parametric equation...

I have a parametric equation which want to solve it , but maple does not .

problem.mw

best regards

How Do I Display Fast Parametric Surface with Smoo...

Dear MaplePrimes team,

For display a beautiful parametric surface with hole (or pierced surface), unfortunately unlike CAD (computer-aided design) tool, Maple requires a large grid number. Therefore the computing is too long and requires huge RAM only with grid of [500,500] on a modern computer.

Fig. 1: For a complex surface such an aircraft fuselage here, Needs high grid, therefore, the compilation is too long with modern computer (Intel Core i7, 2.4 GHz CPU, 16 GB RAM). If displays supplementary windows holes on fuselage, the software may bug when the RAM is full.

Question 1:

In matter of low cost computation, do you have better solution to create a fast surface with smooth hole from given a parametric surface equation S(x,y) and given any convex/concave-closed parametric curve C(t) that is projected on surface S(x,y)?

Fig. 2: These surfaces are been created in Maple 2016 from given initial parametric surface equation and curve projected on the surface. But requires huge grid, huge RAM, and long time to get smooth hole when free CAD tools are fast and low RAM.

Question 2:

Because I noted that the Maple’s view option renderers smooth edges of any surface. My question is: Is it possible to use the internal structure of display/view used by Maple to apply at free boundaries? I think it will be possible to create many class of view, for examples: cylindrical sector, spherical sector views or more rather to be limited with conventional cubic view. And thus, I think it will be possible to create own smooth hole or multiple-hole on surface and get smooth pierced surface.

I know that almost of technicians/engineers will recommend me to use a CAD tool to create surface with hole. But the objective here is to keep purely a mathematical mind and work with exact equations (analytic equations).

On a free CAD tool, even the complex holes are created very fast only with low RAM. Why not on Maple?

Best.

Guy.

Circle in 3d

by: Maple 15

Parametric equation of a circle in 3d by three points. Draghilev method.

CIRCLE_3_POINTS_geom3d_2.mw

Parametric solution ...

In manual solution is no problem, but i am interest to compute it with any software such maple since i am not familiar, How to find solution in term of parametric equation a(r), b(r), c(r) for r=-5..5 and also visualize this three derivative condition? d(a)=a+b+c, d(b)=a-b+c, d(c)=a-b-c

 > restart:
 > P:=w-10*z-1/5*z^2-1/200*z^3-1/500*z^4-z^5-1/1000*z^6
 (1)
 > solve(P,z)
 (2)
 >
 >
 >

Parametric Plot: 'incorrect fitst argument'...

Hi!!

I am trying to plot the above curve:

restart; with(plots)

> f0 := proc (t) options operator, arrow; t, (-1)*3.9*t*(t-1) end proc;

> IFS := proc (i, x, y) if i = 1 then return (1/2)*y, (1/2)*x end if; if i = 2 then return (1/2)*x, (1/2)*y+1/2 end if; if i = 3 then return (1/2)*x+1/2, (1/2)*y+1/2 end if; if i = 4 then return -(1/2)*y+1, -(1/2)*x+1/2 end if end proc;

> g := proc (t) local j; for j to 4 do if evalf((1/4)*j-1/4) <= evalf(t) and evalf(t) <= evalf((1/4)*j) then return IFS(j, f0(4*t-j+1)); break end if end do end proc;

Thus, the instruction  parametricplot(['g'(t),t=0..1]) return the message

Error, (in plot) incorrect first argument [g(t), t = 0 .. 1]

Some idea or hit to plot this?

How to determine eigenvalues?...

hi.how i can determind  eignvalue of matrix in the form parametric?

thanks1.mw

 (1)

Solve with fsolve...

How I can solve it ? If I want a solution dependent of a. With fsolve? But how?

-x3+ax2-lnx=0

How to plot parametric maximum?...

Suppose I have a function like this: f=cos(2t/m)+cos(2(t+5)/m).

Now for each fixed m, we get the maximum value of f. Then I want to build a plot where x-axis is m and y-axis is f, how could I do that? Please help!

How to animate parametricplot?...

Hi all,

I've got a parametric curve of the form f(x),h(x) x=0..1, and want to make an animation of this curve when changing an exogenous variable h0.

My attempt was to do it like this:

plots[animate](plot, [f(x), h(x), x = 0 .. 1], h0 = 0 .. 1)

but it doesn't work.

Does anyone know if/how this can be done?

Thanks,

Paul

Periodic extention of parametric plot...

Hello,

I would like to build a periodic curve but starting from a parametric curve and not with a function.

Thanks to you tips, I could obtain a periodic function with a piecewise function starting from a function (http://www.mapleprimes.com/questions/208795-Periodic-Piecewise-Function)

I would like to do the same approach but starting from this parametric curve f :

V:=Vector([cos(t),sin(t)]);
f:=unapply(V, t);
plot( [f(t)[1],f(t)[2], t = 0..evalf(Pi)],color=red, scaling=constrained);

And I would like to build a periodic curve (the period is defined on the x axis) g such as :

Unfortunately, the approach presented in the post http://www.mapleprimes.com/questions/208795-Periodic-Piecewise-Function does'nt work anymore.

Do you have ideas to build this periodic curve starting from the parametric curve defined above ?

The aim of my question is more linked to the methodolody than the result.

Sketch plots of two vector-functions...

How I can sketch the helix with parametric equations x=2cost  y=sint  z=t  and the line with parameric equation x=-2t  y=1  z=(pi/2)+t   on a three-dimensional coordinate system?

Showing Oriented Parametric Curve...

Suppose I have the parametric equations of a circle

x=cost

y=sint

where t runs from 0 to 2*pi. How can I show the orientation of this parametric curve on a plot?

How do i plot a curve using a parametric plot...

we have a curve (x^2+y^2)^2=x^2-y^2

parametric representation of the curve is given by

x(t)=cos(t)/1+sin^2(t)

y(t)=sin(t)cos(t)/1+sin^2(t)

and we are asked to plot the curve using a parametric plot for -Pi<t<Pi

Plotting a 3D vector in Maple...

Hi!

For my lecture advanced dynamics, I got the question to make a sketch of the coordinate system and the particle’s motion, with the following position vector:

r(t) = (a cos(ωt))i + (b sin(ωt))j + (ct)k

In this function, ω is in [rad/s], a and b are in [m], t in [s] and c is [m/s].

I have no idea what this should look like, and I was thinking about plotting this with Maple, but thus far I'm not succeeding in plotting it. Which function or method can I use to visualize this in Maple?

Thanks a lot!

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