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Often, a NURBS model must be converted into a polygonal model so that it can be exported to another rendering application Another reason for converting a NURBS model into polygons might be to have control over the UV (texture) coordinates in the UV Texture Editor (discussed further in 18) When it comes to NURBS models that are created out of multiple patches, such as our car, it may be desirable to convert the NURBS patches into polygons and then merge the resulting polygons into one complete surface This is particularly the case when the model will be deformed during animation Deforming a multipatch model can cause the seams between the surfaces to become visible during the animations Combining these surfaces into one surface keeps this from being a problem You can quickly generate a polygonal approximation of a multipatch NURBS model by choosing certain settings in the NURBS to Polygons Options window Let s take, for example, the hood of the car This model was made up of six different NURBS patches Choose Modify | Convert | NURBS to Polygons r to open the Options window for this command The options are shown in Figure 7-3

We can use MATLAB to generate tables of values for the Beta function If m = 1, we find that the first ten values of beta(1, n) are:

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If the Attach Multiple Output Meshes check box is enabled, Maya combines all of the selected NURBS surfaces into one mesh The overlapping vertices along the edges of the original patches will be merged as long as they fall within a distance of the value set in the Merge Tolerance attribute The Type attribute should be set to Quads so that the resulting tessellated faces will be converted to four-sided faces wherever possible Setting the Tessellation Method to General lets you have precise control over how many faces are created from each NURBS patch, based on the conditions specified in the Initial Tessellation Controls section of this window If the U Type and V Type attributes are set to Per Span # of Iso Params, you can specify how many polygonal faces will be created for each span in the U and V directions This illustration shows the NURBS model at the bottom and the converted polygonal mesh above it While this method of conversion is fast, the resulting polygonal mesh does not offer the flexibility that we need to finish our model

Because we want to be able to add surface details to the car and then subdivide it for rendering, converting the mesh using the General method is not going to work for us, as the poly approximation is already based on a smooth, interpolated mesh Instead we need to convert the NURBS patches into polygonal surfaces at their control vertices When a surface is converted this way and then subdivided, the result will match the original NURBS surface This means that there is going to be some work involved For one, all of the surfaces must be combined and the vertices merged manually since the Attach Multiple Output Meshes option is not available for the Control Vertices conversion method Another problem is that all of the edges that are created from a tangent row of CVs in the NURBS surfaces must be removed between all surfaces that were merged Since the purpose of these vertices was to control the direction of the surfaces outer edges, they are no longer needed now that they are in the middle of a continuous surface Leaving them will result in the subdivided model flattening out where that geometry is Let s work on the front of the car

>> x = (1:1:10)'; y = beta(1,x); A = [x y] A = 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 10000 05000 03333 02500 02000 01667 01429 01250 01111 01000

In this section, we will convert some of the NURBS patches in our car to polygons at the control vertices These surfaces will be combined, merged, and cleaned up to produce a geometry that will work as a subdivision surface model

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