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As in free-form triangle meshes (type 4), each patch has an edge ag that tells which edge, if any, it shares with the previous patch An edge ag of 0 begins a new patch, unconnected to any other This must be followed by 12 pairs of coordinates, x1 y1 x2 y2 x12 y12 , which specify the B zier control points that de ne the four boundary curves Figure 422 shows how these control points correspond to the cubic B zier curves C1 , C2 , D1 , and D2 identi ed in Figure 420 on page 251 Color values are then given for the four corners of the patch, in the same order as the control points corresponding to the corners Thus, c1 is the color at coordinates (x1 , y1 ), c2 at (x4 , y4 ), c3 at (x7 , y7 ), and c4 at (x10 , y10 ), as shown in the gure
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Use this side when next f = 1 5 c2 C2 4 3 This side already attached to previous patch Start a new patch when next f = 0 D1 6 8 D2 Use this side when next f = 2 9 10 C1 c4 11 7 c3
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FIGURE 422 Color values and edge ags in Coons patch meshes
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Figure 422 also shows how nonzero values of the edge ag (f = 1, 2, or 3) connect a new patch to one of the edges of the previous patch In this case, some of the previous patch s control points serve implicitly as control points for the new patch as well (see Figure 423), and so are not explicitly repeated in the data stream Table 432 summarizes the required data values for various values of the edge ag
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fB = 1 2 1 c1 5 c2 4 3 When f B = 0, start a new patch 6 8 3 c3 7 2 c1 1 4 c2
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FIGURE 423 Edge connections in a Coons patch mesh
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If the shading dictionary contains a Function entry, the color data for each corner of a patch must be speci ed by a single parametric value t, rather than by n separate color components c1 cn All linear interpolation within the mesh is done using the t values; after interpolation, the results are passed to the function(s) speci ed in the Function entry to determine the color at each point
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TABLE 432 Data values in a Coons patch mesh
EDGE FLAG NEXT SET OF DATA VALUES
x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 c1 c2 c3 c4 New patch; no implicit values
x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 c3 c4 Implicit values: (x1 , y1 ) = (x4 , y4 ) previous (x2 , y2 ) = (x5 , y5 ) previous (x3 , y3 ) = (x6 , y6 ) previous (x4 , y4 ) = (x7 , y7 ) previous c1 = c2 previous c2 = c3 previous
x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 c3 c4 Implicit values: (x1 , y1 ) = (x7 , y7 ) previous (x2 , y2 ) = (x8 , y8 ) previous (x3 , y3 ) = (x9 , y9 ) previous (x4 , y4 ) = (x10 , y10 ) previous c1 = c3 previous c2 = c4 previous
x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 c3 c4 Implicit values: (x1 , y1 ) = (x10 , y10 ) previous (x2 , y2 ) = (x11 , y11 ) previous (x3 , y3 ) = (x12 , y12 ) previous (x4 , y4 ) = (x1 , y1 ) previous c1 = c4 previous c2 = c1 previous
Type 7 Shadings (Tensor-Product Patch Meshes)
Type 7 shadings (tensor-product patch meshes) are identical to type 6, except that they are based on a bicubic tensor-product patch de ned by 16 control points, instead of the 12 control points that de ne a Coons patch The shading