refcurve

R2026b

Add reference curve to plot

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Syntax

refcurve(p)
refcurve(ax,p)
refcurve
hline = refcurve(___)

Description

refcurve(p) adds a polynomial reference curve to the current axes. The vector p contains the polynomial coefficients in descending powers.

example

refcurve(ax,p) adds a reference line to the plot in the axes specified by ax.

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

hline = refcurve(___) returns the reference line object hline using any of the input argument combinations in the previous syntaxes. Use hline to modify properties of a specific reference line after you create it. For a list of properties, see Line Properties.

example

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(0,"twister") % For reproducibility
y = polyval(p,t) + 0.5*randn(size(t));

Plot the 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

Define 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 the 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 Baseball Trajectories, xlabel Distance (m), ylabel Height (m) contains 2 objects of type line. These objects represent With drag, Without drag.

Input Arguments

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Polynomial coefficients, specified as a numeric vector of length n +1, where n is the polynomial degree. The coefficients in p are in descending powers, where

p(x)=p1xn+p2xn−1+...+pnx+pn+1.

Axes for the plot, specified as an Axes object. If you do not specify ax, then refcurve creates the plot using the current axes. For more information on creating an Axes object, see axes.

Output Arguments

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Graphics handle for a line object, returned as a Line graphics handle. Graphics handles are unique identifiers that you can use to query and modify the properties of a specific line on the plot.

To view and set properties of line objects, use dot notation. For information on using dot notation, see Access Property Values. For information on the Line properties that you can set, see Line Properties.

Version History

Introduced before R2006a

See Also

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