all these plots of you guys completely obscure what the surface really is.
The grid lines are projections of a rectangular grid on to the surface and have nothing to do with the intrinsic topology of the surface.
The surfaces are not in opposition as your colors suggest, you colored it to suggest they are. You can color the surface how you please but most will be meaningless mathematically.
None of these posts address my original question about color the grid lines properly and dealing with transparency. They are all just different ways to plot the complex function sqrt(z).
The Riemann surface sqrt(z) is a surface generated by sqrt(z), or sqrt(abs(z))*exp(i*ang(z)/2)
That is, it is a surface that involves a "rotation" of the sqrt(x) in complex space. Hence the reason I drew the gridlines the way they were.
All those grid lines are sqrt(z) functions You can see the obvious parabola, the inverse of sqrt, but every other one also is a "parabola", but they are also related to other functions such as cubics, quartics, etc. (the surface can also be seen to be generated by a parabola)
In the image the "grid lines" are all the same color(the purple/magenta) and I do not want that. I want to color them based on their position and values.
The coloring is somewhat arbitrary here but ultimately I was tryign to color it based on a feature of the curve, rather than "opposition" of the two surfaces. That is, we have color to show another dimension, no need to waste it. Since this is the real part it is nice to use the color to show the imaginary value or the magnitude, or whatever. It's not just about displaying a surface but packing in as much relevant information as possible in a nice way.
1. I do not want the same color for all the lines. I want the colors to depend on the surface in some way(but contrasting to the surface color enough, such as having them darker).
2. It would be nice if there was some type of visual depth cue... that is, more distant point are darker and thinnner.
Mable really fails at doing this stuff ;/ I feel like I'm going to have to switch to a program that really excells at graphing both visually and speed wise. (I do use some programming libraries in programming languages but they tend to be more work to do simple plots. I like maple for it's general feature set but plotting quality and interaction and performance are a major drawback for me ;/)
I use matlab sometimes but I just like maples symbolic side... but any time I get beyond simple plotting I really get discouraged from using it ;/ Is there any way to speed it up and to make the plots better? I could potentially write an external library if I have to if it would not be a huge amount of work and could be done.
mayavi seems to be the absolute best I've seen as far as speed and quality(well, not best but good)
What would be cool is if I could use maple and somehow interface with some library like this(well, what would be better is if maple itself was faster and prettier).