Re: Moving an outsider to the closest point on the boundary
- To: mathgroup at smc.vnet.net
- Subject: [mg63666] Re: Moving an outsider to the closest point on the boundary
- From: Peter Pein <petsie at dordos.net>
- Date: Mon, 9 Jan 2006 04:49:01 -0500 (EST)
- References: <dogkjg$pui$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Borut Levart schrieb:
> Respected subscribers of comp.soft-sys.math.mathematica,
>
> I have bumped into a problem which I cannot solve.
> I have defined a distance function d(x,y) that says True in the inside
> of the closed geometry of interest and False outside. Initially there
> are some points inside the geometry. My iterating algorithm moves those
> points. Some stay inside while others may drift away over the boundary
> to the outside. I would like to select those outsiders and move them
> back in, however, not in any way: I want to move them back to the
> closest point on the boundary. (This corresponds to the physical
> analogy of my work.)
> Here is an example of a unit circle as defined geometry and two points:
>
> In[1]:=
> d[x_, y_] := x^2 + y^2 = 1
> p1 = {0, 0};
> p2 = {.8, .5};
> dp1 = {-.1, -.1};
> dp2 = {.3, -.3};
>
> In[2]:=
> DensityPlot[
> If[d[x, y], 1, -1],
> {x, -2, 2}, {y, -2, 2},
> PlotPoints -> 100,
> Mesh -> False,
> Epilog -> {
> Hue[0], PointSize[.02],
> Point /@ {p1, p2},
> Hue[.6], Point /@ {p1 + dp1, p2 + dp2}
> }
> ]
>
> After each iteration I would like to correct the set of points by doing
> something like this:
>
> In[3]:=
> If[! d @@ #, bringBack[#, d2 @@ #], #] & /@ {p1 + dp1, p2 + dp2}
>
> Out[3]:=
> {{-0.1, -0.1}, bringBack[{1.1, 0.2}, d2[1.1, 0.2]]}
>
> But, bringBack?
>
> Thank you for your time and suggestions,
> Borut Levart
>
Hello,
I'm sure you found a solution in the meantime, but here are my 2 cent:
In[9]:=
bringBack[{x_, y_}] := ComplexExpand[(#1[Exp[I*Arg[x + I*y]]] & ) /@ {Re, Im}]
In[10]:=
bringBack[p2 + dp2]
d @@ %
Out[10]=
{0.9838699100999074, 0.17888543819998318}
Out[11]=
True
Peter