In CAD, we often need to draw different types of objects onto the screen. Objects are not flat all the time and we need to draw curves many times to draw an object.

**Types of Curves**

A curve is an infinitely large set of points. Each point has two neighbors except endpoints. Curves can be broadly classified into three categories. Explicit, implicit and parametric curves.

**Implicit Curves:**

Implicit curve representations define the set of points on a curve by employing a procedure that can test to see if a pint in on the curve. Usually, an implicit curve is defined by an implicit function of the form,

$F(x,y) = 0$

It can represent multivalued curves (multiple y values for an x value). A common example is the circle, whose implicit representation is,

$x^2+y^2-R^2$

**Explicit Curves:**

A mathematical function $y = f(x)$ can be plotted as a curve. Such a function is the explicit representation of the curve. The explicit representation is not general, since it cannot represent vertical lines and is also single- valued. For each value of x, only a single value of y is normally computed by the function.

**Parametric Curves:**

Curves having parametric form are called parametric curves. The explicit and implicit curves representation can be used only when the function is known. In practice the parametric curves are used. A two dimensional parametric curves has the following form:

$P(t) = x(t), y(t)$

The points are obtained when the parameter t is varied over a certain interval, normally 0 to 1.