Drawing a Bezier Patch with DirectX

What Is a Polynomial?

I have defined a curve as the graph of a function, so I should begin by defining a polynomial function.

At this point, even my chance of receiving Christmas cards from the mathematicians is pretty low. To put it another way, this means it takes the following form:

Definition

An nth degree polynomial function is defined as a series of n powers of one or more variables multiplied by constant coefficients.

 

(1.1) The form of a polynomial function with a single variable. 

This shows that the degree of the polynomial is the value of the highest exponent. Remember, some of the coefficients can be zero; this does not affect the degree. Therefore, the two following equations are both fourth-degree polynomials .

(1.2) Two equations of the same degree but different numbers of terms. 

According to my definitions, a polynomial curve is a graph of a polynomial function. The remainder of the chapters will focus on the properties of curves of different degrees. The simplest polynomial function is a first-degree polynomial known to its friends as a line.