How to reshape a curve?

Hello, Masters:

I have a shock wave emission curve in water like this:

x is the distance from shock wave center and y is the shock wave pressure. The calculation was done by the Kirkwood-Bethe method.

However, this curve is physically "unreasonable" because liquid does not allow a broken wave.What we normally do is use a vertical guide line (as red line in figure) to let the left region equals the right region (as shown in the green line). After reshaping the wavefront, it should like this:

For less than 10 figures, we normally do it manually. However, we have now hundreds of these figures, and thus need a nice matlab algorithm to handle it.

Anyone has met this kind problem before? Would you please provide any idea to solve this problem...

Thank you!!!

Joe

p.s. the data is attached.

[José-Luis]

Where should the vertical line be placed?

[Joe Liang]

Hi, José-Luis:

You are right. Where to place the vertical line to make the left and right areas equal.

Regards,

Joe

[Andrei Bobrov]

Where all data?

Answer 1

[Andrei Bobrov]

load data
[~,iymax] = max(y);
yx = griddedInterpolant(y(end:-1:iymax),x(end:-1:iymax),'pchip');
y0 = fminsearch(@(x)yx(x),y(end));
x0 = yx(y0);
jj = find(x(1:iymax)<x0,1,'last');
f1 = griddedInterpolant(x(jj:iymax),y(jj:iymax),'pchip');
xx = x(iymax:end);
yy = y(iymax:end);
t0 = yy > y0;
t00 = x0 < xx;
t1 = t0 & t00;
f2 = griddedInterpolant([x0;flipud(xx(t1))],[y0;flipud(yy(t1))],'pchip');
t2 = ~t0 & t00;
f3 = griddedInterpolant([x0;xx(t2)],[y0;yy(t2)],'pchip');

xout = fzero(@(X)integral2(@(x,y)ones(size(x)),X,x(iymax),@(x)f2(x),@(x)f1(x))...
- integral2(@(x,y)ones(size(x)),x0,X,@(x)f3(x),@(x)f2(x)),[x0,x(iymax)]);

[Joe Liang]

Dear Andrei Bobrov:

Thank you very very much for your reply! It works!

It's really a genius idea to segment lines in such a elegant way!Especially the use of function "griddedInterpolant". Great!

Regards,

Joe

One small questions on your last line of code.You use integral2 to integrate an area. Here you used @(x,y)ones(size(x)). Is it similar to use @(x,y)1 or the latter is not allowed in Matlab?