A curve segment is a point bounded collection of points whose coordinates are given by continuous, one-parameter, single-valued mathematical functions of the form.
The parametric value of u is constrained to the interval u Є [0,1]. The curve is bounded between two points at u=0 and the other at u=1.
Any point on the curve can be treated as a component of vector p(u). This p(u) is the vector to the point x(u), y(u), z(u) and pu(u) is the tangent vector to the curve at the same point.
vector components are:
and the tangent vector is:
A simple example of parametric equation of a curve would be a set of linear parametric equations above is gives a straight line starting at Point p(0) = [a b c] and ending at point p(1) = [(a + l) (b + m) (c + n)] where a, b, c and l, m, n are constants. The direction cosines of the line would be proportional to l, m, n.