Message Boards

4466 Views

7 Replies

2 Total Likes

View groups...

Follow this post

Share this post:

GROUPS:

Mathematics Graphics and Visualization Wolfram Language Optimization

Find the contour of a pair of multi-variable functions?

Posted 6 years ago

I have two functions `f[x,y,z,a,b]` and `g[x,y,z,a,b]`, where the variables are restricted to a set of values: `x ? [x0, x1]`, `y ? [y0, y1]`, `z ? [z0, z1]`, `a ? [a0, a1]`, `b ? [b0, b1]`. I can find the minimum and maximum values within the restrictions using Minimize and Maximize. These two functions are the X and Y coordinates of a point, I am using them to show some paths using `ParametricPlot` and to draw graphics using `Graphics`. The thing is, I need to know the boundaries which define the possible locations of the point. How could I find the contour of the area for which the `(X,Y)` plot of these two functions is defined? I have been trying to use `ParametricRegion`, but it takes an awful lot of time to give the results with 2/5 variables. It is kind of strange that using `ParametricPlot` with 2 variables is much faster than `ParametricRegion` with the same 2 variables.

POSTED BY: JOSE OLIVER

7 Replies

Sort By:

Posted 6 years ago

I have tried to do it in two different ways. 1. Using `ParametricRegion`: R = ParametricRegion[{Xt[X2, Th3, La1, La2, La3, La4, La5] /. {X2 -> X2in, La3 -> La3in} /. {Th3 -> Th3in, La4 -> La4in, La5 -> La5in}, Yt[X2, Th3, La1, La2, La3, La4, La5] /. {X2 -> X2in, La3 -> La3in} /. {Th3 -> Th3in, La4 -> La4in, La5 -> La5in}}, {{La1, dA1min, dA1max}, {La2, dA2min, dA2max}}]; And trying to represent it by: Region[R] This is not able to give a result (it is still running after about 10h and 8GB of RAM). 2. Using `ParametricPlot` ParametricPlot[{{Xt[X2, Th3, La1, La2, La3, La4, La5], Yt[X2, Th3, La1, La2, La3, La4, La5]}} /. {X2 -> X2min, Th3 -> Th3min, La3 -> dA3min, La4 -> dA4min, La5 -> dA5min}, {La1, dA1min, dA1max}, {La2, dA2min, dA2max}, AspectRatio -> Automatic] This is able to give a result relatively fast (40s and <2GB of RAM). But unfortunately, `ParametricPlot` can't plot regions depending on more than 2 variables. Just to give some insight into the problem, (`Xt`, `Yt`) give the position of a point from a body in a machine. I need to obtain the 'range of action' of this point. I need to find the contour of the area (or the area itself) in which the point can be located. The problem is that the point depends on 5 (6) variables.

POSTED BY: JOSE OLIVER

Posted 6 years ago

You may choose a finite grid in your 5 or 6-dimensional cuboid, calculate the corresponding points in the plane and visualize it as a cloud of points. This may give some insight into the shape of your region.

POSTED BY: Gianluca Gorni

Posted 6 years ago

It is suggested that you post any code you have already written so your problem can be examined more closely.

POSTED BY: Moderation Team

Posted 6 years ago

I guess the way to go is trying to get a discrete representation as a cloud of points, I was hoping to be able to get a complete region. Going back to the `ParametricPlot` output, what do the different shades of blue mean? EDIT: The dark blue region is the place where different combinations of parameter values give the same (X,Y) combination. Maybe this superposition of points is the reason why `ParametricRegion` is not able to give an output.

POSTED BY: JOSE OLIVER

Posted 6 years ago

I assume it is an overlap.

POSTED BY: Gianluca Gorni

Posted 6 years ago

I have more or less found the solution to this: plotting variables in pairs with the correct choice of maximum and minimum values and overlapping them. The output is: Once checked that this visual representation covers the whole region, it is now possible to identify the curves that define the edges and draw only them.