# Is this valid parametric equation to create control points for a helix in 3D space?

Is this a valid way to compute new points that are on a helix and if not what is it wrong?

The Cartesian coordinates of each new helix control point could be described by the following parametrization:

$x (u)= a n_x u + p_x + b((1- \cos{(u\theta)})/ \theta)$
$y (u)= an_y u + p_y + b(\sin{(u\theta)}/ \theta)$
$z (u)= a n_z u + p_z + u$

where $a$ is the length of the helix, $u$ is in $[0,a)$, $(p_x, p_y, p_z)$ is a given center of a triangle in 3D space, $(n_x, n_y, n_z)$ is the normal of the given center in the triangle, $b$ is the radius of the helix and $\theta$ controls the frequency of the helix's curls.

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 why do you make x(u) equal 2 different things? – Jorge Fernández Jul 18 '12 at 23:25 @ChuckFernández: I think that was a simple typo; fixed now. – David Cary Jul 19 '12 at 1:05

Why don't you just make it $x(u)= a+m(\cos(u)),$ $y(u)=b+n(\sin(u))$ and $z(u)=k*u$?