As mentioned in the discussion of boundary representations, each face is
surrounded by edges, which could be line segments or curve segments, and
the face itself is part of a surface (*i.e.*, a surface patch).
In this unit, we shall discuss the general concept of curve segments
in parametric form.

A *parametric curve* in space has the following form:

wheref: [0,1] -> (f(u),g(u),h(u) )

In this course, functions *f*(), *g*() and *h*() are always
polynomials.

Note that if function *h*() is removed from the definition of
**f**(), **f**() has two coordinate components and becomes a
curve in the coordinate plane.

- We have seen that a straight line is defined as
**B**+*t***d**, where**B**is a base point and**d**is a direction vector. Thus, if**f**() is defined as*f*(*u*) =*b*_{1}+*u**d*_{1}

*g*(*u*) =*b*_{2}+*u**d*_{2}

*h*(*u*) =*b*_{3}+*u**d*_{3}

**B**= <*b*_{1},*b*_{2},*b*_{3}>,**d**= <*d*_{1},*d*_{2},*d*_{3}>, and**f**() is a parametric curve that maps [0,1] to the line segment between**B**and**B+d**, inclusive. - A circle has the following non-polynomial form:
*x*(*u*) =*r*cos(2*PI**u*) +*p*

*y*(*u*) =*r*sin(2*PI**u*) +*q*

*p*,*q*) and radius*r*. Since the parameter*u*is in [0,1], the value of 2*PI**u*is in [0,2*PI] (*i.e.*, from 0 degree to 360 degree).Let us eliminate

*u*. First, change the above equations to the following. For convenience, we drop (*u*) from*x*(*u*) and*y*(*u*).*x*-*p*=*r*cos(2*PI**u*)

*y*-*q*=*r*sin(2*PI**u*)

(

Thus, it shows that the given parametric curve is indeed a circle with center at (*x - p*)^{2}+ (*y - q*)^{2}=*r*^{2}*p*,*q*) and radius*r*. - A space cubic curve has the following form:
*f*(*u*) =*u*

*g*(*u*) =*u*^{2}

*h*(*u*) =*u*^{3} - The circular helix is defined as follows:
**f**(*u*) = (*a*cos(*u*),*a*sin(*u*),*bu*)*a*, 0, 0) and the endpoint is (*a*, 0,*b**4*PI). Note that this curve lies on the cylinder of radius*a*and axis the*z*-axis.