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Re: Locator 3D

• To: mathgroup at smc.vnet.net
• Subject: [mg83626] Re: Locator 3D
• From: "Fred Klingener" <gigabitbucket at gmail.com>
• Date: Sun, 25 Nov 2007 04:36:23 -0500 (EST)
• References: <fi0ndv$5c5$1@smc.vnet.net>
• Reply-to: "Fred Klingener" <gigabitbucket at gmail.com>

<roby.nowak at gmail.com> wrote in message news:fi0ndv$5c5$1 at smc.vnet.net...
> Hi everybody,
>
> is there something like a 3D Locator in Mathematica 6.0 ?
> how could such a thing be realised ?

Other posters have beaten me to suggesting MousePosition and specifying the 
coordinates "Graphics3DBoxIntercepts." This, I think, is the key, but you're 
on your own in figuring out how to apply the information to your 
application. The approach will be different if you have graphics primitives 
or if you have built-up shapes.

I have a background project running in which I'm trying to pick facets from 
a shape generated by RegionPlot3D. I'm running an EventHandler inside a 
Manipulate (an effort than has its own dark, musty corners in which gotchas 
breed and flourish), I'm trying to use MousePosition to get the box 
intercepts, use the intercepts to construct a Pluecker line (which would 
represent the line perpendicular to the display screen through the mouse 
position), disassemble the region into its GraphicsComplex, extract corner 
coordinates for each facet, I think I have to construct Pluecker lines for 
the edges too, then, just by brute force, find the intersected facet (a 
facet for which the moments of all its edge lines about the pick line have 
the same sign.) In the process, I think I'll be able to handle multiple 
intersections, based on the signs of the moments, but that's some way off. 
I wouldn't be able to deal with facets bounded by concave polygons at all, 
but I have no idea whatsoever whether RegionPlot3D generates things like 
that. All triangles would be good.

So far, it's pretty heavy going, having to chop through gotchas at every 
step, and in fact I haven't actually gotten to the point where the real work 
starts. No one is paying me to do it, so it looks like a winter background 
task.

If any of you have something like this running and you're willing to share 
details, I'd love to see how you approach it.

Fred Klingener