%5
%#####

function AXspin(matrix,vector)
center = [mean(matrix(1:end-1,1)),mean(matrix(1:end1,2)),mean(matrix(1:end-1,3))];
a = vector(1);
b = vector(2);
c = vector(3);
d = sqrt((b*b)+(c*c));
T = eye(4);
 for i=1:3
 T(4,i) = -center(i);
 end
Rx = eye(4);
Rx(2,2) = c/d;
Rx(2,3) = b/d;
Rx(3,2) = -b/d;
Rx(3,3) = c/d;
Ry = eye(4);
Ry(1,1) = d;
Ry(1,3) = a;
Ry(3,1) = -a;
Ry(3,3) = d;
Rz = eye(4);
Rz(1,1) = c/d;
Rz(2,1) = b/d;
Rz(1,2) = -b/d;
Rz(2,2) = c/d;
Tminus = inv(T);
RxMinus = inv(Rx);
RyMinus = inv(Ry);
Ro = T*Rx*Ry*Rz*RyMinus*RxMinus*Tminus;
figure
drawPlots(matrix);
hold on;
scatter3(center(1),center(2),center(3));
scatter3(center(1),b,center(3));
plot3([center(1),center(1)],[center(2),b],[center(3),center(3)],'r');
matrix = matrix*Ro;
drawPlots(matrix);
hold off;
end


%7
%#######
function transformation(matrix)
center = [mean(matrix(1:end-1,1)),mean(matrix(1:end1,2)),mean(matrix(1:end-1,3))];
T = eye(4);
Tminus = eye(4);
 for i=1:3
 T(4,i) = center(i);
 Tminus(4,i) = -center(i);
 end
S = [0.5,0.5,0.5,0];
figure
drawPlots(matrix);
hold on;
matrix = matrix * T;
vector = eye(4);
 for i=1:3
 vector_two(4,i) = center(i);
 end
matrix = matrix*vector;
matrix = matrix.*S;
OX = eye(4);
angle = degtorad(30);
OX(2,2) = cos(angle);
OX(2,3) = sin(angle);
OX(3,2) = -sin(angle);
OX(3,3) = cos(angle);
matrix = matrix * OX;
matrix = matrix * Tminus;
drawPlots(matrix);
hold off;
end