Surface of graph
Author
Hi,
I need to solve one problem.
I have for eg. fx(x, y)=sin(x+y) defined
on x=<-pi, pi>, y=<-pi, pi> and I need to
compute surface of it.
Anyone can help me???
Dave007
dave007@volny.cz
You'll need to integrate S(sin(x+y)dx) interval [-pi,pi]
The algorithm is something like this:
2i
I = 1/2(Ii+(b-a)/(2e(i-1))* E( f(a+j*(b-a)/2ej)) i=1(1)infinite
(i+1) i=1(2)
a=lower frontier
b=upper frontier
I=Iteration
j,i current iteration
E...sum
f...function
f(x)...value of f(x)
Numerical integration is not an easy thing to do.
Maybe you get it to work.
Edited by - cruz on October 17, 2000 5:15:56 PM
The algorithm is something like this:
2i
I = 1/2(Ii+(b-a)/(2e(i-1))* E( f(a+j*(b-a)/2ej)) i=1(1)infinite
(i+1) i=1(2)
a=lower frontier
b=upper frontier
I=Iteration
j,i current iteration
E...sum
f...function
f(x)...value of f(x)
Numerical integration is not an easy thing to do.
Maybe you get it to work.
Edited by - cruz on October 17, 2000 5:15:56 PM
In one word: Integrate
This is the only function I can find at the moment:
This is the only function I can find at the moment:
- y = sin(ax + b)
y''= a cos(ax + b)
Author
I know I need to integrate, but
if I''m integrating f(x, y) only over
x....I don''t think it''s right.
Because what can I do when I have
x defined on [-pi, pi] and y on [-2pi, pi]??
so what''s now???
Dave007
[mail]dave007@volny.cz[/mail]
if I''m integrating f(x, y) only over
x....I don''t think it''s right.
Because what can I do when I have
x defined on [-pi, pi] and y on [-2pi, pi]??
so what''s now???
Dave007
[mail]dave007@volny.cz[/mail]
Since you''re going to integrate quantitatively, not analytically, anyway, why don''t you do a nested
loop of two integrations?
Something like this:
S_outer=0
Loop y from -pi to pi with step 0.001 ;or whatever
S_inner=0
Loop x from -pi to pi with step 0.001
S_inner=S_inner+my_cool_func(x,y)
End inner loop
S_outer=S_outer+S_inner
End outer loop
loop of two integrations?
Something like this:
S_outer=0
Loop y from -pi to pi with step 0.001 ;or whatever
S_inner=0
Loop x from -pi to pi with step 0.001
S_inner=S_inner+my_cool_func(x,y)
End inner loop
S_outer=S_outer+S_inner
End outer loop
Oops, almost forgotten:
I''m not sure what you mean by
''I want to compute surface'',
but if it''s the area that you want to
compute, then, in the previous one, function
my_cool_func(x,y)
should actually calculate the area of a square
patch on the surface with dimensions like:
upper left: [x,y,fx(x,y)], where fx(x,y) is your original function
lower right: [x1,y1,fx(x1,y1)], where
x1=x+step (0.001 in our case)
y1=y+step
assuming the patch is small enough to be flat.
I''m not sure what you mean by
''I want to compute surface'',
but if it''s the area that you want to
compute, then, in the previous one, function
my_cool_func(x,y)
should actually calculate the area of a square
patch on the surface with dimensions like:
upper left: [x,y,fx(x,y)], where fx(x,y) is your original function
lower right: [x1,y1,fx(x1,y1)], where
x1=x+step (0.001 in our case)
y1=y+step
assuming the patch is small enough to be flat.
This topic is closed to new replies.
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