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Patch modeling, shown in Figure 5-12, makes the tessellation process simpler because of the matching parameterization, but it can still cause errors in the rendered image Branching In modeling, branching refers to the parts of models that extend, or branch off, from the main surface or a group of surfaces In these cases, the gridlike structure of the topology is broken and the five-point junctions that we saw in 4 are introduced Since a NURBS surface can only contain a quad layout, the NURBS surface must be broken up into individual pieces and arranged to handle the change in the structure While this can amount to a great deal of work, a similar structure in polygons can be created within one mesh by simply executing the Extrude command on a selection of faces Figure 5-12 shows the topology of a NURBS model where the arm branches out from the body FIGURE 5-12 Several individual NURBS surfaces (patches) are arranged to accommodate the topology of the arm branching from the body Notice the areas where there are junctions with five patches meeting (Image courtesy of Shannon Thomas)

>> theta = [0:pi/90:6*pi];

Texture Mapping Across Multiple Surfaces When you re creating very detailed models using NURBS, you will often end up with multiple surfaces While this is not necessarily a bad thing, it can make managing the scene a lot more difficult, especially when it comes to having to apply texture maps across these mismatched surfaces And, while we mentioned having texture coordinates inherent to the model as an advantage of NURBS, it also has limitations, because the UVs cannot be edited separately from the mesh

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Achieving a high level of continuity between two or more curves or surfaces is one of the main challenges in NURBS modeling The level of continuity between surfaces determines whether an obvious change occurs where one surface ends and the adjacent one begins, or whether the transition is smooth and seamless Many times, it takes multiple, individual surfaces to build a model of moderate complexity When these individual patches are supposed to describe a surface that is one smooth piece, care must be taken to make sure the CVs between the patches shape a continuous relationship Several NURBS modeling tools and commands in Maya let you achieve continuity between curves and surfaces: Align Curves, Align Surfaces, Attach Curves, Attach Surfaces, the Stitch tools, the Fillet Curve tool, and all three of the Surface Fillet tools All of these tools will be demonstrated within this and the next chapter

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Maya offers three levels of continuity, called C0, C1, and C2 Figure 5-13 shows examples of two surfaces that meet using the three levels of continuity FIGURE 5-13 Surfaces that match edges with C0 (left), C1 (middle), and C2 (right) continuity

1017 0 05 1 15 2 25 3 t exp( 7t)

of a surface or curve share the exact same place in X, Y, and Z space In other words, the objects touch but the surface connection is not seamless C0 continuity is rarely desirable when modeling, because even the sharpest edges have some degree of smoothness to them in real life

positional continuity, plus the end tangents between the two curves or surfaces match This means that not only are the end points used to calculate the continuity, but the adjacent CVs are used as well This creates a smooth transition between the two objects without leaving a noticeable seam It is best used when two surfaces need to join smoothly, even though the change in surface is abrupt as in an edge or corner An edge with less than C1 continuity will not render a specular highlight (See 18 for more information on specular highlights)

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curvature This means that three control points from the edge inward on each object are used to calculate the continuity The resulting surface will not show any changes where the object surfaces join

As mentioned, several of Maya s modeling tools provide different levels of continuity that result from joining or generating new surfaces:

Loft tool Creates a new surface between two existing surfaces with C0 continuity Fillet tools Create a new surface between two existing surfaces with C1 or C2

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