11.2: Presenting Results with Visualization, an overview

11.2.1 Plotting Functions and other Curves

Mathematically speaking, we often this about functions. However, functions can take on many forms including:

• functions of one variable–plots of this are often function plots with the independent variable on the horizontal axis and function values on the vertical. We saw such function graphs above.

• parametric functions (vector functions in 2D). These are functions in which the x and y variables depend on a parameter (often t or θ). We will see how to plot this in section XXX

• implicit curves .An implicit curve is the set of points $(x,y)$ in which $f(x,y)=0$.The classic example is the circle
  

  $$x^2+y^2=1$$
  which can be written in the form f (x, y) = 0 by subtracting 1 from both sides.

• functions of two variables. These often have the form:
  

  $$z = f(x,y)$$
  and that the two independent variables are x and y and the third variable is the height of the function. There are at least three standard ways of representing such a function:

  • surface plots as in section 11.3.3 which is a 3D rendering of the surface

  • contour plots (section ??), which generates a curve in the plane for a given

    number of heights.

  • heatmaps (section??) which gives a color representing the height of the function.

  • Vector Functions in 3D are often represented as parametric functions of the form:
    

    $$\langle x(t),y(t),z(t) \rangle$$
    where each function gives the $x, y$ or $z$ coordinate at a time $t$. Examples of this are in section XXX