Stretto

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1 years, 69 days

MaplePrimes Activity


These are questions asked by Stretto

Cl := x->max(-1,min(1, x)):

M := 25:
#-sqrt(1-x^2)..sqrt(1-x^2)
f := (x,y)->Re(sqrt(x+_i*y)):
P1 := plot3d([seq([x, y, k*f(x,y)], k=[-1,1])
], x=-1..1, y=-1..1, labels=[x,y,Rew],style=surface, grid=[200,200], thickness=2, colorscheme=["xyzcoloring", [(x,y,z)->y^2,(x,y,z)->x*y,(x,y,z)->x^2]]):
P2 := seq(spacecurve([seq([Cl(t*cos(2*Pi/M*j)), Cl(t*sin(2*Pi/M*j)), sign(k)*(abs(k) - 1.5)/140 + sign(k)*f(Cl(t*cos(2*Pi/M*j)),Cl(t*sin(2*Pi/M*j))),color=[RGB(1,t^2*sin(2*Pi/M*j)^2,1)]], k=[-2,-1,1,2])], t=0..13, thickness=4, transparency=0.7, numpoints=1500),j=1..M):

display(P1, P2);
display(P2);

 

The above draws a Riemann surface for sqrt(z).

 

The problem is that maple doesn't seem to make grid lines nicely project from the function. I added the lines myself but I cannot color them in a way that uses t. the parameter t is completely ignored in the graphing of the lines.

Also, the first graph cannot have transparency set and give meaningful results.

 

adding transparency=0.001 it looks like it is 10% transparent.... and going below that it just turns off all transparency. I want to barely see through the surface.

 

It's really hard to get a nice graph for maple. The lighting, lines, and coloring are always off to reduce the visual impact.

 

L := proc(N) N; end:
plot([seq(L(min(5, max(-5, 5^(x*10) + 5^(x*k))),k=0..10))], x = 0..3);

 

Warning, expecting only range variable x in expression max(-5,5^(10*x)+5^(x*k)) to be plotted but found name k

 

Removing L and everythign works. I want maple to first compute the inner expression before calling L. But even thenn it shouldn't matter in this case, it is just an identity function.

 

There should be no reason why this can't be done. I experience this *type* of problem with maple a lot. Where it seems to try to compute everything symbolically and breaks in some cases for unknown reasons.

 

In my maple ini I redefine I.

 

local a,b,c,I:

 

Every worksheet I create I always end up with an executed line with just "I". It's just annoying to see it as it service no purpose and takes up space at the start of the worksheet.

 

Of course I is a predefined symbol which is why I want to redefine it, redefine it to be _i, say. I've tried unprotect and unassign and all that and it still prints out.

 

Now I always put a restart at the start of a worksheet so I end up getting two lines of the I, which is a total of 4 because it prints a blank line.

 

 

 

I have hacked together some things so I can use previously computed values without too much hassle


_Last := 0:
# Stores N in a global to be used
Last := proc(N)
    global _Last;
    _Last := N;
    N;
end:

 

_Last := 1:

seq(Last(_Last*4 + k),k=1..10);

 

This is quite hacky but does work. It is not very robust. Is there any better way? [The above is just a trivial example, I know it can be solved as a problem easily, that is not the point. The method can also be used in much more non-trivial scenarios to simplify coding them].

 

 

I was playing with some of the geometry plotting in maple for fun(I rarely use it) and came up with an IFS like system. While I'm sure maple sucks for IFS it is somewhat easy to do. I was just using rectangles though.

Is there any way though to modify a shape using a transform such as a complex map? Not just the vertices but the edges too.

 

Also, is there any way to do a complex map in some easy way? e.g., "paint the geometry on to a texture" and then map it with a complex plot. Usually one just uses a pixel coloring map and maps that, which would be fine for playing around but I'd like to have more control.

 

Basically draw something on a plot(geometry, functions, image, etc), transform them in some interesting way(e.g., complex map) and then IFS them to get interesting visuals.

 

I realize one can do this in maple by turning the edges in to curves and all that mess but I'd like to avoid that since maple is not really good at it anyways(would probably end up very slow).

 

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