The most common method of creating patterns on a membrane involves drawing geodesic lines on the membrane. Justification of the layout of the geodesic lines is beyond the scope of this text .
Although the geodesic lines can be drawn freely to form patterns of any shape and position, it is common that the route of the geodesic lines follow some models determined:
how to draw these roughly parallel geodesic lines is something that every user usually does in a particular way depending on different objectives I need repeat the same exercise with a geodesic line located on the Plot3D of f, like generatrix line.
For example, let the function
Plot3D[x + y - x y, {x, -5, 5}, {y, -5, 5}, PlotTheme -> "Scientific"]
Can I draw their lines of geodesic as shown below
A method of multi-geodesic uses end points of the new geodesic lines found at the edge of the membrane. If we are with a membrane formed by different parts, we can not perform the function of multi-geodesic directly.
What we must do is break down the membrane in two simple membranes and find the pattern in each. I would like to create images based on above method as shown below:
Is this possible in Mathematica?
I do not know how this can be implemented. Please Help.