Plotting trajectory until it hits a terrain

I need to plot the trajectory of a particle, using euler's method, until it either hits the ground or contacts a "terrain", given in a file named "mountains". I also need to animate the trajectory, although i haven't completely gotten to that since i get errors, mostly surrounding how i define when the particle contacts the terrain. It seems to be having an issue in my while loop of "calculate_trajectory_t" My trajectory function is:

function [t,x,y,vx,vy] = calculate_trajectory_t(y1, ang, v1, dt, ter)
% This function uses Euler's method to compute the trajectory of a ball. 
%
%
%Initializing values.
load 'mountains' terrain
g=9.81;
v1x=v1*cosd(ang);
v1y=v1*sind(ang);
vx=v1x;
t=0;
x1=0;
x=[0];
t=[0];
y=[y1];
vy=[v1y];
vx=[v1x];   
load 'mountains' terrain
ter=[terrain(1,:), terrain(2,:)]; %Set x&y values of ter to terrain rows 1&2 respectively
hold on;
fill(terrain(1,:),terrain(2,:), 'blue'); %Fill in the ploygon created by terrain data
axis([0 max([terrain(1,:), x]) 0 max([terrain(2,:), y])]); %Set 
%Compute positions with respect to time.
n=1;
while (y>0)&&~inploygon(x,y,terrain(1,n),ter(2,n));
    n=n+1;
    t =[ t t(end)+dt];
    vx =[ vx v1x];
    vy =[ vy vy(end)-g*dt];
    x=[ x x(end)+vx(end)*dt];
    y=[ y y(end)+vy(end)*dt-(1/2)*g*t^2];
end

And the script which makes use of this function is:

    %This program uses the calculate_trajectory_t function, which takes values
    %of y1, ang, v1, dt and ter to calculate t, x, y, vx and vy.
    clear;
    clc;
    %Take user input
    v1=input('Please enter the initial speed of the ball (m/s): ');
    y1=input('Please enter the initial height of the ball (m): ');
    ang=input('Please enter the intial launch angle from the horizontal (degrees): ');
    dt=input('Please enter the time step (seconds): ');
    %Load mountains file to use data for the terrain
    load 'mountains' terrain targx targy
    ter=[terrain(1,:), terrain(2,:)]; %Set x&y values of ter to terrain rows 1&2 respectively
    hold on;
    fill(terrain(1,:),terrain(2,:), 'blue'); %Fill in the ploygon created by terrain data
    [t,x,y,vx,vy] = calculate_trajectory_t(y1, ang, v1, dt, ter);
    %Calculate and print final speed, time, and distances from the target:
    finalspeed = sqrt(vx(end)^2 + vy(end)^2);
    finaltime = t(end);
    xdistance = x(end)-targx;
    ydistance = y(end)-targy;
    disttot=sqrt(xdistance^2+ydistance^2);
    fprintf('Final speed is: %d \n' ,finalspeed);
    fprintf('Final time is: %f \n' ,finaltime);
    fprintf('Distance from target is: %d \n' ,disttot);
    pause(0.15);
    drawnow;
    plot(x, y, '-', 'go'); %Plot trajectory
    hold on;

-Thanks

Answer 1

[Walter Roberson]

Since we don't have your data files, you will have to tell us explicitly what errors you see.

Note that the syntax for load is not

load 'mountains' terrain

but rather simply

load mountains terrain

or better,

load('moutains', 'terrain')

Your error is probably in the line

while (y>0)&&~inploygon(x,y,terrain(1,n),ter(2,n))

After your first loop iteration, y is a vector of values rather than a single value, so y>0 is a vector of logical conditions. You cannot have a vector (or matrix) of logical conditions on either side of the && operator. Perhaps y(end)>0 is what you want?

Also, have another look at the way you initialize ter and see what size it is. Is it at least 2 by n where n is the number of time steps? If not, then indexing ter(2,n) is not right. Remember, n is the number of time steps, but you might not have reached as far as point number n in your terrain list.

I can see other problems but those together should give you enough clues to get you to think more clearly about what you are doing.

[Matt]

Thanks for your timely response.

1. To clarify, "mountains" is a .mat file, and terrain is a 2x11 matrix in the file. So would the syntax be:

load mountains terrain

or

load ('mountains', 'terrain')

?

2. I changed my approach for the while loop to:

while y(end)>0&&~inpolygon(x(end),y(end),terrain(1,:),terrain(2,:));

i.e., take the values from the first row of terrain (x-coordinates) to the last value in that row, and so on for the second row (y-coordinates).

I realized that the approach using n would exceed the data points in the matrix (only 11 points in each row).

I don't get any errors at this point; however, the data isn't right. I only seem to be generating values for ter in a 2x2 matrix (only 4 data points), and only 1x2 matrices each for x, y, vx, and vy.

[Walter Roberson]

For #1, either of those syntaxes is fine.