two or more edges are close together in relation to other neighboring edges. Creases also occur when you have certain shapes of poles or poles with too many edges. Creases created from poles are usually undesirable and should be avoided or hidden. Creases caused by bringing edges close together can be a very useful and necessary modeling technique if used purposefully.

Pole Creasing = Bad

On the left we see creasing due to a pole with too many edges. On top of that, triangles do not subdivide as well as quads.

A Solution

One solution to this problem is to reduce the relative size of the triangles by adding more divisions to the base cage mesh. Upping the subdivisions in the subdivision surface algorithm won’t work and can actually make it worse.

Principle

On the left is an example of a crease becoming more prominent as the selected edge is moved closer to its neighboring edges. You will notice that when the edge loop extends passed the neighboring edge you get a very sharp, ugly crease. This is simply how subdivision surfaces work.

Application

Here you will notice that there is a crease because in the polygonal cage model (shown briefly) there are two edges that overlap slightly. The problem is fixed by pulling the edges apart a little bit. The edges don’t appear to overlap in the subdivision surface, but in reality, they are.

Distribution of Detail

Not every polygon in your mesh is going to be the same size nor should it be. Distribution of detail means keeping the polygons of your mesh relatively the same size as neighboring polygons. More importantly, it means creating smooth transitions between areas of high detail and low detail. This rule mostly applies to subdivision surfaces because of the rule of creases. Unless you want a crease, spread your detail out evenly. Again, when you want a harder edge or a crease you place two or more edge loops close together. If you do not want this effect, then you need to evenly distribute your detail and newly added geometry. Many software programs offer smoothing algorithms which will help to more evenly distribute your vertices. In Maya, for example, the command can be found under Polygons > Average Vertices. Be careful because this type of operation tends to make your mesh shrink a little bit. See Smooth/Average Vertices in the glossary. There’s not much more to say on this subject except for that it’s extremely important!

Detail in the Joints – If you are building an animated character make sure there is enough geometry/edge loops around the areas of most deformation such as knees, elbows, and wrists. Also, don’t forget less obvious places such as the eyelids. Eyelids don’t seem like they need a lot of geometry, but remember that they need to wrap around a spherical object (the eye) and need enough geometry to hold a semi-spherical shape. Sometimes you simply can’t predict how much detail a certain area needs until you start to deform it, in which case you’ll need to go back and add the necessary detail. It’s a simple matter of trial and error that only experience can alleviate.

Edge loops: Modeling for Deformation and Animation

This is arguably the most difficult aspect of modeling to master (from a technical standpoint). It is one thing to model a static shape and an entirely different thing to model a shape that is not overly dense and animates and deforms in a realistic manner. The key to doing this well is edge loops. Edge loops and poles are essentially the “anatomy” of a geometrical mesh. The way edge loops run across a surface, terminate, and change direction is collectively referred to as topology. How well that mesh holds up when it is deformed is dependent on its topology.

Edge loops should be consciously planned out all over your model, especially if it is an animated character. To explain, we will use a face as an example (see Fig. 1). As a general rule, edge loops should run along the length of muscles. In this picture we see the muscular anatomy of the face. Notice the three red rings around the eyes and mouth. These represent the three main edge loops a human face. They are the main ones because that is where most of the movement occurs in the face. All other edge loops in the face extend from these as shown. The main edge loops in a geometric model are shown in Fig. 2. There is ALWAYS an edge loop that makes up the centerline of any model. This centerline usually defines the plane of symmetry for a model.

Remember that even though edge loops generally follow the direction of underlying muscle, it is the flesh that is most important. Skin folds and wrinkles take priority over underlying muscle since they are the features that are actually seen. Notice the edge loop that follows the nasal-labial fold in Fig. 2. This is especially important for defining the skin fold that happens when a character smiles. Apply this concept all over your model and you will have geometry that deforms and animates very well. Be aware that the model shown in Fig. 2 is not complete and would need more geometry in the brow area to define the wrinkles when the character squeezed her eyebrows together for example.

Fig. 1 Notice how edge loops follow the general direction of muscles.

Image from Atlas of Human Anatomy for the Artist [7]

Fig. 2 Critical edge loops are shown in red. Everything else is dependant on these.

Draw your edge loops first – It is often helpful to bring your rotoscope images into a program like Photoshop and draw on top of them in a new layer to plan out how your edge loops will run across your model (similar to Fig. 1). Draw your center line first, then the key areas of deformation (e.g. the mouth and eyes), and then simply fill in between. You don’t have to draw your entire mesh, just the key edge loops and their pole junctions. Doing this will save a lot of mesh re-working later.

Poles (Edge loop junctions)

Poles are defined as any vertex that has anything other than four edges intersecting it[8]. An edge loop stops at a pole. Poles are unavoidable and will be all over you model. Below are the six basic poles/edge loop junctions. Poles serve two main functions and are a normal part of any polygonal model.


Here is a very obvious and common type of pole. Like the poles of the earth.	2 common types of poles that typically result from a polygon extrusion. In this case, the 4 center polygons were extruded inward and a 3 & 5-edge pole resulted.	A 5-edge pole used for reducing 2 edge loops into one.


A not-so-useful pole. This kind of pole really serves no purpose and should be avoided.	A pole used for transitioning 3 edge loops into 1 while maintaining all quad polygons.	This is a unique case because, by definition, there are no poles, but edge loops do stop at triangles and N-gons so it is a junction of sorts. This is an excellent way to add detail to specific areas. You’ll notice that it creates four triangles and four 5-sided polygons (N-gons). It serves similar functionality to the previous pole.

First: They change edge loop direction (continuity)

Second: They transition areas of detail

This is a very critical concept to understand because building an efficient model can often be like putting a jigsaw puzzle together. Learning how to create poles to control the way edge loops flow and how detailed areas transition to less detailed areas will greatly improve your models. If you are not careful in how you create poles you will get pinching. This is not because of non-manifold geometry, but because of the way subdivision surfaces subdivide geometry. A good rule of thumb is to keep your poles to three or five edges (four edges is not considered to be a pole).

Can you find the poles on the mesh below?

Identify the poles and figure out which pole type they correspond to in the above examples. Also, try to figure out where poles were used to change edge loop direction, and where they were used to stop edge loops from going too far (creating extraneous detail). Note that the edge loops generally follow skin folds (e.g. love handles) and major muscles (e.g. deltoids, triceps, and sacrospinalis)

Non-manifold geometry: Keeping your meshes clean

Non-manifold geometry is specific to polygonal meshes and refers to points, edges, and/or polygons that have been connected in an “illegal” manner which results in discontinuity and visual anomalies in the mesh.

In the introduction I mentioned that there are a few things that should always be avoided when modeling. This section will explain those evils that should be shunned like the plague. It should be noted that some modeling software *cough**Maya**cough, cough* is more prone to creating non-manifold geometry than others.

Non-manifold geometry may seem harmless as you model and spin your mesh around in the 3D window, but it WILL cause you grief at some point – the texturing, rigging, rendering process is not so forgiving of bad geometry. You have been warned.

Here are a few tips to help keep your geometry clean. These tips mainly apply to modeling with polygons.

NEVER, NEVER, NEVER:

Extrude an edge other than a border edge.
Weld points that are part of a border edge to points on a non-border edge.
Flip the normals of a partial selection of polygons – this will create visual holes in your mesh (see “back face culling”)
Weld the vertices of overlapping faces. This will create a lamina face.

First we have a lamina face which was created by welding the points of a floating polygon onto an existing polygon. Not very noticeable in a polygonal model, but notice the effect on the subdivision surface model…yuck. The artifact you are seeing on the subdivision surface is referred to as “pinching”.

Secondly we have edges that have been extruded from between polygons. These will NOT render well. If you need this effect, you are better off intersecting a separate model. It should never be physically attached as illustrated.

Turn on Statistics – Many programs have the ability to display statistics (sometimes called a “Heads Up Display”) which will show you on screen how many vertices, edges, or polygons you have selected. This is a very helpful diagnostic tool for pinpointing problem areas in you mesh.

Display a smoothed version of your model – It’s a good idea to have constantly displayed a smoothed version of your model e.g. a subdivision surface or smooth proxy while you work because the smoothed model will display and exploit all the errors in your mesh whereas a plain old polygonal model hides those anomalies quite well. Working this way you will easily be able to tell when you have mad bad geometry. If your working on a character for example a good method is to clone the mesh (keeping the connection with the original), set its scale to -1 in the X axis and subdivide it. Or just make a smooth proxy and set its scale to -1 in X then lock it into its own layer so that you don’t accidentally edit it.

Conclusion

Now that you have all of this knowledge and have read the glossary ten times you are ready to go model. Remember that, despite this computer modeling lingo seeming ridiculously technical and overly complicated, it’s actually the easy part. Mastering the artistic aspect of modeling is what takes lots of practice and patience. Patience should be a word you constantly repeat in your mind while modeling. Many of the “not so good” models I see are simply not good because the artist got lazy with shape, proportion, and anatomy. Sculpting a desired form may take a little longer than it does to draw it on a piece of paper, but that doesn’t mean it’s any less important to pay attention to proportion etc... A keen observation of life and the subject matter you are modeling are also key to success. As you practice and get better/faster, patience will become less of an issue. Learning the proper techniques is definitely a good start. The internet is luckily a great resource for learning the various techniques and especially for receiving endless inspiration.

Happy modeling!

Glossary of Terms

Axis – An axis is defined by a direction in relation to the origin. In 3d graphics there are 3 axes: X, Y, and Z. The X axis could be defined as left and right, the Y axis up and down, and the Z axis as forward and backward (into 3 dimensional space). Axes in relation to the origin are referred to as “world space”. Axes in relation to the object are called “object space” and the axes in relation to individual components are called “local space” – where the Y axis is parallel to the selected component’s surface normal. A program’s ability to edit geometry based on all three spaces is very important and productive. Not all software programs are capable of this.

The origin is the center of the yellow square in the image. Each grid section is a unit of measurement extending away from the origin in both positive and negative directions.

Back Face Culling – A display option that hides components whose normals are facing away from the viewpoint of the user.

Bevel – Selected component is duplicated and averaged to create smooth corners and edges. User has control over bevel width and number of subdivisions. Beveling a vertex is the same as a chamfer.

Edge Bevel Bevel on a polygon

Bezier Spline/Curve – Is a cubic curve which has a knot multiplicity of 3. Bezier curves give you the most control over shape and continuity because tangents (the handles that are attached to the knot points) can be broken – giving you the ability to have both smooth arcs and sharp corners.

Boolean – An operation that combines overlapping meshes by adding them together, subtracting the intersection, or leaving only the intersection behind. Boolean operations require at least 2 separate meshes and the meshes must usually be closed (“water tight”) for best results.

Boolean Subtraction

Border Edge – A border edge can be defined as any edge that belongs to only one polygon.

Border edges are shown in blue. Non-border edges in yellow

Bridge Polygons – Two or more polygons facing each other are extruded to meet in the middle essentially bridging the gap between the

two.

Two opposing polygons being bridged together

CAD – Stands for Computer Aided Design. CAD refers to computer aided modeling as it pertains to industrial applications such as architecture, engineering, and manufacturing. CAD systems aren’t particularly useful for character modeling, but are geared more towards making models that need to be highly accurate. CAD software, for example, is used extensively in the motor industry to design car bodies and car parts that need to be machined with sub-millimeter accuracy.

Chamfer – Essentially “knocks” the corner off of the selected vertex. Subdivisions cannot be set for a chamfer, only distance.

Co-planar Polygons – Two polygons whose points occupy the same 3 dimensional space but are not connected. Co-planar polygons are usually bad, but are occasionally acceptable in subdivision surfaces because the actual surfaces are pulled away from each other when the model is smoothed. Possible visual anomalies would be flickering or popping.

Displacement Map – A greyscale map that is used by rendering engines to subdivide geometry at render time and displace that geometry according to the white and black values of the map. White is up and black is down. The following image explains the process of extracting a displacement map from a high resolution sculpted mesh.

Image Courtesy of Pixologic [9]

Edge Crease – A function that allows the user to define how much influence a particular edge or edges have on the subdivision surface algorithm or in the case of a spline patch model allows you to adjust the bias handles of the Bezier curves that make up the spline patch.

Edge loop – Refers to a continuous row of edges that has a quad on both sides of each edge. An edge loop terminates when it runs into a pole or edge junction.

Notice that the edge loop around the eye makes a complete circle because it is complete surrounded by quads. The other two stop at poles.

Edge Ring – An edge ring is defined by a row of continuous parallel edges that are separated by quads (4 sided polygons).

Edge Ring split – Splits an edge ring, adding a new edge loop until edge ring is terminated (runs into a non-quad polygon).

Notice that the split continues through on the first three and stops on the fourth where there is a pole.

Extrude – An operation that duplicates the selected component and connects the duplicate and original selection with parallel edges or curves. A true extrusion is only possible on polygons, border edges, and profile curves. When a group of polygons is selected they can be extruded individually or together as one if they are touching.

Face – See “Polygon”

Faceted – Refers to a polygonal mesh whose normals are not averaged together to create a smooth appearance. Each individual polygon is flat shaded and distinguishable from the rest giving the appearance of a gem.

Fillet – An operation which creates a curved portion forming a junction of two surfaces that would otherwise intersect at an angle. This operation is typically restricted to NURBS surface modeling, but can be simulated in polygons using a combination of Boolean and bevel techniques.

Geometry – In modeling, geometry is a general term that refers to points, edges, curves, polygons, and/or surfaces.

History/Operator Stack – A feature in some modeling programs that keeps track of every operation you perform on geometry. The user can go back to any operation at any time and change settings allowing ultimate flexibility. Each operation is added together to produce the final result. It is a sort of “non-linear undo”.

Hull/Cage – The low-poly version of a mesh that controls the refined subdivided version of a subdivision surface or smooth proxy model.

Instance/Clone – An identical duplicate of a geometrical mesh. It can be made to be independent from the original or maintain its relationship and mimic all edits made to the original. For example, if you made 20 instances of a window frame and populated it throughout a modeled building and changed the original, all 20 instances would update to reflect the changes.

Isopoint – An arbitrary point/location on a curve.

Lamina Faces – A type of non-manifold geometry in which two or more polygons share all of their edges. Some modeling programs are more prone to creating this type of “bad” geometry than others. The artifacts of such geometry can easily be seen in a subdivision surface. (more)

Lathe/Revolve – An operation that extrudes a polygon, border edge, or profile curve around a central axis in a circular fashion. Resulting geometry has radial symmetry (as if it was made on a potters wheel) and can be NURBS, patches, or polygons.

A profile curve is chosen and lathed around the Y axis. Resulting geometry always has radial symmetry.

Lattice – A 3 dimensional grid that is used to deform geometry. The strength of the deformation is dependant on the subcomponents’ proximity to the vertices on the lattice object.

Lattices are great for manipulating detailed meshes without having to deal with a lot of points.

Loft – Operation that requires two or more profile curves and extrudes geometry between them. Resulting geometry can be either polygons or NURBS.

In this image three profile curves are chosen and polygons are lofted between them. Because the geometry is derived from curves, the subdivision can be set arbitrarily. Tweaks made to the profile curves propagate to the lofted polygons

Low-Poly – Refers to a polygonal model that is considered to have relatively few polygons. This term is also used to refer to the cage/hull version of a subdivision surface or smooth proxy model. Polygonal models used for video games are also called “low poly” models.

Merge/Filter Vertices – Welds points together based on a user-defined distance. This operation can be used to “sew” border edges together or reduce the amount of geometry in dense meshes.

Mesh – A network of points, edges, and polygons in the case of a polygonal mesh, or control vertices and splines in the case of NURBS or spline patches. A geometric object as a whole is referred to as the mesh.

Morph/Shape/Blendshape – These are all synonymous terms (different software uses different terminology) and refer to alternate vertex positions in a geometric object that can be animated. This is a popular technique for facial animation.

N-Gon – A polygon that is made up of more than 4 points. They should generally be avoided in a subdivision surface model, but are sometimes very necessary.

Non-manifold Geometry – Specific to polygonal meshes and refers to points, edges, and/or polygons that have been connected in an “illegal” manner which results in discontinuity and visual anomalies in the mesh. Non-manifold geometry should ALWAYS be avoided. (more)

Non-Planar Polygons – Occur when not all vertices of a polygon lie within the same mathematical plane. The resulting artifact is a “bent” polygon which can cause shading errors because there is no definite plane for the normal to be perpendicular to. Non- planar polygons should be avoided in low-poly models, but are perfectly acceptable in a subdivision surface model because they are smoothed out in the process.

Normal – Surface normals are imaginary lines that extend perpendicular to geometric surfaces (such as polygons, vertices, NURBS patches, and spline patches) that determine which way the component is facing.

Here polygon normals are shown and then vertex normals

NURBS – Stands for Non-Uniform Rational B-Spline and are a type of geometry based on curves. NURBS are used heavily in the industrial design fields. Auto manufacturers, for example, use NURBS to design their car bodies due to their highly accurate mathematical nature. (more)

Origin – In 3d graphics this represents 0, 0, 0 in XYZ 3d coordinate space. It is the center of the virtual world. (See “Axis”)

Orthographic – A point of view that has no perspective or depth. Front, Side, and Top views are usually referred to as the orthographic views while the camera is referred to as a perspective view.

Pinching – Occurs when surface continuity is broken in a subdivision surface or spline patch model. Pinching is usually the result or poles or non-manifold geometry. (more)

Point – See “vertex”

Polygon – A plane that is made up of three or more vertices connected by the same number of edges. A polygon is also often referred to as a “face”.

Pole – In modeling, a pole is referred to as any vertex with anything other than 4 edges intersecting it. 3 or 5 edges converging into one vertex would be considered a pole. Poles can be bad, but are often necessary to transition areas of detail or change edge loop direction. (more)

Primitive – Pre-made geometric objects that can be used as a starting point for building more complex models. A list of primitives includes, but is not limited to: Cube, Sphere, Cone, Cylinder, Torus, Dodecahedron, Icosahedron, and grid (pictured in the same order below).

Profile Curve – A curve that is either not attached to any other geometry or part of an open edge and usually used to perform extrusion operations such as a lathe or loft.

Proportional/Soft Modeling – A gradual falloff from whatever component is selected. This allows you to push, pull, scale, and rotate components with a gradual falloff as if they were clay. This feature is arguably essential for serious digital sculpting.

Quad – A polygon that consists of 4 vertices and 4 edges. Quads are the ideal polygon for subdivision surfaces and should comprise the bulk of your mesh.

Rail Extrusion – Operation that extrudes a profile curve, edge or polygon along the length of a separate curve.

Ray Cast Selection – Selection method that allows you to “paint” over the surface of geometry and select anything under the cursor. Only components facing the camera are selected.

Reference Plane/Edge – Allows you to base the coordinate system off of and arbitrary component. Whenever you are in “reference” mode the world axes are aligned to the component that the reference plane/edge was created from. Very useful for architectural-type modeling.

Render – A computer process that calculates 3d meshes, camera angle, light, surface materials, and deformations and makes a final 2d image based on all of the collected information.

Resolution Independent – In modeling means that the integrity or smoothness of a mesh is NOT dependent on how close or far from the camera it is. It is infinitely smooth. (more)

Rotoscope – This has several meanings in 3d graphics. In modeling it is an imported image used as reference for tracing. For interesting facts on where the term originated go here.

Selection Set – A feature of some modeling applications that allows you to make a component selection and save it to be recalled later. Useful for making complex selections that need to be reused often.

Smooth Proxy – A separate smoothed version of a polygonal model. This is essentially the same as a subdivision surface – using the same algorithm as subdivision surfaces, but is a physically separate mesh and retains a relationship with the low-resolution polygon mesh. This is arguably not as useful as a subdivision surface, but a viable alternative.

Smooth/Average Vertices – Operation that applies a smoothing algorithm to selected components in order to smooth out rough surfaces. No geometry is destroyed or created – just modified (usually along the vertex normal).

Spline Patch – A unique surface type that is neither NURBS or polygons. A spline patch is created by connecting the control points of bezeir splines. Spline patches are limited to 3-5 intersecting curves – no more, no less. (more)

Subcomponent – A general term that refers to points, polygons, edges, splines/curves, patches, and UVs.

Subdivide – An operation that works differently depending on the type of component selected. Subdividing edges results in additional points along the length of the edge between the two endpoints. Subdividing polygons quadruples the amount of polygons with each iteration (1 polygon becomes 4). This is what subdivision surfaces do but additionally apply a smoothing algorithm to average out the newly created geometry. Points cannot be subdivided.

Subdividing and Edge Subdividing Polygons Subdividing with smoothing algorithm

Subdivision Surface – Is essentially a polygonal model that has a smoothing/subdividing algorithm applied to it. Subdivision surfaces allow the user to work on a relatively low-poly model, but the final is smoother and more detailed. There are several different smoothing algorithms which produce different end results. Among the algorithms are Catmull Clark, Doo Sabin, and Butterfly Modified with Catmull Clark being by far the most common. (more)

Ed Catmull and Jim Clark were the scientists behind Catmull Clark subdivision surfaces. Ed Catmull is the president of PIXAR animation studios. PIXAR was the first studio to really push the use of subdivision surfaces in production. Their short film “Geri’s Game” was a test bed for using subdivision surfaces with animated characters.

Surface/Vertex Normal – See “Normal”.

Symmetry – In modeling, usually refers to bi-lateral symmetry where a geometrical component can be reflected across a two dimensional plane (usually the YZ plane). Many programs have the ability to edit and even create geometry in symmetry so that you essentially model one half of your object and the computer models the other half. Go here to see symmetry in action.

Topology – In modeling refers to the way subcomponents are arranged to form geometric surfaces. The technical quality of a model is dependant on its topology. For example, a human face modeled on the computer could consist of a dense grid (which would be considered “bad” topology) or a series of edge loops that followed the contours of the facial muscles and skin folds (which would be considered “good” topology). Both could be made to look very similar as a static model, but the one with “bad” topology would impractical to animate and render with.

Same shape, different topology.

Torus – A doughnut shaped geometric primitive. (see “primitives”)

UV Map – Is used to map 3d geometry to a 2d space in order to apply an image or texture to the surface of a geometric object. “U” and “V” are simply directions in space and are equivalent to X and Y respectively. More specifically, U and V range from 0-1 with zero being left and bottom and 1 being right and top for U and V respectively. For example: U 1, V 1 would be the top right pixel of an image and U .5, V .5 would be the very center pixel of an image. Depending on where components lie within this UV range determines what part of the image is mapped to that component.

Vertex – The official term for a geometric point. In a polygonal mesh a point is referred to as a vertex. In a NURBS surface a point is referred to as a control vertex (CV).

Weld Points – Operation that combines two separate vertices into one essentially collapsing the edge that conjoined them.

Wireframe – Refers to the un-shaded network of points and edges or curves that make up a geometric object.

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Following is a list of current 3d graphics programs (as of March 2007) that are capable of modeling. This is by no means a complete exhaustive list, but these are the main programs used in the entertainment industry. Any program not on this list is more than likely used in the architectural or CAD industries. Use this list merely as a starting point for selecting the program that suites your needs. Also, don’t let the list fool you. For example, 3d Studio Max is capable of all but one of the modeling methods according to the table, but this does not mean it necessarily has the best implementation of those methods. Remember that usability, speed, and price (at least when you’re a poor college student) are just as important as the feature list. All of the programs listed can generate a desired mesh, but how long did it take you and how many hairs did you have to pull out. A beat up ’78 Chevy will get you to work just as a Mercedes will, but which one was the more enjoyable ride? And which one broke down on the way leaving you much frustration. Perhaps that’s a bad analogy but you get the idea.

Clicking on the company name will take you to their website where you can do your own investigating of each program. Prices are listed for the commercial version of the software and educational version if available. Note that in most cases the educational version is identical to the commercial version except that it cannot be used to make money and can only be purchased by student and teachers who can prove their eligibility. Also, several of the programs have multiple versions of the software with slightly different feature sets – hence the price range. Be aware that 98% of the modeling features in all of the software packages can be found in the cheapest version. The really expensive programs are expensive because of high-end dynamics and hair simulation that have almost nothing to do with the modeling feature set.

The programs that do modeling only (no animation) are called stand-alone modelers and are:

Mudbox
Modo
Rhino 3d
Silo 3d
Wings 3d
ZBrush

The remaining programs are full blown modeling, animation, and rendering packages. They are typically more expensive because they simply do a lot more stuff.

My Opinion

My opinion is just that – an opinion. Because I do not have equal experience using all of these programs my opinion will obviously be somewhat biased. Take it for what it’s worth. I should first mention that every software program has its strengths and weaknesses. Considering that this document focuses on polygonal/subdivision surface modeling I will suggest a few programs that I feel have the strongest, most intuitive toolset in this area.

The programs best suited for polygonal/subdivision surface modeling in my opinion are:

Softimage XSI
Modo
Silo 3d
& Wings 3d

These programs have the newest code base of any of the listed programs. That means these programs were “born” most recently and therefore incorporate the latest ideologies in subdivision surface modeling. Of those four, Softimage XSI is the only one capable of both animation and rendering in addition to modeling – which can be useful if you need to test rigging and deformation while modeling. Modo is able to render still frames, but has no animation capabilities. If you want a modeler with a similar feel to Modo, but with animation capabilities, Lightwave 3d (the program that Modo is based off of) would be a good choice. In fact, Lightwave would be a much better value than Modo if you want to do more than model. Silo and Wings are just straight poly/subdivision modelers and are hence cheaper. A good advantage that the first three (listed above) have is the ability to edit directly on the subdivision surface rather than the cage. This makes modeling with subdivision surfaces a lot more fun and productive.

The best advice I can give regarding software is to not limit yourself to just one program. Because each program has different strengths, the more programs you know the more advantage you have. Knowing just one program prevents you from thinking outside of the box. By knowing how one program solves a particular problem you can better harness the power of another program by using it in an unconventional way. Be aware that nearly all modeling packages have a downloadable demo version that you can try out before you buy.

Software Name	Company Name	Street Price/ Educational	Polygons	Subdivision Surfaces	NURBS	Spline Patches	Box Modeler	Displacement Sculpting	Strengths
3d Studio Max	Autodesk	$3,495 / $175.95	Y	Y	Y	Y	Y	N	Lots of plugins available, huge user community.
Animation Master	Hash	$199 / N/A	N	N	N	Y	N	N	Probably the easiest animation program to learn and use. Cheap.
Blender 3d	Blender 3d	Free (open source)	Y	Y	Y	N	Y	Y	A full animation system for free.
Cinema 4d	Maxon	$1,795 / $295	Y	Y	N	N	Y	N	Great renderer, used a lot in broadcast and product design
Lightwave 3d	Newtek	$795 / $195	Y	Y	N	N	Y	N	Great modeler and renderer. Used quite heavily in special effects industry.
Marai	Izware	(discontinued)*	Y	Y	N	N	Y	N	Polygonal modeling
Maya	Autodesk	$1,999 - $6,999 / $289 - $389	Y	Y	Y	N	Y	N	NURBS modeling and particles. Extremely customizable (programmatically)
Modo	Luxology	$895 / $99 - $149	Y	Y	N	Y	Y	N	One of the newest, most intuitive subdivision surface modelers
Mudbox 3d	Skymatter	$650 / $295	Y**	Y**	N	N	N	Y	Most intuitive displacement sculpting software
Rhino 3d	Rhinoceros	$ 895 / $195	N	N	Y	N	N	N	One of the best NURBS modelers
Silo 3d	Nevercenter	$109 / N/A	Y	Y	N	N	Y	Y	A lot of bang for the buck. Like Modo, but cheaper.
Softimage XSI	Avid	$495 - $6,995 / $175 - $295	Y	Y	Y	N	Y	N	Fantastic subdivision surface modeling, animation, and rigging. Geared for character animation.
Wings 3d	Wings 3d	Free (open source)	Y	Y	N	N	Y Only***	N	Solid polygonal modeler for free.
Zbrush	Pixologic	$490 / $330	Y**	Y**	N	N	N	Y	Most full-featured displacement sculpting software. Can paint color textures in 3d as well.

*This program is no longer available for purchase but many of its modeling features live on in Wings 3d which is a free, open source program inspired by Mirai.

** These programs are extremely limited in their ability to edit polygons and subdivision surfaces at the subcomponent level. These programs are meant to push and pull geometry, not create or destroy it.

*** This program is restricted to box modeling only which means that all your meshes must be “water tight” with no border edges. This is somewhat of a limitation as it prohibits the surface modeling technique.

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References