refcurve

Add reference curve to plot

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Syntax

refcurve(p)
refcurve
refcurve(ax,p)
hcurve = refcurve(...)

Description

refcurve(p) adds a polynomial reference curve with coefficients p to the current axes. If p is a vector with n+1 elements, the curve is:

y = p(1)*x^n + p(2)*x^(n-1) + ... + p(n)*x + p(n+1)

refcurve with no input arguments adds a line along the x axis.

refcurve(ax,p) uses the plot axes specified in ax, an Axes object. For more information, see axes.

hcurve = refcurve(...) returns the handle hcurve to the curve using any of the input argument combinations in the previous syntaxes.

Examples

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Open Live Script

Generate data with a polynomial trend.

p = [1 -2 -1 0];
t = 0:0.1:3;
rng default  % For reproducibility
y = polyval(p,t) + 0.5*randn(size(t));

Plot data and add the population mean function using refcurve.

plot(t,y,'ro')
h = refcurve(p);
h.Color = 'r';

Figure contains an axes object. The axes object contains 2 objects of type line. One or more of the lines displays its values using only markers

Also add the fitted mean function.

q = polyfit(t,y,3);
refcurve(q)
legend('Data','Population Mean','Fitted Mean', ...
    'Location','NW')

Figure contains an axes object. The axes object contains 3 objects of type line. One or more of the lines displays its values using only markers These objects represent Data, Population Mean, Fitted Mean.

Open Live Script

Introduce the relevant physical constants.

M = 0.145;      % Mass (kg)
R = 0.0366;     % Radius (m)
A = pi*R^2;     % Area (m^2)
rho = 1.2;      % Density of air (kg/m^3)
C = 0.5;        % Drag coefficient
D = rho*C*A/2;  % Drag proportional to the square of the speed
g = 9.8;        % Acceleration due to gravity (m/s^2)

Simulate the trajectory with drag proportional to the square of the speed, assuming constant acceleration in each time interval.

dt = 1e-2;      % Simulation time interval (s)
r0 = [0 1];     % Initial position (m)
s0 = 50;        % Initial speed (m/s)
alpha0 = 35;    % Initial angle (deg)
v0 = s0*[cosd(alpha0) sind(alpha0)]; % Initial velocity (m/s)

r = r0;
v = v0;
trajectory = r0;
while r(2) > 0
    a = [0 -g] - (D/M)*norm(v)*v;
    v = v + a*dt;
    r = r + v*dt + (1/2)*a*(dt^2);
    trajectory = [trajectory;r];
end

Plot trajectory and use refcurve to add the drag-free parabolic trajectory (found analytically) to the plot of trajectory.

figure
plot(trajectory(:,1),trajectory(:,2),'m','LineWidth',2)
xlim([0,250])
h = refcurve([-g/(2*v0(1)^2),...
    (g*r0(1)/v0(1)^2) + (v0(2)/v0(1)),...
    (-g*r0(1)^2/(2*v0(1)^2)) - (v0(2)*r0(1)/v0(1)) + r0(2)]);
h.Color = 'c';
h.LineWidth = 2;
axis equal
ylim([0,50])
grid on
xlabel('Distance (m)')
ylabel('Height (m)')
title('{\bf Baseball Trajectories}')
legend('With Drag','Without Drag')

Figure contains an axes object. The axes object with title blank Baseball blank Trajectories, xlabel Distance (m), ylabel Height (m) contains 2 objects of type line. These objects represent With Drag, Without Drag.

Version History

Introduced before R2006a

See Also

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