Prev: distance between two points along a curve
Next: Matlab Engine Can't Open.....
From: Luca Turchet on 8 May 2010 12:10
Hi all,
I think I got it.

Please have a look and let me know what do you think:


I define a file gaussian.m:

function [f] = gaussian(x, m, s)

a = 1/sqrt(2*pi*s);
y = (x - m)/s;
f = a*exp(-y.^2/2);


and a file gaussian_der.m:

function [dfdx] = gaussian_der(x, m, s)

a = 1/sqrt(2*pi*s);
y = (x - m)/s;
f = a*exp(-y.^2/2);
dfdx = -y.*f/s;


Then I use the following procedure:


%Point A coordinates
A_x = -15;
A_y = gaussian(A_x, m, s);


m = 0;%mu
s = 2;%sigma


step_increment = 0.01;
X = [A_x:step_increment:15];

distance_integral = sqrt(1 + gaussian_der(X, m, s).^2);


Z = cumtrapz(X,distance_integral)


distance = 10;% wanted distance from A to B

index = find(Z>distance & Z < distance + step_increment)

B_x = X(index)
B_y = gaussian(B_x, m, s)


%PLOT

Y = gaussian(X, m, s);
plot(X,Y)


hold on;
plot(A_x,A_y,'ro');
plot(B_x,B_y,'k*');
hold off;



What do you think? It seems correct to me.

Let me know!


Best regards







"Bruno Luong" <b.luong(a)fogale.findmycountry> wrote in message <hs3lej$6jj$1(a)fred.mathworks.com>...
> Here is the function that computes 1D gaussian pdf and its derivative
>
> function [f dfdx] = gaussian(x, m, s)
>
> a = 1/sqrt(2*pi*s);
> y = (x - m)/s;
> f = a*exp(-y.^2/2);
> dfdx = -y.*f/s;
>
> end
From: Bruno Luong on 8 May 2010 15:08
"Luca Turchet" <tur(a)imi.aau.dk> wrote in message <hs42df$eo0$1(a)fred.mathworks.com>...

> index = find(Z>distance & Z < distance + step_increment)

I think such test is unreliable for many reasons. I let you think why.

Bruno
From: Luca Turchet on 8 May 2010 15:41
Hi Bruno,
to be honest I tried to understand why it is not correct. I only get
to the conclusion that it is as imprecise as the number of points
with which I divide the distance decrease.

What do you suggest? Any proposal?

Thanks

Luca

"Bruno Luong" <b.luong(a)fogale.findmycountry> wrote in message <hs4cqk$b6a$1(a)fred.mathworks.com>...
> "Luca Turchet" <tur(a)imi.aau.dk> wrote in message <hs42df$eo0$1(a)fred.mathworks.com>...
>
> > index = find(Z>distance & Z < distance + step_increment)
>
> I think such test is unreliable for many reasons. I let you think why.
>
> Bruno
From: Roger Stafford on 8 May 2010 15:41
"Luca Turchet" <tur(a)imi.aau.dk> wrote in message <hs42df$eo0$1(a)fred.mathworks.com>...
> Hi all,
> I think I got it.
> .......

I think you should follow John's excellent advice, Luca. It sounds the best to me, since you have a curve y = f(x) with a known formula for its derivative, f'(x). The differential equation you would be solving with 'ode45' is:

dx/ds = 1/sqrt(1+f'(x).^2) .

You integrate with respect to arc length s as your independent variable, starting with x as the x-coordinate of point A at s = 0, and you stop when s has reached the distance you wish to travel along the curve to point B. What could be simpler?

Roger Stafford
From: Bruno Luong on 8 May 2010 16:02
"Luca Turchet" <tur(a)imi.aau.dk> wrote in message <hs4eof$dhe$1(a)fred.mathworks.com>...

> What do you suggest? Any proposal?

Sometime this test would return empty, especially when the function has a large slope.

Bruno
First  |  Prev  |  Next  |  Last
Pages: 1 2 3 4 5
Prev: distance between two points along a curve
Next: Matlab Engine Can't Open.....