Principles of 3d Modeling with Andrew Klein

Week 7 Using NURBS Curves:

Click on the images below for links to Video Tutorials. This series covers creating a Chess piece Bishop using curves to create a NURBS patch model. All images and videos are copyright Andrew Klein.
	In part 1 of this 5 part series, Andrew Klein (www.andrewklein.net) looks at creating NURBS curves, lofting, and using the Hypergraph in Maya.
	In part 2 of this 5 part series, Andrew Klein (www.andrewkleni.net) examines editing control vertices on a NURBS surface, Duplicating a Surface curve from an Isoparm, creating a planar trim shape, Detaching surfaces, and using the Boundary command
	In video 3 of this 5 part series, Andrew Klein (www.andrewklein.net) covers how to create curves with the ARC curve tool, the Pencil Curve tool, and the EP Curve tool. By taking this curve and revolving it, the stem of the bishop is created.
	In part 4 of 5, Andrew Klein (www.andrewklein.net) looks at creating NURBS surface fillet blends, and again covers revolving.
	In the final video of the series, Andrew Klein (www.andrewklein.net) examines how to intersect surfaces and how to use the trim tool to cut out the notch of the bishop's "hat".

MODELING WITH NURBS TUTORIAL: Click on image below:

We will be creating a chess piece using a combination of NURBS and POLYGON opperations:

Lofting- Is the process of creating geometry from one curve to another.

Revolving- Is used to rotate a curve around an axis to create a surface.

Extruding- Is the process of using two curves to create a surface where one curve determines the shape and the other deterimes the length and path.

Boundary- Sets the edges of a NURBS patch with 4 curves. Will only work correctly if all the end points for each curve are snapped to each other.

Planar- Creates a trimed object with an outline in the shape of a closed curve that exists locally on only 2 out of 3 axis.

Fillet Blends- Create surfaces that "jump the gaps" between two existing NURBS surfaces

Boolean Operations- Can be used for Polys and well as NURBS, these operations produce a "either", "both" and "neither" results from intersecting geometry.

Quads versus Triangles, reasons for using an all-quad mesh-

Multisided and Intersecting Polygons from The Guerrilla CG Project on Vimeo.
Lets examine the reasoning behind utilizing an all quad mesh in the construction of our character. It should be noted that there are several reasons for modeling with quads (especially in maya), but that exporting to other applications, especially for the development of video games like the UT editor, will actually require all tris. We will discuss this a little more in a bit. However, even when a software package is requiring an al tri mesh, it is usually best to still create your model in quads, then triangulate when done. This will assure the proper gridflow is in place before hand.

Lets look at Image (a) below. As an all quad surface, when we pull up the center vertex (b), the edges that are drawn in pull up nicely towards the top point, but also there are false edges created by the pull that mimic the effect similar to what we would see if we actually drew in an edge with the split polygon tool as in image (c). This is because at a very basic level, a quad is automatically tesselated by maya based on need to be split as in image (c) OR as in image (d). That "or" is important as we can see becuase based on the needs of the vertex manipulation, we might either need the split in (c) or the split in (d). In this case, as we can see in image (d), the split will give us results that are most likely not desired by altering the falloff from the uppermost vertex toward the lower 8 verticies. This is why it is best to leave the model as an all quad mesh.

Additionally, we should examine the effects of smoothing and subdividing on meshs of different polygon types. In the digram below we can examine how the quad mesh smooths extremely nicely, but a mesh that has been triangulated will give us results for the head, that if we tried to fine tune out model for animation, we would experience odd and improper stretching from each point, since now some verticies are at the intersection of 4 edges, while others sit at the intersection of 7 or 8.

The effect is even more compounded when we convert the low poly model to a subdivisional surface. While our gridflow is behaving nicely for animation in the quad surface with levels 0, 1, and 2 availble for manipulation, the Catmull-Clark Subdivision scheme that maya uses is unable to interpret the architecture properly, and thus we have only level 2 construction detail.