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From: Walter Roberson on 1 Jun 2010 08:42
ZEESHAN MOHIUDDIN wrote:

> 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))]

Those are lower-case P's, and the assignments are perfectly valid


> P0 = (P1 +P2+P3(k))/3;

Those are upper-case P's and that's a vector-valued expression.

> Q1 = t*P1(k)+(1-t)*P0;

Is there a reason that Q1 is not indexed?

> Q2(k) = t*P2(k)+(1-t)*P0;

There, Q2 is indexed and so must be a single value, but P0 is a vector
and so the result is a vector.

> 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.
From: ZEESHAN MOHIUDDIN on 2 Jun 2010 01:12
Thanks Walter for correcting me and showing the errors.
I now change my methodology for getting the co ordinates of the triangle generated by delaunay. I wrote program something like this :

x = randn(1,12);
y = randn(1,12);
tri = delaunay(x,y);

for i=1:length(tri)
for j=1:3
X(i,j)=x(tri(i,j));
Y(i,j)=y(tri(i,j));
end
end

it gives me two different matrices of x and y co ordinates of each triangle of delaunay. Now I want to apply the methodology proposed by Roger. Can you help me to write this.

His methodology is as follows:

" 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;

many Thanks,
Zeeshan
From: Roger Stafford on 2 Jun 2010 15:10
ZEESHAN MOHIUDDIN <zeeextra(a)yahoo.com> wrote in message <430339163.264618.1275469964116.JavaMail.root(a)gallium.mathforum.org>...
>
> for i=1:length(tri)
> for j=1:3
> X(i,j)=x(tri(i,j));
> Y(i,j)=y(tri(i,j));
> end
> end
>
> it gives me two different matrices of x and y co ordinates of each triangle of delaunay. Now I want to apply the methodology proposed by Roger. Can you help me to write this.
>
> His methodology is as follows:
>
> " 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;
>
> many Thanks,
> Zeeshan

Starting with your X and Y arrays above, it could go like this:

t = rand; % <-- Or however you want to make a random no. between 0 and 1
P0 = [sum(X,2),sum(Y,2)]/3;
Q1 = t*[X(:,1),Y(:,1)]+(1-t)*P0;
Q2 = t*[X(:,2),Y(:,2)]+(1-t)*P0;
Q3 = t*[X(:,3),Y(:,3)]+(1-t)*P0;

Each row of the arrays Q1, Q2, and Q3 has the x, y coordinates in their two columns for the three vertices, respectively, of the corresponding inner triangle. You can therefore use these directly to draw those triangles.

By the way, earlier you used randn to generate random t's. That doesn't work because the output of randn is not restricted to lie between 0 and 1. You could get wild triangles that no longer lie inside the delaunay triangles.

Roger Stafford
From: ZEESHAN MOHIUDDIN on 2 Jun 2010 19:19
Thank you so much Roger and Walter for your help. I really aprreciate help from both of you especially Roger.
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