main code init

Author: nguy1708

Main-Code.m

@@ -0,0 +1,103 @@
+n = 1000;
+
+%initialize variables needed
+h = 0.1;
+e = 0.1;
+
+%Take the input value and create input amount of points
+points = rand(n,2);
+%create all the points within the unit circle
+theta = 0:0.01:2*pi;
+p = [cos(theta'),sin(theta')];
+%Take only half the points in the heap and keep the points that are less
+%than 1 to create a simplex
+O = points(:,2) - 2*points(:,1) > 0;
+points(O,:) = [];
+O = points(:,2) + 2*points(:,1) > 2;
+points(O,:) = [];
+%draw the points
+hull = scatter(points(:,1),points(:,2),'yellow');
+hold on;
+
+%Having the graph instantiated, we will dot p and all the points in the
+%simplex. Function takes 2 matrixes.
+maxU = u(p,points);
+
+%Next we want to determine the approximate half spaces of the simplex. This
+%function will take in 3 arguements: p, points, and maxU-h.
+arg3 = maxU-h;
+[result, index] = Nh(p,points,arg3)
+
+%Then we will sort the indexes in descending order
+[g,I] = sort(index, 'descend')
+
+N = zeros(length(points),1);
+ph = zeros(length(points),1);
+for k = 1:length(points)
+ pcount = zeros(length(p),1);
+ a = Inf;
+ for i = 1:length(p)
+ pxDot = p(i,1)*points(k,1)+p(i,2)*points(k,2);
+ for j = 1:length(points)
+ pyDot = p(i,1)*points(j,1)+p(i,2)*points(j,2);
+ if pyDot >= pxDot - h
+ pcount(i) = pcount(i) + 1;
+ end
+ end
+ end
+ [a, i] = min(pcount);
+ N(k) = a;
+ ph(k) = i;
+end
+
+[Nhs, J] = sort(N)
+J(1:20)
+
+dtheta = 0.5;
+thetaList = zeros(0);
+x = -0.1:0.01:1.1;
+j = 1;
+while length(thetaList) <= 2
+ y = (maxU(I(j)) - p(I(j),1)*x) / p(I(j),2);
+ ans = theta(I(j));
+ a = 1;
+ for k = 1:length(thetaList)
+ if abs(ans-thetaList(k)) <= dtheta
+ a = 0;
+ end
+ end
+ if a == 1
+ pause;
+ plot(x,y,'blue')
+ thetaList(end+1) = ans;
+ end
+ j = j + 1;
+end
+pointsList = zeros(0);
+
+i = 1;
+interior = zeros(3,1);
+while length(pointsList) <= 2
+ ans1 = points(I(i));
+ a = 1;
+ for j = 1:length(pointsList)
+ if abs(ans1-pointsList(j)) <= dtheta
+ a = 0;
+ end
+ end
+ if a == 1
+ scatter(points(J(i),1),points(J(i),2),'red')
+ pointsList(end+1) = ans1;
+ interior(i,1) = points(J(i),1);
+ interior(i,2) = points(J(i),2);
+ end
+ for z = 1:length(interior) %Trying to isolate 3 unique points.
+ if points(z,1) == 0
+ points(z,1) = [];
+ end
+ if points(z,2) == 0
+ points(z,2) = [];
+ end
+ end
+ i = i+1;
+end