intersection de la ligne interpolée et une courbe interpolée Matlab

Question

J'ai straightline les données suivantes

xinter=[1.13 1.36 1.62 1.81 2.00 2.30 2.61 2.83 3.05 3.39] 
yinter=[0.10 0.25 0.40 0.50 0.60 0.75 0.90 1.00 1.10 1.25] 

et je veux trouver l'intersection avec un résultat d'une donnée interpolées d'une courbe telle que ci-dessous

 a50= [0.77 0.73 0.77 0.85 0.91 0.97 1.05 1.23 1.43 1.53 1.62 1.71 1.89 2.12 2.42]; 
a25= [0.51 0.60 0.70 0.80 0.85 0.90 0.96 1.09 1.23 1.30 1.36 1.41 1.53 1.67]; 
vel25=[0.43 0.35 0.30 0.27 0.25 0.24 0.22 0.21 0.22 0.24 0.25 0.27 0.30 0.35]; 
vel50=[0.68 0.57 0.49 0.43 0.40 0.38 0.36 0.34 0.36 0.38 0.40 0.43 0.49 0.57 0.68 ]; 


% back up original data, just for final plot 
bkp_a50 = a50 ; bkp_vel50 = vel50 ; 

% make second x vector monotonic 
istart = find(diff(a50)>0 , 1 , 'first') ; 
a50(1:istart-1) = [] ; 
vel50(1:istart-1) = [] ; 

% prepare a 3rd dimension vector (from 25 to 50) 
T = [repmat(25,size(a25)) ; repmat(40,size(a50)) ] ; 
% merge all observations together 
A = [ a25 ; a50] ; 
V = [vel25 ; vel50] ; 

% find the minimum domain on which data can be interpolated 
% (anything outside of that will return NaN) 
Astart = max([min(a25) min(a50)]) ; 
Astop = min([max(a25) max(a50)]) ; 

% use the function 'griddata' 
[TI,AI] = meshgrid(25:40 , linspace(Astart,Astop,10) ) ; 
VI = griddata(T,A,V,TI,AI) ; 

% plot all the intermediate curves 
%plot(AI,VI) 
hold on 
% the original curves 
%plot(a25,vel25,'--k','linewidth',2) 
%plot(bkp_a50,bkp_vel50,'--k','linewidth',2) 
% Highlight the curve at T = 30 ; 
c30 = find(TI(1,:) == 40) ; 
plot(AI(:,c30),VI(:,c30),'--r','linewidth',2) 

xinter=[1.13 1.36 1.62 1.81 2.00 2.30 2.61 2.83 3.05 3.39] 
yinter=[0.10 0.25 0.40 0.50 0.60 0.75 0.90 1.00 1.10 1.25] 


x1inter=(AI(:,c30))'; 
y1inter=(VI(:,c30))'; 


yy2 = interp1(xinter, yinter, x1inter,'spline') 


plot(xinter,yinter, '--k','linewidth',2) 

idx = find((y1inter - yy2) < eps, 1); %// Index of coordinate in array 
px = x1inter(idx) 
py = y1inter(idx) 
plot(px, py, 'ro', 'MarkerSize', 18) 

Mais il y a une erreur dans le résultat quand je modifie x1inter

Answer 1

Vous pouvez utiliser p piecewise curvefitting olynomial et la fonction fzero pour trouver le point d'intersection:

pp1 = pchip(xinter,yinter);   % Curve 1 
pp2 = pchip(AI(:,c30),VI(:,c30)); % Curve 2 
fun = @(x) ppval(pp1,x) - ppval(pp2,x); % Curve to evaluate 
xzero = fzero(fun,mean(xinter)) % intersection x value 
yzero = ppval(pp1,xzero) 
plot(xzero, yzero, 'bo', 'MarkerSize', 18)