How do I shade the xy plane at z=0 of my plot and how to stop the plot after it passes z=0?

I have the following code:

t = 0:0.0001:20; %time
m = 0.4; %mass (kg)
g = 9.8; %gravitational accel. (m/s^2)
b = 0.44; %drag coefficient
w_1 = 10; %Angular Velocity
w_2 = 8; %Angular Velocity
w_3 = 5; %Angular Velocity

x_t_1 = (2349.*m)./(100.*b) - (2349.*m.*exp(-(b.*t)./m))./(100.*b);
y_t_1 = (g.*m.*t.*w_1)./(b.^2 + w_1.^2) - (171.*b.^2.*m.*w_1)./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) - (171.*m.*w_1.^3)./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) - (2.*b.*g.*m.^2.*w_1)./(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4) + (171.*b.^3.*m.*exp(-(b.*t)./m).*sin((t.*w_1)./m))./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) + (171.*m.*w_1.^3.*exp(-(b.*t)./m).*cos((t.*w_1)./m))./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) + (171.*b.^2.*m.*w_1.*exp(-(b.*t)./m).*cos((t.*w_1)./m))./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) + (171.*b.*m.*w_1.^2.*exp(-(b.*t)./m).*sin((t.*w_1)./m))./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) + (b.^2.*g.*m.^2.*exp(-(b.*t)./m).*sin((t.*w_1)./m))./(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4) - (g.*m.^2.*w_1.^2.*exp(-(b.*t)./m).*sin((t.*w_1)./m))./(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4) + (2.*b.*g.*m.^2.*w_1.*exp(-(b.*t)./m).*cos((t.*w_1)./m))./(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4);
z_t_1 = (171.*b.^3.*m)./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) + (171.*b.*m.*w_1.^2)./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) + (b.^2.*g.*m.^2)./(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4) - (g.*m.^2.*w_1.^2)./(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4) - (b.*g.*m.*t)./(b.^2 + w_1.^2) - (171.*b.^3.*m.*exp(-(b.*t)./m).*cos((t.*w_1)./m))./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) + (171.*m.*w_1.^3.*exp(-(b.*t)./m).*sin((t.*w_1)./m))./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) - (171.*b.*m.*w_1.^2.*exp(-(b.*t)./m).*cos((t.*w_1)./m))./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) + (171.*b.^2.*m.*w_1.*exp(-(b.*t)./m).*sin((t.*w_1)./m))./(20.*(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4)) - (b.^2.*g.*m.^2.*exp(-(b.*t)./m).*cos((t.*w_1)./m))./(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4) + (g.*m.^2.*w_1.^2.*exp(-(b.*t)./m).*cos((t.*w_1)./m))./(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4) + (2.*b.*g.*m.^2.*w_1.*exp(-(b.*t)./m).*sin((t.*w_1)./m))./(b.^4 + 2.*b.^2.*w_1.^2 + w_1.^4);

x_t_2 = (2349.*m)./(100.*b) - (2349.*m.*exp(-(b.*t)./m))./(100.*b);
y_t_2 = (g.*m.*t.*w_2)./(b.^2 + w_2.^2) - (171.*b.^2.*m.*w_2)./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) - (171.*m.*w_2.^3)./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) - (2.*b.*g.*m.^2.*w_2)./(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4) + (171.*b.^3.*m.*exp(-(b.*t)./m).*sin((t.*w_2)./m))./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) + (171.*m.*w_2.^3.*exp(-(b.*t)./m).*cos((t.*w_2)./m))./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) + (171.*b.^2.*m.*w_2.*exp(-(b.*t)./m).*cos((t.*w_2)./m))./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) + (171.*b.*m.*w_2.^2.*exp(-(b.*t)./m).*sin((t.*w_2)./m))./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) + (b.^2.*g.*m.^2.*exp(-(b.*t)./m).*sin((t.*w_2)./m))./(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4) - (g.*m.^2.*w_2.^2.*exp(-(b.*t)./m).*sin((t.*w_2)./m))./(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4) + (2.*b.*g.*m.^2.*w_2.*exp(-(b.*t)./m).*cos((t.*w_2)./m))./(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4);
z_t_2 = (171.*b.^3.*m)./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) + (171.*b.*m.*w_2.^2)./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) + (b.^2.*g.*m.^2)./(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4) - (g.*m.^2.*w_2.^2)./(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4) - (b.*g.*m.*t)./(b.^2 + w_2.^2) - (171.*b.^3.*m.*exp(-(b.*t)./m).*cos((t.*w_2)./m))./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) + (171.*m.*w_2.^3.*exp(-(b.*t)./m).*sin((t.*w_2)./m))./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) - (171.*b.*m.*w_2.^2.*exp(-(b.*t)./m).*cos((t.*w_2)./m))./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) + (171.*b.^2.*m.*w_2.*exp(-(b.*t)./m).*sin((t.*w_2)./m))./(20.*(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4)) - (b.^2.*g.*m.^2.*exp(-(b.*t)./m).*cos((t.*w_2)./m))./(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4) + (g.*m.^2.*w_2.^2.*exp(-(b.*t)./m).*cos((t.*w_2)./m))./(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4) + (2.*b.*g.*m.^2.*w_2.*exp(-(b.*t)./m).*sin((t.*w_2)./m))./(b.^4 + 2.*b.^2.*w_2.^2 + w_2.^4);

x_t_3 = (2349.*m)./(100.*b) - (2349.*m.*exp(-(b.*t)./m))./(100.*b);
y_t_3 = (g.*m.*t.*w_3)./(b.^2 + w_3.^2) - (171.*b.^2.*m.*w_3)./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) - (171.*m.*w_3.^3)./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) - (2.*b.*g.*m.^2.*w_3)./(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4) + (171.*b.^3.*m.*exp(-(b.*t)./m).*sin((t.*w_3)./m))./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) + (171.*m.*w_3.^3.*exp(-(b.*t)./m).*cos((t.*w_3)./m))./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) + (171.*b.^2.*m.*w_3.*exp(-(b.*t)./m).*cos((t.*w_3)./m))./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) + (171.*b.*m.*w_3.^2.*exp(-(b.*t)./m).*sin((t.*w_3)./m))./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) + (b.^2.*g.*m.^2.*exp(-(b.*t)./m).*sin((t.*w_3)./m))./(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4) - (g.*m.^2.*w_3.^2.*exp(-(b.*t)./m).*sin((t.*w_3)./m))./(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4) + (2.*b.*g.*m.^2.*w_3.*exp(-(b.*t)./m).*cos((t.*w_3)./m))./(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4);
z_t_3 = (171.*b.^3.*m)./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) + (171.*b.*m.*w_3.^2)./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) + (b.^2.*g.*m.^2)./(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4) - (g.*m.^2.*w_3.^2)./(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4) - (b.*g.*m.*t)./(b.^2 + w_3.^2) - (171.*b.^3.*m.*exp(-(b.*t)./m).*cos((t.*w_3)./m))./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) + (171.*m.*w_3.^3.*exp(-(b.*t)./m).*sin((t.*w_3)./m))./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) - (171.*b.*m.*w_3.^2.*exp(-(b.*t)./m).*cos((t.*w_3)./m))./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) + (171.*b.^2.*m.*w_3.*exp(-(b.*t)./m).*sin((t.*w_3)./m))./(20.*(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4)) - (b.^2.*g.*m.^2.*exp(-(b.*t)./m).*cos((t.*w_3)./m))./(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4) + (g.*m.^2.*w_3.^2.*exp(-(b.*t)./m).*cos((t.*w_3)./m))./(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4) + (2.*b.*g.*m.^2.*w_3.*exp(-(b.*t)./m).*sin((t.*w_3)./m))./(b.^4 + 2.*b.^2.*w_3.^2 + w_3.^4);

plot3(x_t_1, y_t_1, z_t_1)
hold on
plot3(x_t_2, y_t_2, z_t_2)
plot3(x_t_3, y_t_3, z_t_3)
xlabel('X')
ylabel('Y')
zlabel('Z')
legend('\omega = 10 rad/s', '\omega = 8 rad/s', '\omega = 5 rad/s')
hold off

I would like to shade the xy plane at z=0 to make the plot more visually appealing but I am not sure how to do this. I also only need the portion of each individual plot that appears before it goes below z=0 again. This plot is the trajectory of a soccer ball and at z=0 is the ground so mathematically the plots continue below z=0 but realistically this is not the case and I am not sure how to set this limit. Thank you in advanced for your help!

Answer 1

[Adam Danz]

The easiest solution is simply

zlim([0,inf])

I also added grid on so we can see the 3D coordinates better. However, the data below z=0 still exist; you just can't see it.

Another approach would be to simply replace unwanted data with NaN.

idx = z_t_1 > 0; 
x_t_1(~idx) = NaN; 
x_t_1(~idx) = NaN; 
z_t_1(~idx) = NaN; 
plot3(x_t_1, y_t_1, z_t_1)

And another approach is to split the data up into groups that 'bounce' above the z=0 axis. There's more than one way to do that. This appoach requires the image processing toolbox due to the use of bwlabel().

bwidx = bwlabel(z_t_1 > 0);  % group the sections above z=0
splitGroups = @(data)splitapply(@(x){x},data(bwidx>0).',findgroups(bwidx(bwidx>0)).');  % Function that splits the data
axes(); 
hold on
cellfun(@plot3, splitGroups(x_t_1), splitGroups(y_t_1), splitGroups(z_t_1))
view(3)