 | | | Random points on a unit sphere without biasing | Random points on a unit sphere without biasing 2005-06-14 - By Bradley R. Gabe
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It's an interesting exercise. I'm not a mathematician by any stretch, but
here's a little jscript that'll distribute points in a unit sphere by
randomly calculating a quaternion rotation, then transforming 1 unit from
origin. I use a particle cloud to visualize the point distribution.
// SPHERICAL POINT DIST
var radius = 0.5;
var pnts = 1000;
// Create New particle Type
var pTypeColl = CreateParticleType();
pType = pTypeColl(0);
// Create Cloud
var cloud = ActiveSceneRoot.AddParticleCloud();
var cloudPrim = cloud.ActivePrimitive;
cloudPrim.AddParticles(pnts, pType);
particles = cloudPrim.Particles;
// For each particle, set a random distribution
for(var i=0; i<pnts; i++){
// Get XSIMath objects for calculating random rot
var rot = XSIMath.CreateRotation();
var q1 = XSIMath.CreateQuaternion();
var trans = XSIMath.CreateTransform();
var pos = XSIMath.CreateVector3();
var radPos = XSIMath.CreateVector3();
radPos.Set(radius, 0,0);
// Calculate random quaternions
var W = Math.random() * 2 - 1;
var X = Math.random() * 2 - 1;
var Y = Math.random() * 2 - 1;
var Z = Math.random() * 2 - 1;
q1.set(W,X,Y,Z);
// Create a unit transform from quaternion rotation
rot.SetFromQuaternion(q1);
trans.SetRotation(rot);
trans.AddLocalTranslation(radPos);
trans.GetTranslation(pos);
// Set particle to unit transform;
particles(i).position = pos;
}
>Hi All,
>
>This is to the maths geniuses in the room. I want to generate X number
>of points on a unit sphere, but be sure I won't have any biasing
>involved.
>
>My first thought was just to use a couple of random numbers (let's
>assume they don't have any bias) and then use those with a few sin and
>cos function etc to generate the points. Though I have a feeling that
>would give me more points around the poles.
>
>Anyone have some good suggestions?
>
>Cheers,
>
>Alan.
>
>---
>Unsubscribe? Mail Majordomo@(protected) with the following text in body:
>unsubscribe xsi
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<body>
It's an interesting exercise. I'm not a mathematician by any stretch, but
here's a little jscript that'll distribute points in a unit sphere by
randomly calculating a quaternion rotation, then transforming 1 unit from
origin. I use a particle cloud to visualize the point
distribution.<br><br>
// SPHERICAL POINT DIST<br>
<font face="Courier, Courier">var radius = 0.5;<br>
var pnts = 1000;<br><br>
// Create New particle Type<br>
var pTypeColl = CreateParticleType();<br>
pType = pTypeColl(0);<br><br>
// Create Cloud<br>
var cloud = ActiveSceneRoot.AddParticleCloud();<br>
var cloudPrim = cloud.ActivePrimitive;<br>
cloudPrim.AddParticles(pnts, pType);<br>
particles = cloudPrim.Particles;<br><br>
<br>
// For each particle, set a random distribution<br>
for(var i=0; i<pnts; i++){<br>
<x-tab> </x-tab><br>
<x-tab> </x-tab>// Get
XSIMath objects for calculating random rot<br>
<x-tab> </x-tab>var rot =
XSIMath.CreateRotation();<br>
<x-tab> </x-tab>var q1 =
XSIMath.CreateQuaternion();<br>
<x-tab> </x-tab>var trans
= XSIMath.CreateTransform();<br>
<x-tab> </x-tab>var pos =
XSIMath.CreateVector3();<br>
<x-tab> </x-tab>var radPos
= XSIMath.CreateVector3();<br>
<x-tab> </x-tab>radPos.Set
(radius,
0,0);<br>
<x-tab> </x-tab><br>
<x-tab> </x-tab>//
Calculate random quaternions<br>
<x-tab> </x-tab>var W =
Math.random() * 2 - 1;<br>
<x-tab> </x-tab>var X =
Math.random() * 2 - 1;<br>
<x-tab> </x-tab>var Y =
Math.random() * 2 - 1;<br>
<x-tab> </x-tab>var Z =
Math.random() * 2 - 1;<br>
<x-tab> </x-tab>q1.set(W,X,Y,Z);
<br>
<x-tab> </x-tab><br>
<x-tab> </x-tab>// Create
a unit transform from quaternion rotation<br>
<x-tab> </x-tab>rot
.SetFromQuaternion(q1);<br>
<x-tab> </x-tab>trans
.SetRotation(rot);<br>
<x-tab> </x-tab>trans
.AddLocalTranslation(radPos);<br>
<x-tab> </x-tab>trans
.GetTranslation(pos);<br>
<x-tab> </x-tab><br>
<x-tab> </x-tab>// Set
particle to unit transform;<br>
<x-tab> </x-tab>particles(i)
.position
= pos;<br><br>
}<br><br>
<br><br>
</font><blockquote type=cite class=cite cite="">Hi All,<br><br>
This is to the maths geniuses in the room. I want to generate X
number<br>
of points on a unit sphere, but be sure I won't have any biasing<br>
involved.<br><br>
My first thought was just to use a couple of random numbers (let's<br>
assume they don't have any bias) and then use those with a few sin
and<br>
cos function etc to generate the points. Though I have a feeling
that<br>
would give me more points around the poles.<br><br>
Anyone have some good suggestions?<br><br>
Cheers,<br><br>
Alan.<br><br>
---<br>
Unsubscribe? Mail Majordomo@(protected) with the following text in
body:<br>
unsubscribe xsi</blockquote></body>
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