11.2: Presenting Results with Visualization, an overview

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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