Project structure

main.jl

This is the file that should be run to the the experiment. No console parameters are required. It is divided into:

• A synthetic data generation step at the start where cylinder of random transform (or identity for testing) and radiuses are generated
• Then a fictitious camera is created
• The relative quadrics, dual quadrics, singular points, planes, points are projected into conics, dual conics, etc
• A function to find a cylinder silhouette is declared and is used to find the lines defining it for each cylinder. Those are used both for visualization and for solving the problem
• A visualization step where the 3D scene is show on the left and the projected scene seen throug the camera is shown on the right
• The solver part:
  • We pick 3 lines (the minimum) from the ones that we found for the silhouettes
  • A parametrization of the rotation matrix using only linear equations in R is defined and solved for using (11)
  • Once the rotation is found the same thing is done for the translation using the original dual quadric

asserts are placed inside a begin - end block so they can be collapsed in the editor when not used

cylinder.jl

Definitions of factory methods for quadrics creation from full parameter definitions, or randomly generatered ones

camera.jl

Factory methods to generate camera matrices

space.jl

Type definitions and factory methods for low level primitives related to 3D objects

plotting.jl

Functions to plot points, lines, cylinders, conics onto the figure of Makie.jl

fromMatrixToFormula.jl

A tool for converting from matrix or vector form to equations in x, y, z to be plotted on external online tools for debugging

debug.jl

Functions used only during debugging like extra plotting or extra steps

utils.jl

Definition of functions for random generation of data and notably of the ≃ "almost equal" sign used in a similar way of the ≈ approximate sign but with a precision that does not the depend of the machine epsilon but is manually choosed depending on the problem at hand

docker-compose.yml

A docker compose for a julia environment that stays up and to which you can connect to to run and test the code

camera.stl / camera.blend

A 3d model of a camera used for visualziation