Hi Jay,
In your case, the parameterized helix curve is given by the equations:
t=linspace(0,2*pi,50);
x=cos(t); y=sin(t); z=t;
The tangent direction < u,v,w > at point < x,y,z > can be calculated as the gradient of the above parameterized equations:
u = -sin(t)
v = cos(t)
w = 1
Now, any tangent line on this curve passing through a point < x,y,z > will be in direction of < u,v,w >. This modifies the above equations as follows:
u = x – y
v = y + x
w = z + 1
In order to draw a line passing through a given point < x,y,z > and in the gradient direction, Let s = linspace(-0.75, 0.75, 50).
The following code will draw the tangents at every 10th point on the helix curve:
function tangentCurve
t=linspace(0,2*pi,50);
x=cos(t); y=sin(t); z=t;
figure;
plot3(x,y,z,'r');hold on;
view([2 2 2]); grid on
s = linspace(-0.75, 0.75, 50);
for i = 1:10:length(x)
u=@(s)x(i)-y(i)*s;
v=@(s)y(i)+x(i)*s;
w=@(s)z(i)+1*s;
plot3(u(s),v(s),w(s));
end
end
I hope this helps resolve the issue.
Thanks,
Tushar
