这可以做的工作..
t = 0:4/5*pi:4*pi;
x = sin(t);
y = cos(t) ;
y = y-mean(y);
x = x-mean(x); % # barycentric coordinates
% # rotation and translation
trasl = @(dx,dy) [dy; dx]; % # this vector will be rigidly added to each point of the system
rot = @(theta) [cos(theta) -sin(theta); sin(theta) cos(theta)]; % # this will provide rotation of angle theta
for i = 1:50
% # application of the roto-translation
% # a diagonal translation of x = i*.1 , y = i*.1 is added to the star
% # once a rotation of angle i*pi/50 is performed
x_t = bsxfun(@plus,rot(i*pi/50)*([x;y]), trasl(i*.1,i*.1) );
star = plot(x_t(1,:), x_t(2,:));
axis([-1 11 -1 11])
pause(.1)
end
原则上,齐次坐标(在这种情况下是2D 投影空间)允许人们以更简洁的方式完成相同的工作;事实上,他们只允许使用一个线性算子(3x3 矩阵)。
齐次坐标版本:
Op = @(theta,dx,dy) [ rot(theta) , trasl(dx,dy) ; 0 0 1];
for i = 1:50
x_t = Op(i*pi/50,i*.1,i*.1)*[x;y;ones(size(x))];
star = plot(x_t(1,:), x_t(2,:));
axis([-1 11 -1 11])
pause(.1)
end