Prev: Pdepe, problem by setting the faktor c (from [c,f,s]) as a function of radius
Next: Sample Time & integration
From: ZEESHAN MOHIUDDIN on 18 May 2010 23:53
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
From: Roger Stafford on 19 May 2010 11:09
ZEESHAN MOHIUDDIN <zeeextra(a)yahoo.com> wrote in message <2030930001.184872.1274255660644.JavaMail.root(a)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
From: ZEESHAN MOHIUDDIN on 20 May 2010 18:20
Thanks Roger for the reply

Actually I couldnt able to find a logic so that I can determine the vertices of the triangles generated by the delaunay triangulation mesh. Can you help me to find it?
From: Roger Stafford on 20 May 2010 23:06
ZEESHAN MOHIUDDIN <zeeextra(a)yahoo.com> wrote in message <1354626748.198425.1274408468681.JavaMail.root(a)gallium.mathforum.org>...
> Thanks Roger for the reply
>
> Actually I couldnt able to find a logic so that I can determine the vertices of the triangles generated by the delaunay triangulation mesh. Can you help me to find it?
- - - - - - - - -
In your function call tri=delaunay(w,y), tri is an m x 3 array for m triangles in which each row contains three indices which determine which three of the x,y pairs are a set of triangle vertices. Each of the m rows therefore represents one of the triangles of your triangulaton.

For the k-th triangle, the three vertices would (in my previous notation) therefore be

P1 = [x(tri(k,1)),y(tri(k,1))];
P2 = [x(tri(k,2)),y(tri(k,2))];
P3 = [x(tri(k,3)),y(tri(k,3))];

So then you would draw the corresponding Q1, Q2, Q3 triangle within this triangle. And then onto the k+1-st triangle, ...

Roger Stafford
From: ZEESHAN MOHIUDDIN on 31 May 2010 23:10
Thanks Roger,

Actually I try to run this code:
x = randn(1,12);
y = randn(1,12);
tri = delaunay(x,y);

t=randn(1,1)

for k=1:12
p1=[x(tri(k,1)),y(tri(k,1))]
p2=[x(tri(k,2)),y(tri(k,2))]
p3=[x(tri(k,3)),y(tri(k,3))]

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

end

but it returns the following error :

In an assignment A(I) = B, the number of elements in B and I must be the same.

I think it might be due to the fact that I am trying to save in P1, the array of 2 variables. However what I think is that I have to store the co-ordinates of each vertice of the triangle in some form.

Please guide me to solve this problem.

Once Again, Many Thanks
Zeeshan
 |  Next  |  Last
Pages: 1 2
Prev: Pdepe, problem by setting the faktor c (from [c,f,s]) as a function of radius
Next: Sample Time & integration