Monte Carlo Simulation question?

Question

Andrew Ardolino 2014-10-27

0
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https://ww2.mathworks.cn/matlabcentral/answers/160317-monte-carlo-simulation-question

编辑： Andrew Ardolino 2014-10-27

Hey, I need to make a program that proves monte carlo sampling to find the area of a circle. So basically, there is a circular pond inside of a rectangular field and the cannon shoots cannonballs into the field.

we need to use functions, and i'm stuck on one that's supposed to have parameters: pond radius, x hit spot, and y hit spot. The function then plots the point x, y in one of two styles depending on whether it landed in the pond or not.

The plot function accepts a third argument that indicates the shape of the point to plot and the point's color. For instance this plots a blue asterisk: plot(x, y, 'b*') and this plots a green circle: plot(x, y, 'go') The statements in the function must do this: If the shot hit the pond, plot a blue star, otherwise plot a green circle. You will need to use an if/else statement, and you will need to call the hitPond function and the plot function. Also,this function mustreturn a result: • It returns true if the shot lands in the pond. • It returns false if the shot lands in the field. Be very careful here: The function should not display true or false, it should return true or false. Also note that the choice of using true and false as return values is completely arbitrary. I could have chosen −1 and 1, or 1 and 0, or 99 and 33, or even strings like 'splash' and 'thud'.

so far, what i have is:

.m function

function []=setupField(fieldSize)
title('Shots fired into a field with a perfectly round pond');
axis([-fieldSize/2, fieldSize/2, -fieldSize/2, fieldSize/2]);
axis equal;
hold on;
end

plotpond.m

function []=setupField(fieldSize)
title('Shots fired into a field with a perfectly round pond');
axis([-fieldSize/2, fieldSize/2, -fieldSize/2, fieldSize/2]);
axis equal;
hold on;
end
    if true
      % code
    end

hitPond.m

    function hitPond(pondRadius, xhit, yhit)
    %use distance formula to find length between points.
    x=0
    y=0
    %because of the axis^
    %we are finding the distance between the axis and the point where it hit
    step1=(xhit-x)^2;
    step2=(yhit-y)^2;
    step3=step1+step2;
    distance=sqrt(step3);
    if (distance<1);
        disp('1');
    elseif distance=1;
        disp('1');
    elseif distance>1;
        disp('0');
    end
    end

driver script, monteCarlo.m

clc       %clear commands 
clear     %clear all variables
clf       % clear plot area
rng('shuffle') %shuffle random number generator
fieldSize = 4;
pondRadius= 1;
numShots  = 100;
setupField(fieldSize);
x=0;
y=0;        %axis should be 0,0
radius=1;   %radius will be 1.
plotPond(x, y, radius)
hitPond(1, 1, 1)