T-Splines
T-Splines

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What are T-Splines / What is the T-Splines Maya Plugin?
Why should I buy the T-Splines Maya Plugin Version 1?
Can I try the T-Splines Maya Plugin Learning Edition on my Maya Personal Learning Edition?
How would I use T-Splines in my workflow?
How do T-Splines compare with subdivision surfaces?

Hasn't this been around since the late 90's?
Looks similar to HSubDs/HSplines.
Looks similar to Hash's Animation:Master's Patches/Hooks.
What are T-Splines / What is the T-Splines Maya Plugin?
T-Splines are a new type of modeling surface, similar to and compatible with NURBS and subdivision surfaces. The T-Splines Maya Plugin is the first commercialization of the T-Splines technology, and was created to enhance the workflow of organic NURBS modelers. Because T-Splines are fully compatible with NURBS, you might think of the T-Splines Maya Plugin as an enhancement for your NURBS modeling in Maya.

There are a couple of different ways of thinking about T-Splines.

T-Splines are like Nurbs, with the difference that you can have partial isoparms.

T-Splines are like SubDs, with the difference that you can insert geometry without changing the surface, and certain kinds of n-gons will shade like quads.

The main difference is T-Junctions. A T-Junction is a vertex where on one side, there is an isoparm, and on the other side, there isn't.
T-Junctions

There is no limit to the number of T-Junctions you can have on a face. This allows lines of detail to end elegantly. Also, because of the way T-Junction CVs affect the surface, the surface will always be C2 smooth.
Why should I buy the T-Splines Maya Plugin Version 1?
The T-Splines Maya Plugin Version 1 was built with NURBS modelers in mind. While future versions of the plugin will feature expanded functionality with subdivision surface characteristics, the objective of this plugin is to make modeling organic NURBS objects in Maya easier. If you are an organic NURBS modeler, we promise significant enhancements to your current set of tools.

T-Splines offers the biggest time savings to NURBS artists who
  • create organic models with high detail in some areas and low detail in others
  • could benefit by having seamless models instead of models comprised of multiple NURBS patches
  • animate NURBS models

Can I try the T-Splines Maya Plugin Learning Edition on my Maya Personal Learning Edition?
No, unfortunately, there is no plugin architecture for the Maya Personal Learning Edition, so our plugin cannot run on Maya’s Personal Learning Edition.
How would I use T-Splines in my workflow?
The T-Splines Maya Plugin Version 1 was designed to accommodate two basic workflows: using T-Splines to create a new model and converting existing models to T-Splines for simplification.

1. Using T-Splines when creating a new model.
There are a number of ways to take advantage of T-Splines when creating a new model. Since the main advantage of T-Splines is in editing and detail work, many artists create the general shape of their model with polygons, then convert to T-Splines to add detail and make changes. It is also possible to begin modeling directly in T-Spline primitives, which are actually hijacked Maya NURBS primitives.
  
2. Using T-Splines to simplify and merge existing models
As 3d models become more and more realistic, every industry is demanding more high-detailed models. Achieving this level of detail in NURBS or polygons can result in heavy models that are unwieldy to edit and expensive to render. By converting existing NURBS and polygon models to T-Splines, you can subsequently cleanse the model of unneeded data and merge multiple-patch NURBS models into a single surface. This results in a T-Spline model that is easy to animate and edit, and accomodates areas of high detail while leaving less detailed areas of the surface uncluttered with control points.
How do T-Splines compare with subdivision surfaces? 
T-Splines are quite similar to SubD surfaces.  Specifically, T-Splines are a superset of Catmull-Clark SubDs.  You can convert any SubD into a T-Spline, with the same resulting surface, the same topology, and the same verts in the same locations.  The main difference between SubDs and T-Splines is the issue of n-gons.  With a T-Spline, you can have lines in your model terminate in a T-Junction.  The T-Junction continues the influence of that point two faces over, as if the line continued, which avoids the weird deformation and shading artifacts.  You don't need to worry about adding complete edge loops, or ending off the edge loops by combining the lines together - you can just end them.  Another big difference is that you can insert geometry in T-Splines without changing the current surface.
Hasn't this been around since the late 90's?
No, it was first published in Siggraph 2003. Perhaps you’re thinking of Hierarchical Splines (HSubDs and HSplines), or perhaps Hash’s Animation:Master Patches. Read below for the differences from those surface types.
Looks similar to HSubDs/HSplines.
The main difference between T-Splines and HSplines is really the differences between T-Junctions and a hierarchy. While a hierarchy can be desirable, it can also be a pain - depends on what you're modeling or animating. With T-Splines, we don't force a hierarchy on the user. Not that there's anything stopping us from making hierarchical T-Splines - we just don't think there's enough demand to justify the more complicated implementation.

With Hierarchical Splines and SubDs, there are UI issues of how to let the user change which level of the hierarchy they're currently editing, and the fact that moving the same CV changes the surface differently depending on the current level of the hierarchy. A hierarchy can also be slower to display and render, although there are ways around that. Finally, in most HSpline implementations, you can only split faces evenly into four smaller faces. With T-Splines, you can split a single edge and just get 1 new CV instead of 5, and you can split at whatever percentage you'd like. That also means that you can make surfaces with T-Splines that would be difficult to equally represent with HSplines. A good example of this is dynamic, terminating creases.
Looks similar to Hash's Animation:Master's Patches/Hooks.
The main differences between A:M’s surfaces and T-Spline surfaces are compatibility and continuity. It’s possible to exactly convert back and forth between T-Splines, Nurbs, and SubDs (see above). Hash's patches on the other hand are a special purpose surface that is optimized for realtime editing and animation on low-end hardware. They aren’t compatible with B-Splines, meaning that an exact conversion to or from Nurbs or Catmull-Clark SubDs is impossible.

In terms of continuity, A:M’s hooks only maintain tangency, while T-Junctions maintain tangency and curvature. In other words, A:M’s surfaces are C1, while T-Splines are C2 everywhere.

You can also have T-Splines of higher degree, where the surface is be C(degree-1) everywhere, just like Nurbs.

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