Next, let's consider smoothness of local flow.
That is, each "flat tile" assumes ...
Shown below is an example of the condition.
Suppose that the gradient of the preceding flat tile is x1x2 and the current flat tile is on the downward side as shown on the right. Then, with each of the three gradient values, we could associate a slant tile over the current flat tile as shown on the left.
In the case of x1x2, the "blue" and "white" slant tiles are connected smoothly. In the case of x2x3, the slant tiles are also connected smoothly. But in the case of x1x3, the slant tiles are not connected smoothly. The smoothness condition means that the current flat tile assumes one of the first two values.