# Error using surf, X, Y, Z, and C cannot be complex

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Adas Urbonas on 3 Apr 2015
Edited: Thomas Koelen on 3 Apr 2015
i run below code, but get X, Y, Z, and C cannot be complex error, any idea what is wrong?
function simple_math_functions_animation1
clc, close all, clear all
hf1=figure(1);hold on,grid on,axis equal, view([1 -1 1])
set(hf1,'Color','w');set(hf1,'Position',[300, 600, 500, 400]);
xlabel('x');ylabel('y'),zlabel('z');
k=1;
u = linspace(0,2*pi,72);
v = [-3:.2:-1,1:.2:3];
[U,V] = meshgrid(u,v);
r=sqrt((4*V.^-k)./(cos(U).^2+k*sin(U).^2));
X = r.*cos(U);
Y = r.*sin(U);
Z = V;
surf(X,Y,Z,'EdgeColor',[0.5 1. 0.2],'FaceColor',[1 0.2 0.8],'FaceAlpha',0.6);
XYZ=[reshape(X,1,prod(size(X)));
reshape(Y,1,prod(size(Y)));
reshape(Z,1,prod(size(Z)));
ones(1,prod(size(Z)))];
phi=[0 : pi/20 : 50*pi];
h=[]; axis([-20 20 -20 20 -20 20]);
for beta=phi % animation loop *****************
T=[cos(beta) -sin(beta) 0 0; % rotation matrix
sin(beta) cos(beta) 0 0;
0 0 1 0;
0 0 0 1];
XYZ1=T*XYZ; % coordinates changing
X1=reshape(XYZ1(1,:),size(X));Y1=reshape(XYZ1(2,:),size(Y));Z1=reshape(XYZ1(3,:),size(Z));
pause(0.1);if ~isempty(h),delete(h);end
h=surf(X1,Y1,Z1,'EdgeColor',[0.5 1. 0.2],'FaceColor',[0.2 0.2 0.8],'FaceAlpha',0.6);
end % ******************************************
end

Thomas Koelen on 3 Apr 2015
Edited: Thomas Koelen on 3 Apr 2015
you were taking square roots of negative values, thus giving complex values.
r=abs(sqrt((4*V.^-k)./(cos(U).^2+k*sin(U).^2)));
should work