Welcome to cspiro, a command-line tool for making spirographs. The mathematical basis of the program follows the definitions laid out in the Spirograph Wikipedia page
There are two different drawing modes, spirograph and epicycle. An epicycle is a more general version of a spirograph and gives the user more control, its mathematical basis can be found on the Epicycle Wikipedia page.
Some important definitions:
- C_o : Fixed outer circle.
- C_i : Smaller inner circle that rolls inside C_o without slipping.
- R : Radius of C_o.
- r : Radius of C_i.
- A : Location of the drawing head. Physically, this should be within C_i.
- rho : Distance from A to center of C_i.
- l : Ratio between rho and r. Physically must follow 0<l<1, but mathematically can exceed these bounds. Negative values will result in equivalent spirographs. Values larger than 1 will exceed the size of the output SVG.
- k : Ratio between r and R. Must follow 0<k<1. In order for the spirograph to be periodic (thus not eventually be just a filled disk), this value must be a rational fraction, thus numerator and denominator are input seperatly as integers.
An epicycle is constructed from a set of circles, where the firs circle's center is fixed at the origin and each next circle is connected to a point on the previous circle's circumference. Each circle accepts three variables, the radius, the angular velocity, and the initial rotation.
The program uses CMake for building, once in the project directory use the following commands.
mkdir -p build
cd build
cmake -DCMAKE_BUILD_TYPE=Release ..
cmake --build .
If you want to also have a debug build use -DCMAKE_BUILD_TYPE=Debug instead.
To run the program use .\bin\cspiro.exe (from within the build directory). For the debug build use .\bin\cspiro_debug.exe.
Below the output of the help message.
Usage: cspiro [options]
Options:
-h, --help, -? Print this message and exit.
-x, --no-cli, -? Use app without command line interface. Must specify other arguments.
If previous option is set:
-m, --mode, -? Set drawing mode for the --no-cli option.
int : 0 for spirograph, 1 for epicycle.
If spirograph (see README for detailed description):
float : l, ratio between rho and r.
int : k_n, numerator of k.
int : k_d, denominator of k.
int : precision.
int : size, output SVG size.
If epicycle:
int : n, number of construction circles, must be at least 2.
float,... : radius, comma separated list of circle radii [px], must be of length n.
float,... : speed, comma separated list of circle angular velocities [rad/s], must be of length n.
float,... : angle_i, comma separated list of circle initial angles [rad], must be of length n.
int : size, output SVG size.