Constant speed lines–curves—NURBS reference pulse IPOs (part I)

Huypens, Valere

doi:10.1007/s00170-020-05339-1

Cited by 2 publications

(9 citation statements)

References 33 publications

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“…The simplified state diagram computes one perfect major axis point and possibly a perfect nonmajor axis point. Table 4 of [1] indicates that the computation of one best point is not sufficient to generate the perfect 3D-line. The perfect 3D-lines and QSICs RMD algorithms use the simplified state diagram (Table 5) to generate the perfect 26-connected curves.…”

Section: The Simplified State Diagrammentioning

confidence: 99%

“…The calculated length equals LS= 2 Bresenham's algorithm B a is imperfect (due to the major axis algorithm and the projected 3Ddistance) and therefore its accuracy is 37% worse than the accuracy of the perfect IPO R a , but its execution speed is two times faster the RMD algorithm. NPULS equals 120 instead of 121 and the LN TAM [1] kcs TAN [ This small correction has no practical influence on the constant feedrate machining; therefore, the other examples give the small correction without comments.…”

Section: While Loop Of Bresenham's 3d-curve-ipomentioning

confidence: 99%

“…The calculated length equals   [5]] } = { {250, -354, 250}, {250, 354, 250}, {250, -354, -250}, {250, 354, -250} }. The points EG[ [3]] and EG[ [4]] are identical with the singular point EW[ [1]] and are deleted in EG. The segment Segsb equals {EG[ [1]], EW[ [1]] }.…”

Section: Example "B" the Intersection Of The Sphere H1 And The Cylind...mentioning

confidence: 99%

“…The points EG[ [3]] and EG[ [4]] are identical with the singular point EW[ [1]] and are deleted in EG. The segment Segsb equals {EG[ [1]], EW[ [1]] }. The accuracy of Bresenham's algorithm is ~16% worse than the accuracy of the perfect IPO R b , but its execution speed is four times faster than the execution speed of the perfect algorithm.…”

Section: Example "B" the Intersection Of The Sphere H1 And The Cylind...mentioning

confidence: 99%

“…Example "b2" the intersection of the sphere h1 and the cylinder g1 ( = PP = EW[ [1]]={500, 0, 0}. Using the virtual algorithm with startpoint E1 P and monotonic direction x y z {S ,S ,S }=Sign[ EG[ [6]] -EW[ [1]]]={-1,1,1}, the next LSD point is the point S2 P = {500, 1, 1}. So, the new path is Segsb2 equals {EG[ [1]], EW[ [1]] , S2 P , EG[ [6]]}.…”

Section: 3mentioning

confidence: 99%

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Relative Minimum Distance 3D-curve and 3D-Offsets Real Time Constant Feedrate Algorithms

Huypens¹

2022

Preprint

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<p>The constant feedrate 3D RMD algorithms avoid most of the constraints introduced by the sampled-data system (chord error, inaccuracy, jerk). The main bottlenecks were the computations of the intersections (QSICs) of the implicit quadrics, the determination of the candidate point with the minimum distance to the QSIC (the best incremental step), the small execution time per step and the fast determination of the small 3D-offsets.The Twopoint RMD IPO is the extension to implicit polynomials of degree higher than two.</p>

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Section: The Simplified State Diagrammentioning

confidence: 99%

Section: While Loop Of Bresenham's 3d-curve-ipomentioning

confidence: 99%

Section: Example "B" the Intersection Of The Sphere H1 And The Cylind...mentioning

confidence: 99%

Section: Example "B" the Intersection Of The Sphere H1 And The Cylind...mentioning

confidence: 99%

Section: 3mentioning

confidence: 99%

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Relative Minimum Distance 3D-curve and 3D-Offsets Real Time Constant Feedrate Algorithms

Huypens¹

2022

Preprint

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Clarification of the Relative Minimum Distance (RMD) Theorems

Huypens¹

2022

Preprint

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<p>The well-known Bresenham and the midpoint algorithm of Pitteway and Van Aken belong to the RMD algorithms. The RMD theorem proves why they have the highest accuracy and the fastest real time execution time. Nowadays the RMD’s have constant feedrate and they even measure the rounded arclength in real time. That was until now a main property of the Pythagorean-hodograph curves of Farouki, which also have applications in offsetting curves. The RMD algorithms implement the basic offset curves from the connected points, the implementation with the high degree PH-curves is complex. This paper proves that everyone can generate a “classic” OoA error and that everyone can correct that OoA error at an amazingly straightforward way, and furthermore the OoARange is inversely proportional with the rounded radius. Therefore, rejecting RMD algorithms for the sake of OoA is hair-splitting.</p>

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Constant speed lines–curves—NURBS reference pulse IPOs (part I)

Cited by 2 publications

References 33 publications

Relative Minimum Distance 3D-curve and 3D-Offsets Real Time Constant Feedrate Algorithms

Relative Minimum Distance 3D-curve and 3D-Offsets Real Time Constant Feedrate Algorithms

Clarification of the Relative Minimum Distance (RMD) Theorems

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