Page: Curves and Types of curve
0

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.