## Plotting help intersection 3 surfaces...

Given 3 surfaces:

,(the xy base plane) and

To plot these I suggested to use cylindrical coordiates knowing x=r*cos(t) and y=r*sin(t)

However i got problems knowing how to plot this object and dearly ask for help.

plothelp.mw

## making a 3d logplot...

I'd like ot make a 3d graph that is log scaled on at least one of the axis. So far I haven't found a way of doing this that gives a graph that I genuinely like.

The following worksheet shows two ways of making the graph- the first generates the lines on the surface in a very bunched way, the second typesets the tickmarks in a very ugly way.

How can I get a graph with well placed lines and nicely typeset tickmarks?

How do other people make 3d logplots?

 >
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## Erroneous 3D plot outcome....

Hi All.

I keep getting a incorrect plot of: plot3d(2*x/(x^2+y^2), x = -10 .. 10, y = -10 .. 10)

The negative range excursion is not appearing.

I have tried changing the domains and range settings but to no avail.

I have also tried placing brackets around the numerator and denominator but again to no avail. I also repeated the plot of earlier functions, on the same sheet, below the above function and had no problems with them. See the function below as an example of a good graph plot.

I noticed that the program flashes a negative value graph on screen and then only displays a positive result as shown above.

Good plot of: plot3d((-2*x^2+2*y^2)/(x^2+y^2)^2, x = -10 .. 10, y = -10 .. 10)

This example shows both the negative and positive f(x,y) values and surfaces.

Can anyone explain what is going on.

What I may be overlooking.

Is there a flaw in Maple 15?

I can get the correct graph using Microsoft Math which is a much less sophisticated program.

Omicron1

## How to paint 3D plots with a sophisticated colorfu...

I've been tasked with generating "phase plots" which are visualizations of complex functions.

A 2D phase plot is easy to create: Given a complex function F : C -> C colour points (x, y) in R^2 by [ arg(F(x+I*y)), 1, 1, colortype=HSV].   Something like the following seems to do the trick

```p := plot3d(          1,         x=-5..5,         y=-5..5,         scaling=constrained,         color=[ argument(f(x+I*y))/2/Pi, 1, 1, colortype=HSV],         axes=none,         style=patchnogrid,     ):```
```         g := plottools[transform]((x,y,z)->[x,y],p);     plots[display]( g(p) ):```

Now, "colouring each point of R^2" is only possible using some type of bijection onto the Riemann sphere or Pseudosphere.

The pseudosphere is:

```    x := (u,v) -> sech(u)*cos(v);     y := sech(u)*sin(v);     z := u - tanh(u);          return  plot3d(         [x(u,v),y(u,v),z(u,v)],         u=0..3,         v=0..2*Pi,         numpoints=2^10,         lightmodel=none,         color=ColorFunc(u,v) );```

In this case I need  ColorFunc to be:

```ColorFunc := proc(u,v)     x, y := v, exp(u);     ans  := Re( f(x+I*y) );     if ans > 2*Pi then        return [0,0,0,colortype=HSV];     end if;     return [ans/2/Pi,1,1,colortype=HSV]; end proc;```

But it seems that "ColorFunc" cannot be very sophisticated.  Namely, it cannot contain "frems" or even "if" statements because (as far as I can tell) of the order of evaluations.

It seems possible that I can generate a psuedosphere then change colours AFTER by swapping out the COLOR information in a more sophisticated way.  How can I do this?  I really just need to know how to identify and swap out points from a MESH.

## plot3d for a complex function ...

I want to plot the argument for a complex function. The input (x,y) represented in polar coordinates (r,phi) by default puts the cut at -I*Pi. Likewise the argument function:

argument(f(x)) plots the range -Pi..Pi.

However the function f(x)=x^2 could typically be plotted with 2 riemann surfaces on top of each other. When phi becomes 2Pi f(x) becomes 4Pi and only then I want to identify the 0 with 4Pi again since the points are equivalent in the preimage.

On the other hand the function f(x)=sqrt(x) never surpasses its own domain. The values always stay within the argument range of (0,2Pi) (in fact it only goes till Pi, or -Pi/2..Pi/2 in maple) when the preimage is taken to be (0,2Pi). Thus when plotting a preimage value of (x,y) with argument phi and 2Pi+phi they will have the same value since phi=2Pi+phi and I see a step in the plot. This step is actually there since the function has a cut at this point.

This step in the plotting image is also shown for f(x)=x^2 (e.g. at phi=+-Pi/2) but it is not of importance since it just comes from the argument function being constrained to -Pi..Pi.

So is it possible to change this behaviour?

## How to give a specific color in my plot 3d (MAPLE ...

I want to run a specific color red outside and yellow inside on my equation here using MAPLE 8.00:

plot3d([(0.5+cos(5*u))*sin(2*v),(0.5+cos(5*u))*cos(2*v),0.5*(cos(5*u)-0.3*cos(15*u)+0.02*cos(25*v))],u=0..2*Pi,v=0..2*Pi,axes=FRAMED);

is there some one here can help me? thanks...here is the example of color I want Eg:

## Getting a smooth DEplot3d from a stiff system of e...

I've been trying to make a smooth plot of some ODEs. It should show C rapidly increasing at the innitiation, until they get into a quassi steady state,  and then all three variables increase much slower. This should look like a roughly straight line that elbows sharply into a smooth curve.

Any attempt to DEplot3d it i've made either just shows the time before the quassi steady state is reached, so shows the straight line; or smooths that time together with the next period, making the straight line look like a part of the smooth curve.

Model := [diff(B[1](t), t) = k[a1]*C(t)*(R-B[1](t)-B[2](t))-k[d1]*B[1](t), diff(B[2](t), t) = k[a2]*C(t)*(R-B[1](t)-B[2](t))-k[d2]*B[2](t), diff(C(t), t) = (-(k[a1]+k[a2])*C(t)*(R-B[1](t)-B[2](t))+k[d1]*B[1]+k[d2]*B[2](t)+k[m]*((I)(t)-C(t)))/h];
DissMod := subs((I)(t) = 0, Model);
AssMod := subs((I)(t) = C[T], Model);

Pars := [k[a1] = 6*10^(-4), k[d1] = 7*10^(-3), k[a2] = 5*10^(-4), k[d2] = 10^(-2), R = .5, k[m] = 10^(-4), C[T] = 100, h = 10^(-6)]

StateSol := DEplot3d(subs(Pars, AssMod), [B[1](t), B[2](t), C(t)], t = 0 .. 1000, number = 3, B[1] = 0 .. .5, B[2] = 0 .. .5, [[B[1](0) = 0, B[2](0) = 0, C(0) = 0]], scene = [B[1](t), B[2](t), C(t)], maxstep = .1, maxfun = 0, method = l)

## plotting the intersection of two deformed planes...

I have two deformed planes, that i would like to draw with 3dplot, as well as drawing a curve marking their intersection.

the curves are given by the expressions:

C = -(k[d2]*B[2]+I*k[m]+k[d1]*B[1])/((B[1]+B[2]-R)*k[a1]+(B[1]+B[2]-R)*k[a2]-k[m]),

C = k[d1]*B[1]/(k[a1]*(R-B[1]-B[2]))

evaluated at

Pars := [k[a1] = 6*10^(-4), k[d1] = 7*10^(-3), k[a2] = 5*10^(-4), k[d2] = 10^(-2), R = .5, k[m] = 10^(-4), C[T] = 100, h = 10^(-6)]

with the variables B[1],B[2] and C within the bounds [0..0.5],[0..0.5],[0..100].

My method was to try and use solve to find a formula for the intersection curve- but i couldn't get 3dplot to plot it!

## how to change "box ratio", or 3D aspect ratio for ...

in Mathematica, there is the option called BoxRatios

"is an option for Graphics3D that gives the ratios of side lengths for the bounding box of the threedimensional picture."

It is sort-of like aspect ratio, but for 3D. It is set by default so make 3D plot looks "nice". I can't seem to find equivalent Maple option. The closest is the option "s=" for plot3d, but this just turns of/on "constrained scaling" and does not allow one to modify the "BoxRatios"

Let me give an example. Here is 3D plot in Mathematica and the same in Maple. I'd like to get the Maple 3D to look similar to Mathematica 3D in terms of the "aspect ratio". Maple on the z-axis is using the same size as in the x and y axis, and even though this is realistic, it does not make the plot as nice. I want to change this ratio.

T0[x_, y_, m_] :=20/Pi Sum[ (-1)^(n + 1)/n Exp[- (n Pi/10) y] Sin[ (n Pi/10) x], {n,1, m}]
Plot3D[T0[x, y, 70], {x, 0, 10}, {y, 0, 10}, PlotRange -> All,  AxesLabel -> {x, y, z}]

In Maple:

T0:= (x,y,m)-> 20/Pi*sum( (-1)^(n+1)/n*exp(- n*Pi/10*y)*sin(n*Pi/10*x),n=1..m);
plot3d(T0(x,y,50),x=0..10,y=0..10,scaling=unconstrained);

So Maple is using 1:1:1 box ratio. Mathematica default is 1:1:0.4, and I wanted to see if I can change Maple to be the same.

I get same plot in Maple using scaling=unconstrained or scaling=constrained. So this option is not very useful for what I want.

Is there a way to change the "BoxRatios" as defined above in Maple? There must be, right? Do I need to use different package?

## problems with plot3d...

Hi,

i would like to plot a graph in R^3 of a function f(n,t), where n is integer and t is real. For every t i would like to have a sequence of points. Is it possible?

thanks, anna rita

## Maple doesn't recognize 'complexplot3d'...

I'm new here, so I'm not totally sure this is the right place to ask this. I apologize if it isn't, please let me know in that case.

My problem is that Maple won't recognize the built-in command 'complexplot3d'. For example, typing:

complexplot3d(z^2, z = -1-I .. 1+I)

doesn't do anything, and it's displayed again in blue as if it was not a command.

Any kind of help would be extremely helpful, as I have no clue of what's going on. Thanks in advance!

## How to draw a sphere?...

Im trying to draw a shpere but it always saying:

Error, (in plot3d) unexpected option: z = -2 .. 2

this is the equation: x^2+y^2+z^2-4=0

i'm writing this way

plot3d(x^2+y^2+z^2-2^2, x = -2 .. 2, y = -2 .. 2, z = -2 .. 2)

what should I do? this is my first time with this software

best from Brazil,
Nina

## Combining two plots...

Hello,

does anyone know a way to combine two plots in one where one is created with ScatterPlot3D (Package:Statistics) and the other one with plot3D (Package:plots)?

Normally you would write something like this:

but that only works if the plots are from the same package...

## How to plot this in Maple...

Hi,

I am having trouble in plotting the following surface (it is a quite complicated expression, but should be fine).

OwnSurface := [-Re(arctan(exp(I*Pi*(1/4))*(u^2+v^2)^(1/2)))-(1/2)*ln((1+(u^2+v^2)^2)^(1/2)), -arctan(1/((2*(u^2+v^2))^(1/2)-1))+7*Pi*(1/4), (1/8)*ln(u^2+v^2-(2*(u^2+v^2))^(1/2)+1)-(1/8)*ln(u^2+v^2+(2*(u^2+v^2))^(1/2)+1)-(1/4)*arctan(1/((2*(u^2+v^2))^(1/2)+1))+(1/4)*arctan(1/((2*(u^2+v^2))^(1/2)-1))];

plot3d(OwnSurface, u = -.4 .. .4, v = -.4 .. .4, labels = [x1, x2, x3]);

The only thing maple does is plotting a box with a diagonal line. How can I fix this?