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Subject: Re: Inscribed triangle in delaunay trianglation mesh
Date: Wed, 19 May 2010 15:09:04 +0000 (UTC)
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ZEESHAN MOHIUDDIN <zeeextra@yahoo.com> wrote in message <2030930001.184872.1274255660644.JavaMail.root@gallium.mathforum.org>...
> Dear All
> 
> I need your help in MATLAB for constructing a shape. 
> 
> First I need to draw the set of triangular mesh . Inside the each triangle of the mesh, I need to draw an inscribed triangle. The boundary of the inscribed triangle is placed at certain distance with that of the triangluar mesh triangle.
> 
> I used the following program to create the triangular mesh :
> 
> x=rand(1,12);
> y=rand(1,12);
> tri=delaunay(x,y);
> trimesh(tri,x,y)
> 
> Now I would like to generate an inscribed triangle in this mesh in such a way that the distance between the inscribed and mesh triangle lies between 0-1 ( using normal or lognormal distribution). Can you please provide some help in this matter.
> 
> BR

  If the vertices of a triangle are three-element vectors P1, P2, P3, then with t a number between 0 and 1 do this:

 P0 = (P1+P2+P3)/3;
 Q1 = t*P1+(1-t)*P0;
 Q2 = t*P2+(1-t)*P0;
 Q3 = t*P3+(1-t)*P0;

These give the vertices of a triangle within the above triangle and sides parallel to its sides.  Choose t according the desired relative spacing. With t = 1, the triangles coincide.  With t = 0 the second triangle shrinks to a point.  You want it spaced somewhere in between randomly, so let t be a random number according to whatever distribution you wish.

Roger Stafford