Sorry for having to ask such a basic question, but what's the basic differences between these three types of modeling?  I was having a discussion on it and ended up more confused as it progressed.    The types are box, polygon, and spline (also which is subdivision modeling a part of).

Box modeling is where you start with a shape that is closed on all sides (such as a cube, thus the name "box") and extend the faces. This method is often touted as being good for making non-organic things like buildings, that have naturally sharp edges.

Polygon modeling is kind of the same thing, but focuses on models where the edges are not all connected. This is more like starting with a flat sheet of paper instead of a cube and going from there.

Spline modeling is... well, first of all, a spline is a kind of curved line, that's defined by control points. You can make very elegant curves with a limited amount of input. These lines can be extended out into surfaces. Splines were invented originally to help model cars in the computer, as the french curve was breathing its last, gasping breath. Many people like to work with non-uniform rational B-splines (most people just say NURBS, I'm kind of a geek and love my tech-speak).

There are many combinations of these kinds of modeling, though, and they're just general terms. For example, I just learned in Carrara how to make a spline, match it with a separate polygon, and make an extruded curved box. Kind of a combo of all three modes.

Also, before someone tells you otherwise, there is no "best" way. What you really want to do is work with a modeler and learn how it works, without worrying too much about one style of modeling over another. As with all things, modelers and modeling methods have their rabid, die-hard fans who won't hear a word against their particular toys.

Okay thanks CaptainJack.  Some people were talking about the various ways of modeling but it wasn't getting through my head for some reason.  That clears things up for me a little more.

You will find that some tasks are suited to one particular method more than the others, but when you do a variety of modeling tasks, you realize that no single strict method is good for all tasks. 

Tasks like modeling tube shapes, e.g a neon sign or a pipe, naturally lend themselves to "spline" modeling (extruding a shape along a spline path).; mimicking the behavior of a machinist's lathe (typically called "lathe" in modelers); or taking a floorplan drawing made of splines and "lofting" walls from those splines.  All are fairly easy with different applications of spline modeling.

Tasks like modeling a box (duh) are well suited to box modeling; any task where you need a shape that has volume and is "watertight"; also there are many applications with strictly 2-d surfaces where you extrude the edges, e.g. in character or clothing modeling.  Good applications for box/extrusion modeling.

Tasks where you need exact control of the overall structure of a model are well suited to poly-by-poly modeling, e.g. when you're modeling a character's face and you absolutely must define specific loops of polygons for the eye and mouth; when you're using polygon snapping to start a clothing model that will match the shape of a specific character; or you need to model a specific flat polygonal structure like the sail of a boat.  These are good tasks for poly-by-poly modeling.

However as your models get more complex and detailed, you find that you need to use a variety of different techniques, and strictly constraining yourself  to just one method makes the job much harder.

spline patch (where you define a surface with a number of curves ) is very useful for modelling stuff like car bodies.   Some people find it easier to start with a shape and pull it into place while others prefer to build the final shape directly.   Its largly a matter of personal preferance  although some depends on exactly what you are trying to build.

Whatever works for you and gets the model built without a lot of nasty geometry is the right way. At the end of the day you cant really tell if an obj file was built via box, polygon, spline or any other method , though you may see hints .

Quote - Sorry for having to ask such a basic question, but what's the basic differences between these three types of modeling?  I was having a discussion on it and ended up more confused as it progressed.    The types are box, polygon, and spline (also which is subdivision modeling a part of).

A lot of the confusion comes from people not knowing what their modeling method is called.  And then some modeling methods can over lap each other in some areas also.  Then there is the situation where a model is an organic or mechanic shape.  And whether it will be animated by bending or by axis/gear rotation.  And then there are the dynamics surrounding the model such as hair and cloth and spilt water.  And don't forget, the model still has to be textured some how.  Either by procedural texturing or by UV mapped image texturing.  And will the model be made up of all one piece or made up of groups of smaller pieces.  Each piece might use a different modeling method.

Just make sure your software can model the way you're planning on modeling.  Otherwise, modeling becomes harder than necessary.

Also note that box modeling and polygon modeling both fall under subdivision modeling. Since either method tends to be followed by Catmull-Clark subdivision. And with a few exceptions with some software that can create edges with variable hardness or use the Doo-Sabin method, the smoothing alogrithm works the same. So as a modeler, regardless of modeling program, you're going to want to understand how edge placement and edge flow works in relation to the subdivision process.

To say that one is better suited to organic and one is suited to mechanical is a bit wrong. The real difference is where the focus is in the approach to modeling. Box modeling has a focus on defining volume. Polygon (face-based) modeling has a focus on directly defining the surface. Once sufficient topography or mass of a model is defined, then the differences between the two subsets of subdiv modeling really blurs since the tools past the beginning work pretty much the same. (Moving a vertex, edge, or face, is moving a vertex, edge ,or face indifferent to how it got there.) A good modeler (in the artist sense of the word) can make organic or mechanical models, it's more about practice and the understanding of the topology behavior than anything to do with the software's starting approach.

NURBS is a whole other can o' worms, but it's already been explained better than I could. And the B in B-splines part is Bezier. A.k.a. the mathematician that is the French-curve guy.

pauljs75 - You've made an excellent comparison of  the approaches of both poly and box modeling, but I think your choice of words was errant in suggesting that both methods "tends to be followed" by subdivion of any sort.

While subdivision may be the route a modeler chooses to go, there's plenty of cases where neither method receives any subdivision [ low-poly / game-art for example ], and both methods can be used to make a quality finished mesh without any further subdivision.

I do agree, once you get past the initial phase of laying in the geometry, the workflow for both methods tends to blur a good deal.

Generaly I agree with you, I just don't want see anyone drawing the conclusion from what you've said that subdivision modeling is the best or only next-step for either modeling approach.

Non-subdivision modeling [that' isn't hacked together using boolean operations :rolleyes:], is becoming a lost art of sorts, for high poly work anyway. :unsure:

Winterclaw: Don't forget modelling with Particles - they can either have a surface mesh applied or each particle can be rendered which allows for models to have true volume (with appropriate software).