PART I 2D-IPO's for constant speed Lines, Curves, NURBS

Corrected version of 19-12-10 (YR-Month-Day) of Part I 2D IPO's for constant speed Lines, Curves, NURBS.<br>Mainly corrected typos and some clearer formulations.<div>The manuscript (44 pages) “Constant Speed Lines – Curves – NURBS Reference Pulse IPOs (Part I)” of Valere Huypens has been accepted for publication in “The International Journal of Advanced Manufacturing Technology” of Springer<br></div>

PART I 2D-IPO's for constant speed Lines, Curves, NURBS

Corrected version of 19-12-10 (YR-Month-Day) of Part I 2D IPO's for constant speed Lines, Curves, NURBS.<br>Mainly corrected typos and some clearer formulations.<div>The manuscript (44 pages) “Constant Speed Lines – Curves – NURBS Reference Pulse IPOs (Part I)” of Valere Huypens has been accepted for publication in “The International Journal of Advanced Manufacturing Technology” of Springer<br></div>

2D IPO's for Constant Speed Lines, Curves, NURBS

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

2D IPO's for Constant Speed Lines, Curves, NURBS

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