курсачи / matlab

h = input('Введите h '); %шаг сетки

m = input('Введите размер сетки '); %размер

r=input('Введите значение радиуса разбиваемой области '); %задание области

if m<=r || h<=0 || m<=0 || r<=0 || m/h<1.6

disp('Некорректный ввод')

else

[X,Y] = meshgrid(-m:h:m); %формирование массива

Z = X*0;

surf(X,Y,Z); %построение сетки

xlabel('x');

ylabel('y');

alpha 0

hold on

x=-r:0.0001:r;

y1=sqrt(r^2-x.^2);

y2=-sqrt(r^2-x.^2);

plot(x,y1,x,y2);

max_i=floor(m*2/h+1); %округление в меньшую сторону

max_j=floor(m*2/h+1);

rasst_do_uzlov=zeros(1000,1000);

coord_uzlov=zeros(1000,1000);

coord_toch_okr=zeros(1000,1000);

h_mezhdu_uzlami=zeros(1000,1000);

irregular_nodes=zeros(1000,1000);

for i=1:1:max_i

for j=1:1:max_j

rasst_do_uzlov(i,j)=sqrt((X(i,j)).^2+(Y(i,j)).^2);

end

end

o=1;count=1;

for i=1:1:max_i %цикл для формирования массива с координатами нерегулярных узлов

for j=1:1:max_j

if rasst_do_uzlov(i,j)<r && (rasst_do_uzlov(i,j-1)>=r || rasst_do_uzlov(i,j+1)>=r || rasst_do_uzlov(i+1,j)>=r || rasst_do_uzlov(i-1,j)>=r)

coord_uzlov(o,1)=X(i,j);

coord_uzlov(o,2)=Y(i,j);

irregular_nodes(o,1)=count;

irregular_nodes(o,2)=X(i,j);

irregular_nodes(o,3)=Y(i,j);

o=o+1;

stem(X(i,j),Y(i,j),'fill', 'b');

end

count=count+1; %счётчик узлов

end

end

o_max=o;

for o=1:1:o_max-1 %цикл для формирования массива с координатами точек на окружности, которым соответствуют нерегулярные узлы

coord_toch_okr(o,1)=sqrt(r^2-(coord_uzlov(o,2)).^2);

coord_toch_okr(o,2)=sqrt(r^2-(coord_uzlov(o,1)).^2);

end

for o=1:1:o_max-1 %цикл для формирования массива с расстояниями от точек на окружности до узлов

h_mezhdu_uzlami(o,1)=abs(abs(coord_uzlov(o,1))-abs(coord_toch_okr(o,1)));

h_mezhdu_uzlami(o,2)=abs(abs(coord_uzlov(o,2))-abs(coord_toch_okr(o,2)));

end

for o=1:1:o_max-1

if coord_uzlov(o,1)<0 && coord_uzlov(o,2)<0 %x<0;y<0

irregular_nodes(o,4)=h_mezhdu_uzlami(o,1);

irregular_nodes(o,5)=h_mezhdu_uzlami(o,2);

irregular_nodes(o,6)=h;

irregular_nodes(o,7)=h;

if irregular_nodes(o,4)>h

irregular_nodes(o,4)=h;

end

if irregular_nodes(o,5)>h

irregular_nodes(o,5)=h;

end

end

if coord_uzlov(o,1)<0 && coord_uzlov(o,2)>0 %x<0;y>0

irregular_nodes(o,4)=h_mezhdu_uzlami(o,1);

irregular_nodes(o,5)=h;

irregular_nodes(o,6)=h;

irregular_nodes(o,7)=h_mezhdu_uzlami(o,2);

if irregular_nodes(o,4)>h

irregular_nodes(o,4)=h;

end

if irregular_nodes(o,7)>h

irregular_nodes(o,7)=h;

end

end

if coord_uzlov(o,1)>0 && coord_uzlov(o,2)>0 %x>0;y>0

irregular_nodes(o,4)=h;

irregular_nodes(o,5)=h;

irregular_nodes(o,6)=h_mezhdu_uzlami(o,1);

irregular_nodes(o,7)=h_mezhdu_uzlami(o,2);

if irregular_nodes(o,6)>h

irregular_nodes(o,6)=h;

end

if irregular_nodes(o,7)>h

irregular_nodes(o,7)=h;

end

end

if coord_uzlov(o,1)>0 && coord_uzlov(o,2)<0 %x>0;y<0

irregular_nodes(o,4)=h;

irregular_nodes(o,5)=h_mezhdu_uzlami(o,2);

irregular_nodes(o,6)=h_mezhdu_uzlami(o,1);

irregular_nodes(o,7)=h;

if irregular_nodes(o,5)>h

irregular_nodes(o,5)=h;

end

if irregular_nodes(o,6)>h

irregular_nodes(o,6)=h;

end

end

if coord_uzlov(o,1)==0 && coord_uzlov(o,2)<0 %x=0;y<0

irregular_nodes(o,4)=h_mezhdu_uzlami(o,1);

irregular_nodes(o,5)=h_mezhdu_uzlami(o,2);

irregular_nodes(o,6)=h_mezhdu_uzlami(o,1);

irregular_nodes(o,7)=h;

if irregular_nodes(o,4)>h

irregular_nodes(o,4)=h;

end

if irregular_nodes(o,5)>h

irregular_nodes(o,5)=h;

end

if irregular_nodes(o,6)>h

irregular_nodes(o,6)=h;

end

end

if coord_uzlov(o,1)<0 && coord_uzlov(o,2)==0 %x<0;y=0

irregular_nodes(o,4)=h_mezhdu_uzlami(o,1);

irregular_nodes(o,5)=h_mezhdu_uzlami(o,2);

irregular_nodes(o,6)=h;

irregular_nodes(o,7)=h_mezhdu_uzlami(o,2);

if irregular_nodes(o,4)>h

irregular_nodes(o,4)=h;

end

if irregular_nodes(o,5)>h

irregular_nodes(o,5)=h;

end

if irregular_nodes(o,7)>h

irregular_nodes(o,7)=h;

end

end

if coord_uzlov(o,1)>0 && coord_uzlov(o,2)==0 %x>0;y=0

irregular_nodes(o,4)=h;

irregular_nodes(o,5)=h_mezhdu_uzlami(o,2);

irregular_nodes(o,6)=h_mezhdu_uzlami(o,1);

irregular_nodes(o,7)=h_mezhdu_uzlami(o,2);

if irregular_nodes(o,5)>h

irregular_nodes(o,5)=h;

end

if irregular_nodes(o,6)>h

irregular_nodes(o,6)=h;

end

if irregular_nodes(o,7)>h

irregular_nodes(o,7)=h;

end

end

if coord_uzlov(o,1)==0 && coord_uzlov(o,2)>0 %x=0;y>0

irregular_nodes(o,4)=h_mezhdu_uzlami(o,1);

irregular_nodes(o,5)=h;

irregular_nodes(o,6)=h_mezhdu_uzlami(o,1);

irregular_nodes(o,7)=h_mezhdu_uzlami(o,2);

if irregular_nodes(o,4)>h

irregular_nodes(o,4)=h;

end

if irregular_nodes(o,6)>h

irregular_nodes(o,6)=h;

end

if irregular_nodes(o,7)>h

irregular_nodes(o,7)=h;

end

end

if r<h

irregular_nodes(o,4)=r;

irregular_nodes(o,5)=r;

irregular_nodes(o,6)=r;

irregular_nodes(o,7)=r;

end

end

g=1; max_g=2*r/0.0001+1; %начало проверки

coord_toch_okr_proof=zeros(1000,1000);

for o=1:1:o_max-1

for g=1:1:max_g

if coord_uzlov(o,1)==x(1,g)

coord_toch_okr_proof(o,2)=abs(y2(1,g));

coord_toch_okr_proof(o,1)=abs(x(1,g));

end

end

end

h_mezhdu_uzlami_proof=zeros(1000,1000);

for o=1:1:o_max-1 %цикл для формирования массива с расстояниями от точек на окружности до узлов

h_mezhdu_uzlami_proof(o,1)=pdist2(abs(coord_uzlov(o,1)),abs(coord_toch_okr(o,1)));

h_mezhdu_uzlami_proof(o,2)=pdist2(abs(coord_uzlov(o,2)),abs(coord_toch_okr(o,2)));

coord_toch_okr_proof(o,1)=coord_toch_okr_proof(o,1)+h_mezhdu_uzlami_proof(o,1);

end

irregular_nodes_proof=zeros(1000,1000);

rasst_do_uzlov_proof=zeros(1000,1000);

for i=1:1:max_i

for j=1:1:max_j

rasst_do_uzlov_proof(i,j)=sqrt((X(i,j)).^2+(Y(i,j)).^2);

end

end

o=1;count=1;

for i=1:1:max_i %цикл для формирования массива с координатами нерегулярных узлов

for j=1:1:max_j

if rasst_do_uzlov_proof(i,j)<r && (rasst_do_uzlov_proof(i,j-1)>=r || rasst_do_uzlov_proof(i,j+1)>=r || rasst_do_uzlov_proof(i+1,j)>=r || rasst_do_uzlov_proof(i-1,j)>=r)

coord_uzlov(o,1)=X(i,j);

coord_uzlov(o,2)=Y(i,j);

irregular_nodes_proof(o,1)=count;

irregular_nodes_proof(o,2)=X(i,j);

irregular_nodes_proof(o,3)=Y(i,j);

o=o+1;

stem(X(i,j),Y(i,j),'fill', 'b');

end

count=count+1; %счётчик узлов

end

end

o=1;

for o=1:1:o_max-1

if coord_uzlov(o,1)<0 && coord_uzlov(o,2)<0 %x<0;y<0

irregular_nodes_proof(o,4)=h_mezhdu_uzlami_proof(o,1);

irregular_nodes_proof(o,5)=h_mezhdu_uzlami_proof(o,2);

irregular_nodes_proof(o,6)=h;

irregular_nodes_proof(o,7)=h;

if irregular_nodes_proof(o,4)>h

irregular_nodes_proof(o,4)=h;

end

if irregular_nodes_proof(o,5)>h

irregular_nodes_proof(o,5)=h;

end

end

if coord_uzlov(o,1)<0 && coord_uzlov(o,2)>0 %x<0;y>0

irregular_nodes_proof(o,4)=h_mezhdu_uzlami_proof(o,1);

irregular_nodes_proof(o,5)=h;

irregular_nodes_proof(o,6)=h;

irregular_nodes_proof(o,7)=h_mezhdu_uzlami_proof(o,2);

if irregular_nodes_proof(o,4)>h

irregular_nodes_proof(o,4)=h;

end

if irregular_nodes_proof(o,7)>h

irregular_nodes_proof(o,7)=h;

end

end

if coord_uzlov(o,1)>0 && coord_uzlov(o,2)>0 %x>0;y>0

irregular_nodes_proof(o,4)=h;

irregular_nodes_proof(o,5)=h;

irregular_nodes_proof(o,6)=h_mezhdu_uzlami_proof(o,1);

irregular_nodes_proof(o,7)=h_mezhdu_uzlami_proof(o,2);

if irregular_nodes_proof(o,6)>h

irregular_nodes_proof(o,6)=h;

end

if irregular_nodes_proof(o,7)>h

irregular_nodes_proof(o,7)=h;

end

end

if coord_uzlov(o,1)>0 && coord_uzlov(o,2)<0 %x>0;y<0

irregular_nodes_proof(o,4)=h;

irregular_nodes_proof(o,5)=h_mezhdu_uzlami_proof(o,2);

irregular_nodes_proof(o,6)=h_mezhdu_uzlami_proof(o,1);

irregular_nodes_proof(o,7)=h;

if irregular_nodes_proof(o,5)>h

irregular_nodes_proof(o,5)=h;

end

if irregular_nodes_proof(o,6)>h

irregular_nodes_proof(o,6)=h;

end

end

if coord_uzlov(o,1)==0 && coord_uzlov(o,2)<0 %x=0;y<0

irregular_nodes_proof(o,4)=h_mezhdu_uzlami_proof(o,1);

irregular_nodes_proof(o,5)=h_mezhdu_uzlami_proof(o,2);

irregular_nodes_proof(o,6)=h_mezhdu_uzlami_proof(o,1);

irregular_nodes_proof(o,7)=h;

if irregular_nodes_proof(o,4)>h

irregular_nodes_proof(o,4)=h;

end

if irregular_nodes_proof(o,5)>h

irregular_nodes_proof(o,5)=h;

end

if irregular_nodes_proof(o,6)>h

irregular_nodes_proof(o,6)=h;

end

end

if coord_uzlov(o,1)<0 && coord_uzlov(o,2)==0 %x<0;y=0

irregular_nodes_proof(o,4)=h_mezhdu_uzlami_proof(o,1);

irregular_nodes_proof(o,5)=h_mezhdu_uzlami_proof(o,2);

irregular_nodes_proof(o,6)=h;

irregular_nodes_proof(o,7)=h_mezhdu_uzlami_proof(o,2);

if irregular_nodes_proof(o,4)>h

irregular_nodes_proof(o,4)=h;

end

if irregular_nodes_proof(o,5)>h

irregular_nodes_proof(o,5)=h;

end

if irregular_nodes_proof(o,7)>h

irregular_nodes_proof(o,7)=h;

end

end

if coord_uzlov(o,1)>0 && coord_uzlov(o,2)==0 %x>0;y=0

irregular_nodes_proof(o,4)=h;

irregular_nodes_proof(o,5)=h_mezhdu_uzlami_proof(o,2);

irregular_nodes_proof(o,6)=h_mezhdu_uzlami_proof(o,1);

irregular_nodes_proof(o,7)=h_mezhdu_uzlami_proof(o,2);

if irregular_nodes_proof(o,5)>h

irregular_nodes_proof(o,5)=h;

end

if irregular_nodes_proof(o,6)>h

irregular_nodes_proof(o,6)=h;

end

if irregular_nodes_proof(o,7)>h

irregular_nodes_proof(o,7)=h;

end

end

if coord_uzlov(o,1)==0 && coord_uzlov(o,2)>0 %x=0;y>0

irregular_nodes_proof(o,4)=h_mezhdu_uzlami_proof(o,1);

irregular_nodes_proof(o,5)=h;

irregular_nodes_proof(o,6)=h_mezhdu_uzlami_proof(o,1);

irregular_nodes_proof(o,7)=h_mezhdu_uzlami_proof(o,2);

if irregular_nodes_proof(o,4)>h

irregular_nodes_proof(o,4)=h;

end

if irregular_nodes_proof(o,6)>h

irregular_nodes_proof(o,6)=h;

end

if irregular_nodes_proof(o,7)>h

irregular_nodes_proof(o,7)=h;

end

end

if r<h

irregular_nodes_proof(o,4)=r;

irregular_nodes_proof(o,5)=r;

irregular_nodes_proof(o,6)=r;

irregular_nodes_proof(o,7)=r;

end

end

end