Given an equation, i have to graph it in 3D and it should look like a water ripple

hi. i need help urgently. i was given an equation: z(x,y)=(amp*cos(sqrt((x^2+y^2)*const1))/exp((x^2+y^2)*const2)) amp is the amplitude which is 200 and x and y range from 0 to 100 const1 and const2 can be any number I am required to surf plot this equation so that it can look like a water ripple.

Please help me

Answer 1

[Paulo Silva]

amp=200;
[x,y]=meshgrid(0:100,0:100);
const1=1;
const2=0.001;
z=(amp*cos(sqrt((x.^2+y.^2)*const1))./exp((x.^2+y.^2)*const2)); 
surf(x,y,z)

[12ar.af]

hi..thnx...i tried the code but the graph is no way near the solution which is a water ripple....please help

[Paulo Silva]

You can see the ripples by rotating the graph, tweak the values of const1 and const2 for better results.

[12ar.af]

the ripples have to be circular..i am sorry..i am very bad at this stuff and need the answer today.please could you help me

[Paulo Silva]

amp=200;

[x,y]=meshgrid(-100:100,-100:100);

const1=1;

const2=0.001;

z=(amp*cos(sqrt((x.^2+y.^2)*const1))./exp((x.^2+y.^2)*const2));

surf(x,y,z)

[12ar.af]

thank you very much....i appreciate it

[12ar.af]

i got one more question....how can you make the graph look more smoother ?

[Paulo Silva]

make more points inside the mesh, example

amp=2;

[x,y]=meshgrid(-50:0.6:50,-50:0.6:50); %notice the new limits and step 0.6

%smaller steps give smother waves but use more memory and takes more time

const1=1;

const2=0.001;

z=(amp*cos(sqrt((x.^2+y.^2)*const1))./exp((x.^2+y.^2)*const2));

surf(x,y,z)

colormap(winter) %looks more natural with this colormpa

[Paulo Silva]

here's a better version

amp=200;

[x,y]=meshgrid(-50:.1:50,-50:.1:50);

const1=1;

const2=0.001;

z=(amp*cos(sqrt((x.^2+y.^2)*const1))./exp((x.^2+y.^2)*const2));

s=surf(x,y,z);

colormap(winter)

set(s, 'edgecolor','none') %without the black lines, closer to real water ripples

[Paulo Silva]

for even better results use set(s, 'edgecolor','none','FaceColor','interp')

that removes the black lines and other colored lines, also the meshgrid can be created like this [x,y]=meshgrid(-50:.1:50); because both arguments were the same vector.

[Paulo Silva]

finally you might want some transparency on your water ripples, add this line to the end of the code: alpha(0.9) %the argument must be inside the interval [0 1]

[12ar.af]

Thanks....now it looks exactly as i wanted to be...much appreciated mate