В настоящее время я работаю над проектом для моего класса химической инженерии, который называется игла Буффона.Цель этого проекта - использовать MATLAB для получения оценки числа пи, а затем создать «карикатуру», которая будет отображать иглы на графике 10x10 с линиями через каждые 1 единицу, с иглами, пересекающими линию одного цвета, и игламине переходя, будучи другим.Я нашел оценку числа пи и создал график, но мои линии имеют длину не одну единицу, как это должно быть, а все иглы разной длины.если бы кто-нибудь мог помочь мне с этой проблемой, это было бы очень ценно.мои два сценария ниже
clear all;
close all;
clc;
format compact
% Script to illustrate the estimation of pi value by using Buffon's needle
% experiment
% set number of separate experiments
nExperiments = 1000;
% set number of separate trials
nTrials = 3;
% total number of dropped needles is directly based on number of trials and
% number of experiments
ndropped=nTrials.*nExperiments;
% spacing between the parallel lines
spacing = 1;
% length of the needle
L = spacing;
% the lower bound of x coordinate.
a = 10;
totalhits = 0;
for i = 1:nTrials
% keeps track of the number of hits
hits = 0;
% keeps track of the number of times the needle doesn't hit the
% any of the lines
nothits = 0;
for j = 1:nExperiments
[outcome,endpoints,angle] = needle_drop(spacing,L);
if outcome
hits = hits + 1;
endpointsHitList(:,:,hits) = endpoints;
else
nothits = nothits + 1;
endpointsNotHitList(:,:,nothits) = endpoints;
end
angleList(j) = angle;
end
scatter(1:nExperiments,angleList);
xlabel('Experiments');
ylabel('Angles');
piestimate(i) = (2*L/spacing)/(hits/nExperiments);
end
fprintf('The average value of pi is %f plus or minus %f after %d trials of %d experiments with %d total number of dropped needle.\n',mean(piestimate),std(piestimate),nTrials,nExperiments,ndropped);
figure
hold on
% plot the vertical separations
for i = 0:spacing:a
p1 = plot([i,i],[0 11],'k','LineWidth',2);
end
% plot the needles that hit the vertical separation
for i = 1:hits
p2 = plot(endpointsHitList(:,1,i),endpointsHitList(1,:,i),['-','b']);
end
% plot the needles that don't hit the vertical separation
for i = 1:nothits
p3 = plot(endpointsNotHitList(:,1,i),endpointsNotHitList(1,:,i),['-','r']);
end
axis([-2,12 -2 12]);
legend([p1 p2 p3],'Vertical Separations','Hits','Not Hits')
title('Buffon Needle Experiment');
xlabel('x-axis');
ylabel('y-axis');
figure
histogram(piestimate)
title('Histogram of pi estimate');
Это ниже моя функция needle_drop:
function [outcome,endpoints,theta] = needle_drop(spacing,L)
% spacing = spacing between the parallel lines spacing
% L = length of the needle
% spacing = 1;
% % In the special case where the length of the needle is equal to the grid spacing
% % between the parallel lines
% L = spacing;
% a is the lower bound of x coordinate. b is the upper bound.
% the needle position will be randomly between 0 and 10.
a = 0;
b = 10;
% generate random number r1 in [0,1]
r1 = rand;
% sample a value of the angle uniformly distributed over the interval
% from zero to ninety degrees
theta = (pi/2)*r1;
% the projection of half the length of the needle horizontally: S
S = (L/2)*cos(theta);
% Another random number r2 is generated
% this corresponds to x,y coordinate
r2 = a + (b-a).*rand(1,2);
% we need to take care of the offset.
% if the x coordinate is between 0 and d then offset is 0 if xcord is
% between d and 2d then offset is d and likewise for other values.
offset = floor(r2(1));
% The sampled position T of the center of the needle is next compared to the
% sampled projection of half the length of the needle
if r2(1)-S <=0+offset || r2(1)+S >=spacing+offset
outcome = 1;
else
outcome = 0;
end
% the projection of half the length of the needle vertically: V
V = L/2*sin(theta);
endpoints = [r2(1)-S,r2(2)+V;r2(1)+S,r2(2)-V];