Eg 1: Stage 4: Making Regions

Now its time to draw curves to connect between the feature and flow lines. While doing this you have to always keep in mind that the regions will eventually be filled with rectangular patches. Even though its possible to fill in areas with more than four sides, in practice a whole lot of problems can be avoided if limit them to four sides.

Figure 179. Five Sided Region

Figure 179 shows a five sided region on the left that has been filled with a rectangular patch. If you look closely at the sharp point, the patch boundary (in red) overlaps both of the two adjacent patches.

Figure 180. Still Problematic

Even if the boundary curve is rounded (see Figure 180), there's still an overlapping problem at the junction between the three patches.

Figure 181. Solved By Splitting Region

Figure 181 shows the best way to patch out that junction. The five sided region is cut in half to make two four sided regions.

Figure 182. Be Careful With T-Junctions

Figure 182 shows, in a simplistic case, once of the problems you might encounter when using T-junctions. In the network on the left, the adjacent patches at the T-junction on the top aren't matched. That's easy to fix; just add one division point to the lower curve segment.

But then if you look at the resulting network on the right, now the two left patches aren't matched. If you then add a division point at that boundary to make them matched, the lower two patches won't match. If you keep on fixing up the next unmatched boundary in the loop, you'll eventually get back to the first boundary, which will then be unmatched. There is no solution to this puzzle; you will never get all four patches matched.

If you use T-junctions a lot in a network, you increase the chance of one of these cyclic dependencies catching you out. Its possible to waste much time chasing your own tail - I know, I've done it myself.

Figure 183. The Solution

OK, so there is a solution (see Figure 183). By using 1 to N matching you can get all four patches tangent. Notice how there are an even number of division on each boundary; this important hint is explained further in the following "Matching Boundaries" section.

Figure 184. All Regions Marked Out

Figure 184 shows all the regions for the head marked out. There are a small number of T-junctions, but none that are going to cause any sort of problem when it comes time to getting matched boundaries.

Figure 186. Some Regions Filled

Figure 186 shows the network after a handful of patches have been created. You'll see that some patches are matched (purple boundaries) and some aren't (blue boundaries). At this stage there's no need to worry about matching boundaries and tangency. Just work your way around the polymesh, filling in all empty regions with the "place_seed -> space -> check_corners -> space" sequence.

Figure 187. All Regions Filled

Figure 187 shows the network with all regions filled. The density of patches in the face area is just about right, but those down the neck and over the back of the head probably need to be reduced.