How to located a point on top, in between and below two curves.

I need help I have two curves ploted which meets at both ends. I want , when a user enters a point, it should tell the user whether the point entered is above the upper curve or on the upper curve or in between the curves or on the lower curve or below the lower curve. Below is my code;

if true 
X = 0 : 20 : 100;
y1 = [ 1085 1160 1230 1310 1380 1453 ]; 
y2 = [ 1085 1198 1280 1350 1405 1453 ];
plot(x, y1,'r'); % plot lower curve
Hold on;
plot(x, y2, 'b'); %plot upper curve
X = input('enter the value of x: ');
Y = input('enter the value of y: ');
plot (X , Y ,'g'); % user ploted points
end

So all i am saying is that; After the user has entered the X and the Y values and it is ploted , there should be some codes to determine whether the point ploted or entered is above the upper curve or on the upper curve or in between the curves or on the lower curve or below the lower curve . I hope am making sense since am not quite matlab friendly. Please help.

[John D'Errico]

Do you kow how to use interpolation, for example, interp1? If not, then it is time to learn.

Can you interpolate each curve, at the given x value? How would that tell you if the point is above or below each curve? How will that allow you to answer your question?

[Paul Kpantey]

Thanks for the comment.

Ihavent used that function before. will try that.

But at the meantime can you help me ith that algorithm?

Answer 1

[the cyclist]

You should be able to use the inpolygon function to solve this.

[Paul Kpantey]

Thanks for your comment

So does that means that my plot will form a polygon?. I tried reading about about it but couldn't figure it out how to implement on my data.

I would be grateful if you would help me with the algorithm. Help

[the cyclist]

Your data do form a polygon, right? There are line segments between each point, and they are connected at the ends.

So, the algorithm would be something like this:

• Use inpolygon on the polygon defined by your two curves
• Use inpolygon on the polygon defined by your top curve + two more line segments that define an area above that curve
• Use inpolygon on the polygon defined by your bottom curve + two more line segments that define an area below that curve

From the information obtained by those three calls to inpolygon, you can conclude in which region the point lies.

[Paul Kpantey]

Thank you for the reply

but see the result of my plot, below

if a user enters the X and the Y values. The entered point is the small green color in the plot.

X = 40
Y = 1250

So i will want to display a message, say .... You are between the two curves

[the cyclist]

You are right.

Did you read my post? Did you try to understand it? Did you open the documentation for the inpolygon command, to understand how to apply it for your situation?

[Paul Kpantey]

I did read the post. I understood it and used the documentation as well but get errors.

I believe the points does not define polygon

[the cyclist]

Your two "curves" form a polygon. They are connected line segments.

x = 0 : 20 : 100;
y1 = [ 1085 1160 1230 1310 1380 1453 ]; 
y2 = [ 1085 1198 1280 1350 1405 1453 ];

figure
hold on
plot(x, y1, 'r'); % plot lower curve
plot(x, y2, 'b'); %plot upper curve

X = 20;
Y = 1180;

plot (X , Y ,'go'); % user ploted points

inpolygon(X,Y,[x flip(x)],[y1 flip(y2)])

ans =

  logical

   1

[Paul Kpantey]

It works well !!

Thank you so so much. You really have patience.. I love you man.

I added these codes to check for the positions of the points.

Keep helping!.

[inbetween,onCurve] = inpolygon(X,Y,[x flip(x)],[y1 flip(y2)]);

disp(inbetween & ~onCurve) % display True if strictly in between curves
disp(onCurve) % display True if On curves
disp(~onCurve) % display True if outside curves

[Paul Kpantey]

I have a follow up question if you can help me out.

If the user point falls in between the curves or (polygon) and you want to find the value of x1 and x2 coordinate if say, you draws horizontal line(but not to be drawn) through the point to touch both curves or (polygon) (as shown below in the edited image). And then traces the path down to find the corresponding values of x1 and x2 . I don't want to draw those lines on the graph but just using it to explain my point

Is this possible to get x1 and x2 values?. if yes then help me out on how to do this.

Thanks you.

[Image Analyst]

You were going to look into interp1(), remember? So just reverse y and x and use it. Something like (untested)

x1 = interp1(yBlue, xBlue, yGreen);
x2 = interp1(yRed, xRed, yGreen);

[Paul Kpantey]

works perfectly @ Image Analyst

Thanks so so much

i did this according to what you stated up

x1 = interp1(y2, x, Y);
x2 = interp1(y1, x, Y);