What is your favorite color?
The color of fresh air.
By the way, do you use Sage and POV-Ray tracer?
No, but I know Sage and POV-Ray are great free tools.
How do you trace the curve in order to plot the distances corresponding to θ?
I don't need to trace the curve in order to plot it. The software do the work for me.
If you use Graph or gnuplot, you can see this page for examples of parametric plots.
Graph can help you trace parametric curves. Select the parametric function you want
to evaluate or trace, and then press Ctrl+E. See this page for more details.
What is your favorite color?
By the way, do you use Sage and POV-Ray tracer? If you use any ray-tracer, then which is your favorite?
]]>Did you plot both y with θ and x with θ? For example, in your first plot, the blue curve was the distance along the x axis for corresponding values of θ, and the red curve was for distance along y axis?
Yes, blue for x and red for y.
The function used in the first two plots is y = sin(x).
The equation of the monster in the third image is here.
The ring of green circles in the last image can be expressed as follows:
x = cos(t-mod(t,s)) + r*cos(n*mod(t,s))
y = sin(t-mod(t,s)) + r*sin(n*mod(t,s))
r=0.1, n=32, s=2*pi/n,
t=0...2*pi.
Thanks for sharing!
]]>However, they can still be drawn. Are you able to have a computer draw these?
Case 1: Polar functions r = f(θ)
Use a function grapher to plot
y = f(θ)*cos(θ) in θ-y plane.
Case 2: Implicit equations f(x,y) = 0
Use an implicit equation plotter to plot
f(y*cot(θ), y) = 0 & y/sin(θ) > 0 in θ-y plane.
Case 3: Parametric equations (x,y) = (f(t),g(t))
Use a parametric curve plotter to plot
(θ, y) = (atan2(g(t),f(t)), g(t)) in θ-y plane.
Case 4: Functions y = f(x)
Let g(x,y) = y - f(x) and see Case 2
or let (x,y) = (t,f(t)) and see Case 3.
All these cases can be done using Graph or gnuplot.
]]>
I think they can be drawn.
]]>There are still many functions you could do this to where the resulting graph will not be solvable with elementary functions. However, they can still be drawn. Are you able to have a computer draw these?
]]>What I am doing is just taking