#### 5.9 3d plots with patch (10.5.00)

I am plotting a function where I need an `100x100`

grid for the 3D plot to look reasonable.
My problem is that I would like the see the plot with PATCH.

When I plot it with PATCH the patching is so dense that the ZHUE cannot be seen as the
plt is very black. Is it possible to plot every second or 3rd PATCH line? Or is there
another method to getting a lower PATCH grid compared the to plot grid? (I
realize why maple may not want to do that as the line of te patch may cut the
surface.)

My suggestion would be to combine (using display) a plot using patchnogrid and plots of
grid lines. It would be simplest to do the latter using spacecurve, but if you want, you can
extract them from the plot structure, e.g. as follows:

p1:= plot3d(f(x,y), x=a..b, y=c..d, grid=[100,100], style=patchnogrid):
A:= op([1,3],p1): # this should be the hfarray of z values
dx:= (b-a)/99: dy:= (d-c)/99:
lines:= seq([seq([a+(i-1)*dx, c+3*(j-1)*dy, A[i,3*j-2]], i=1..100)],
j=1..34),
seq([seq([a+3*(i-1)*dx, c+(j-1)*dy, A[3*i-2,j]], j=1..100)],
i=1..34):
plots[display]({p1, PLOT3D(CURVES(lines),COLOR(RGB,0,0,0))});

If I understand correctly, you can get round the problem by combining two plots, as
in:

p1:=plot3d((x*y)+2*x+3+y,x=-1..2,y=-2..1,grid=[100,100]):
display(p1);

this is all black

p2:=plot3d((x*y)+2*x+3+y,x=-1..2,y=-2..1,grid=[100,100],style=PATCHNOGRID):
display(p2);
p3:=plot3d((x*y)+2*x+3+y,x=-1..2,y=-2..1,grid=[10,10],style=WIREFRAME,colour=BLACK):
display(p3);
display({p2,p3});

this seems OK

As far as I know there is no possibility to omit selected grid lines. However, you may omit all
grid lines by choosing patchnogrid from the style menu (or by including the option
style=patchnogrid into the plot3d-statement).

To improve the impression you may include contour lines that may be seen under
style-patch and contour. Here you can either choose the number of contour lines
or you may specify a list of function values, for which you wish to see contour
lines.

An example of a summit and two saddles:

f:=16-2*x^2-4*y^2+x^2*y;
plot3d(f,x=-5..5,y=-4..4,view=-16..16,grid=[50,50],shading=ZHUE,
style=patchnogrid);
plot3d(f,x=-5..5,y=-4..4,view=-16..16,grid=[50,50],shading=ZHUE,
style=patchcontour,contours=6);
plot3d(f,x=-5..5,y=-4..4,view=-16..16,grid=[50,50],shading=ZHUE,
style=patchcontour,contours=[-2,0,2]);