Mumbai University > mechanical engineering > Sem 7 > CAD/CAM/CAE

Marks: 8 Marks

Year: Dec 2015

Parametric:

The coordinates of points of a parametric curve are expressed as functions of a variable or parameter such as t. A curve in the plane has the form C(t) = (x(t), y(t)), and a curve in space has the form C(t) = (x(t), y(t), z(t)). The functions x(t), y(t) and z(t) are called the coordinates functions. The image of C(t) is called the trace of C, and C(t) is called a parametrization of C. A subset of a curve C which is also a curve is called a curve segment. A parametric curve defined by polynomial coordinate function is called a polynomial curve. The degree of a polynomial curve is the highest power of the variable occurring in any coordinate function. A function p(t)/q(t) is said to be rational if p(t) and q(t) are polynomials. A parametric curve defined by rational coordinate functions is called a rational curve. The degree of a rational curve is the highest power of the variable occurring in the numerator or denominator of any coordinate function. Most of the curves considered in this book are parametric.

Non-parametric explicit:-

The coordinates (x, y) of points of a no parametric explicit planner curve satisfy y = f(x) or x = g(y). Such curve have the parametric form C(t) = (t, f(t)) or C(t) = (g(t), t). For non-parametric explicit spatial curves, two of the coordinates are expressed in terms of the third : for instance, x = f(z), y = g(z).