How do I reuse randomly generated numbers?

below is the question i have to answer but i dont now how to replicate the results from part 3 to use in part 4. i would also like a different way of genarating the numbers for part 2 than the code provided

1. plots the needle at a random position on the floor considering that the point A of the needle can only be located in the square domain represented in Fig 1. This domain is a square of 20- cm centered at the origin of coordinates (𝑥𝑥 , 𝑦𝑦 ), as shown. The plot should be between -10 and 10 cm in the abscissas and in the ordinates. Use a solid black line to represent the needle and do not try to colour the background. Include a black horizontal line at y = 0. To represent the joint.

(10 marks)

2. uses a FOR loop to create a new plot with 50 needles distributed randomly on the floor. Use the same style and limits of the plot as in the previous section.

(10 marks)

3. counts how many of the 50 needles intersected (crossed) the joint of the floor in the previous plot and displays in the Command Window the proportion of the intersecting needles with respect to the total number of needles on the floor.

(20 marks)

4. creates a third plot that is the same as the second one but that represents the needles that intersect the joint in red colour and with a linewidth of 2 units, whilst the rest are plotted in black colour and with a linewidth of 1 unit. Use the same limits for the plot as in the previous sections.

for i=1:50
xb=20; yb=20
while (abs(xb)>10)||(abs(yb)>10)
xa=-10+rand()*20;
ya=-10+rand()*20;
theta=rand()*2*pi;
xb=xa+3*cos(theta);
yb=ya+3*sin(theta);
end
if(ya*yb<0)
count=count+1;
end
line([xa, xb], [ya, yb], 'color', 'k')
end
proportion=count/50            

[Dominique Eseinune]

also how do i ensure the length of the ploted lines is 3cm?

[Walter Roberson]

See by the way

https://blogs.mathworks.com/loren/2011/08/29/intersecting-lines/

https://matlabgeeks.com/tips-tutorials/computational-geometry/find-intersection-of-two-lines-in-matlab/

https://www.mathworks.com/matlabcentral/fileexchange/27205-fast-line-segment-intersection

Answer 1

[Walter Roberson]

The question does not require that you "re-use" random numbers. Just store the random numbers in an array when you generate them.

The question does not strictly require that plotting be done within a for loop: if you generated the points within a for loop and did the plotting afterwards then the for loop requirement of question 2 would be satisfied. Questions 3 and 4 do not require that you use for loops: program them however is convenient for you.

[John D'Errico]

Actually, we are now supposed to be recycling even random numbers.

To that end, MATLAB now provides a little blue barrel, where all random numbers should be placed immediately after use. This barrel will be collected with other refuse on a periodic basis, and then returned for re-use. There is some question as to whether you need to separate the random integers from floating point numbers, so perhaps two barrels will be necessary. ;-)

[Walter Roberson]

@John D'Errico

But is that safe?? What happens if the numbers in the collection barrel happen to combine together to form an Illegal Number ?

[Dominique Eseinune]

how do i save the numbers that are generated in the loop?

[Walter Roberson]

N = 50;
my_random_numbers = zeros(N, 3);
for K = 1 : N
   start_x = rand() * 20 + 10;
   start_y = rand() * 20 + 10;
   angle = rand() * 2*pi;
   my_random_numbers(K, :) = [start_x, start_y, angle];
end

[Dominique Eseinune]

this is my current code. i dont know how to integrate the code you gave me so that i can have figure thre satisfy whas asked in part 3 and 4

xb=20; yb=20;
while (abs(xb)>10)||(abs(yb)>10)
xa=-10+rand()*20;
ya=-10+rand()*20;
theta=rand()*2*pi;
xb=xa+3*cos(theta);
yb=ya+3*sin(theta);
end
  
line([-10,10],[10,10])
line([-10,10], [-10,-10])
line([-10,10], [0, 0], 'Color', 'k', 'LineWidth',4)
line([xa, xb], [ya, yb], 'color', 'k')

figure
line([-10,10],[10,10])
line([-10,10], [-10,-10])
line([-10,10], [0, 0], 'Color', 'k', 'LineWidth',4)
count=0;

for i=1:50
xb=20; yb=20
while (abs(xb)>10)||(abs(yb)>10)
xa=-10+rand()*20;
ya=-10+rand()*20;
theta=rand()*2*pi;
xb=xa+3*cos(theta);
yb=ya+3*sin(theta);
end
if(ya*yb<0)
count=count+1;
end
line([xa, xb], [ya, yb], 'color', 'k')
end
proportion=count/50
disp(proportion);

figure 
line([-10,10],[10,10])
line([-10,10], [-10,-10])
line([-10,10], [0, 0], 'Color', 'k', 'LineWidth',4)
count=0;
for i=1:50
xb=20; yb=20;
while (abs(xb)>10)||(abs(yb)>10)
xa=-10+rand()*20;
ya=-10+rand()*20;
theta=rand()*2*pi;
xb=xa+3*cos(theta);
yb=ya+3*sin(theta);
end
if(ya*yb<0)
count=count+1;
line([xa, xb], [ya, yb], 'color', 'r','LineWidth', 2)
else
line([xa, xb], [ya, yb], 'color', 'k', 'LineWidth',1)
end
end

[Walter Roberson]

xb=20; yb=20;
while (abs(xb)>10)||(abs(yb)>10)
xa=-10+rand()*20;
ya=-10+rand()*20;
theta=rand()*2*pi;
xb=xa+3*cos(theta);
yb=ya+3*sin(theta);
end
  
line([-10,10],[10,10])
line([-10,10], [-10,-10])
line([-10,10], [0, 0], 'Color', 'k', 'LineWidth',4)
line([xa, xb], [ya, yb], 'color', 'k')

figure
line([-10,10],[10,10])
line([-10,10], [-10,-10])
line([-10,10], [0, 0], 'Color', 'k', 'LineWidth',4)
count=0;

N = 50;
my_random_numbers = zeros(N, 3);
for i=1:N
xb=20; yb=20
while (abs(xb)>10)||(abs(yb)>10)
xa=-10+rand()*20;
ya=-10+rand()*20;
theta=rand()*2*pi;
xb=xa+3*cos(theta);
yb=ya+3*sin(theta);
end
my_random_numbers(i,:) = [xa, ya, theta];
if(ya*yb<0)
count=count+1;
end
line([xa, xb], [ya, yb], 'color', 'k')
end
proportion=count/N;
disp(proportion);

figure 
line([-10,10],[10,10])
line([-10,10], [-10,-10])
line([-10,10], [0, 0], 'Color', 'k', 'LineWidth',4)
count=0;
for i=1:N
xa = my_random_numbers(i,1);
ya = my_random_numbers(i,2);
theta = my_random_numbers(i,3);
xb=xa+3*cos(theta);
yb=ya+3*sin(theta);
if(ya*yb<0)
count=count+1;
line([xa, xb], [ya, yb], 'color', 'r','LineWidth', 2)
else
line([xa, xb], [ya, yb], 'color', 'k', 'LineWidth',1)
end
end

[Dominique Eseinune]

great that worked but i dont get why in my command window i get yb=20 repeated continously and i did really understand what the xb=20 and yb=20 at the beginning are intially for

[Walter Roberson]

Change

xb=20; yb=20

to

xb=20; yb=20;

The context is that you then have

while (abs(xb)>10)||(abs(yb)>10)

and when you set xb=20 and yb=20 you are forcing the abs() tests to be true, so you are forcing the loop to execute at least once.