Comparison of algorithms for converting 3D objects into rolls, using a spiral coordinate system

Abstract

The definition of a point’s location in volume by Cartesian, spherical and cylindrical coordinate systems requires three dimensions (x, y, z), (r, θ, ϕ) and (ρ, ϕ, z) accordingly. It is obvious that superfluity, only two dimensions and the constant (a point’s height or plane thickness) are enough because, when the plane is transformed into a roll, the third dimension appears. It is easy to convert a three-dimensional space to a two-dimensional one if you know the thickness of the spatial layer and the equation of equivalence between 3D and 2D spaces. This work discusses several advantages of conformal transformation methods to convert different volume objects into a ribbon, based on its symmetry and the spiral coordinate system for roll powder sintering (RPS) [Shulunov, V.R., 2014. A high performance, high precision, low cost rapid prototyping and manufacturing technology. AUSMT Copyright ©. International Journal of Automation Smart Technology, 4 (3). doi:10.5875/ausmt.v4i3.718, Shulunov, V.R., 2015a. A roll powder sintering additive manufacturing technology. Applied Mechanics and Materials, 789–790, 1212–1216. © Trans Tech Publications, Switzerland. doi:10.4028/www.scientific.net/AMM.789-790.1212, Shulunov, V.R., 2015b. Several advantages of the ultra high-precision additive manufacturing technology, © Springer-Verlag London. International Journal of Advance Manufacturing Technology. doi:10.1007/s00170-015-7533-0] additive manufacturing technology. RPS requires slicing a 3D object with Archimedes spiral scanning. The proposed methods can be used to transform 3D objects into 2D objects.

Keywords

• three-dimensional printing
• 3d graphics and realism
• three-dimensional