Eg 1: Stage 6: Matching Boundaries

If you want adjacent patches to have positional (C0) or tangential (C1) continuity, then they need to be matched at their boundaries. This means that the knot lines should line up, either 1-to-1, or at least 1-to-N. And you control this matching by adding or removing division points from the boundary curves. And so, the next step in this head surfacing example is to add and remove division points to get matched patches.

Figure 188. Even Number Of Divisions Best

But before we continue, a hint: Figure 188 shows three patches on the left, matched 1-to-2 at their adjacent boundaries, and three patches on the right, matched 1-to-1. As you can see, the patches on the left maintain a consistent density across the page, while those on the right are compacting towards the narrow end.

Sometimes you'll want patches to pack more densely into parts of the polymesh. But at other times you won't, and in those cases you'll have to use 1-to-N matching to maintain continuity while decreasing and increasing the density. And the big hint to remember if you plan to use 1-to-N matching - "Even Divisions are Best".

Figure 188 clearly shows the possible problems if you don't have an even number of divisions. On the left the divisions easily go from 8 to 4 to 2. But on the right there's no way to cut 7 into half, or thirds or any whole divisor (it is a prime number), and so there is no way to drop the density down while maintaining matched boundaries.

Figure 189. Some Patches Matched

Figure 189 shows the matching process about half complete. All patches in the face have been matched, but the ears and the rest of the head needs more work. The patches covering the neck and the top of the head have been lightened (i.e. UV dimensions reduced); there is no need to have dense patches in those areas.

Figure 190. All Patches Matched

Figure 191 shows the network with all patches matched. On closer examination there are a couple of small problem areas around the nostril and top of ear (see Figure 191).

Figure 192. Fixed

The first problem is fixed by adding an extra curve to direct the flow of the patches around the natural curve of the nostril. The ear problem is fixed by playing around a bit with the arrangement of curves in that area to reduce the twisting (see Figure 192).

Figure 193. Half Of The Head Complete

Figure 193 shows the network for one half of the head complete. It is now ready to mirror to the other side.