Question

First order continuity is also called as?

Answer 1

The point of modeling with smooth curves and surfaces is to create realistic smooth shapes. But what exactly do we mean by "smooth"? How precisely do we determine if a given curve or surface is smooth? The simplest way to answer this question is to look at continuity.

Recall that a parametric curve is defined as:

x(s)

y(s)

z(s)

Now the functions x(s) will need to satisfy a lot of geometric constraints typically (think of a curve that represents a hand-written word or a spiral). Rather than trying to do this with a single smooth function, its more often done with many smooth functions (polynomials or rational functions) that are smoothly joined.

Generally a function is smooth if its derivatives are well-defined up to some order. There are actually two definitions for curves and surfaces, depending on whether the curve or surface is viewed as a function or purely a shape.