How to plot a tangent line between two lines
3 views (last 30 days)
Show older comments
Abdullah Alhebshi
on 31 Oct 2021
Answered: Sulaymon Eshkabilov
on 31 Oct 2021
I'm attempting to plot a tangent line to the red curve, but the tangent line must begin at the pinch point on the yellow line, which has been highlighted in black.
% Required Data
G = 1.356; L = 1.356; CL = 4.187*10^3; TL2 = 43.3; TL1 = 29.4;
% Red line data
x = linspace(TL1-10,TL2,1000);
y = 20312*exp(0.0524*x);
% Calculation to optain the yellow line data
H1 = 0.0165; TG1 = 29.4;
Hy1 = (((1.005+(1.88*H1))*1000)*(TG1 - 0)) + ((2.501*10^6)*H1);
Hy2 = ((L*CL*(TL2 - TL1))/G) + Hy1;
P1 = [TL1 Hy1];
P2 = [TL2 Hy2];
% Values for the yellow line
x_values = [TL1 TL2];
y_values = [Hy1 Hy2];
I want it to be like this black line
2 Comments
Accepted Answer
Paul
on 31 Oct 2021
Can use the Symbolic Math Toolbox for the exact result
syms x real
y_yellow(x) = 4187*x - 51372;
y_red(x) = 20312*exp(0.0524*x);
TL1 = sym(29.4); TL2 = sym(43.3);
x1 = TL1 - 10;
y1 = y_yellow(x1);
y_redslope(x) = diff(y_red(x),x);
syms m real
y_black(x,m) = m*(x - x1) + y1;
sol = solve([y_black(x,m) == y_red(x), m == y_redslope(x)],[x m]);
sol.x;
sol.m;
double(sol.x)
Looks lik we want the first solution, because sol.x(1) > TL1 - 10
figure; hold on;
fplot(y_red(x),double([TL1-10 TL2+10]),'r')
fplot(y_yellow(x),double([TL1-10 TL2+10]),'g') % make it green for better visibility
fplot(y_black(x,sol.m(1)),double([TL1-10 TL2+10]),'k')
Make y_black into a numeric function if desired
y_black_func = matlabFunction(y_black(x,sol.m(1)))
Or more simply expressed
y_black_func = matlabFunction(y_black(x,double(sol.m(1))))
0 Comments
More Answers (1)
Sulaymon Eshkabilov
on 31 Oct 2021
Here is how it can be done with a relatively simple polyfit() and polyval() fcns along with syms and diff():
% Required Data
G = 1.356; L = 1.356; CL = 4.187*10^3; TL2 = 43.3; TL1 = 29.4;
% Red line data
x = linspace(TL1-10,TL2,1000);
y = 20312*exp(0.0524*x);
% Calculation to optain the yellow line data
H1 = 0.0165; TG1 = 29.4;
Hy1 = (((1.005+(1.88*H1))*1000)*(TG1 - 0)) + ((2.501*10^6)*H1);
Hy2 = ((L*CL*(TL2 - TL1))/G) + Hy1;
P1 = [TL1 Hy1];
P2 = [TL2 Hy2];
% Values for the yellow line
x_values = [TL1 TL2];
y_values = [Hy1 Hy2];
TL2 = 43.3; TL1 = 29.4;
x = linspace(TL1-10,TL2,1000);
y = 20312*exp(0.0524*x);
plot(x, y, 'b-x', 'LineWidth', 0.5);
hold on
FM = polyfit(x,y, 2); % Polynomial fit
syms z
FM_sym = FM(1)*z^2+FM(2)*z+FM(3);
dY = diff(FM_sym,z);
dY_Model = double(coeffs(dY));
z = x-TL1;
m = polyval(fliplr(dY_Model), TL1); % Slope
HY1 =polyval(FM, TL1); % y1 value
yy = m*z+HY1*1; % Tangent Line
plot(x, yy, 'k-', 'linewidth', 2), shg
legend('Fcn', 'Tangent Line', 'location', 'best')
hold off
0 Comments
See Also
Categories
Find more on Assumptions in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!