2D IPO's for Constant Speed Lines, Curves, NURBS
preprintposted on 15.11.2019, 01:01 authored by Valere HuypensValere Huypens
Current constant speed IPO's, usually, use Sampled-data IPO's and constant speed lines use the
wrong initialized software DDA-ipo's, which make these IPO's unusable. The Bresenham- and
midpoint IPO's are non-constant speed reference pulse IPO's with bounded inaccuracy.
By adding an ultra-fast 3-lines algorithm "PRM-cs" to the actual midpoint or Bresenham algorithms,
we convert these midpoint-ipo's to very fast, constant speed, reference pulse IPO's.
This applies to 2D-lines, 3D-lines, 2D-curves and 2D-NURBS.
The PRM-cs measures, in real-time, the length of the discrete curve and the PRM-cs is completely new.
We define the best IPO, the major axis principle and the LSD-priority.
The major axis principle holds for the actual 3D-line IPO's. These IPO's are, generally, inaccurate,
but they can be updated to constant speed 3D-line IPO's, when the production manager agrees.
The Digital Geometric Geometry (DAG) defines the discrete lines globally, but this global
definition of a discrete 3D-line, gives discrete 3D-lines whose accuracy is much less than the
accuracy of the best discrete 3D-lines (e.g. 37% worse).
We describe the three causes of the inaccurate (imperfect) discrete 3D-lines.
All existing pulse-rate or PRM-ipo's use a wrong initialization, which deteriorates the accuracy.
We determine the right initialization for the new PRM-cs and the updated PRM-ipo.
We propose the benchmark-ipo "listSIM-ipo". This constant speed IPO can, also, be used in real-
time for every 2D- and 3D-curve.
The 3rd-degree Trident NURB shows that the constant speed reference pulse method is much
better than the existing sampled-data methods.