20.500.12556/RUP-7739 C [sup] 1 Hermite interpolation with spatial Pythagorean-hodograph cubic biarcs In this paper the ▫$C^1$▫ Hermite interpolation problem by spatial Pythagorean-hodograph cubic biarcs is presented and a general algorithm to construct such interpolants is described. Each PH cubic segment interpolates ▫$C^1$▫ data at one point and they are then joined together with a ▫$C^1$▫ continuity at some unknown common point sharing some unknown tangent vector. Biarcs are expressed in a closed form with three shape parameters. Two of them are selected based on asymptotic approximation order, while the remaining one can be computed by minimizing the length of the biarc or by minimizing the elastic bending energy. The final interpolating spline curve is globally ▫$C^1$▫ continuous, it can be constructed locally and it exists for arbitrary Hermite data configurations. V članku je obravnavana ▫$C^1$▫ Hermiteova interpolacija s prostorskimi loki, katerih hodograf je pitagorejski. Opisan je splošen algoritem za njihovo konstrukcijo. Vsak segment loka, ki je sestavljen iz dveh delov, interpolira pozicijo in tangento v robni točki. Segmeta sta v sredini spojena ▫$C^1$▫ gladko. Dobljen lok je podan v zaključeni obliki s tremi prostimi parametri. Dva sta izbrana na podlagi asimptotične analize, tretjega pa izberemo tako, da minimiziramo dolžino loka ali elastično napetostno energijo. Končni rezultat je interpolacijski zlepek, ki ga je mogoče konstruirati lokalno in obstaja za poljubno konfiguracijo podatkov Hermiteovega tipa. mathematics parametric curve PH curve Pythagorean-hodograph Hermite interpolation biarc cubic curve matematika parametrična krivulja PH krivulja pitagorejski hodograh Hermiteova interpolacija lok kubična prostorska krivulja true true false Angleški jezik Angleški jezik Delo ni kategorizirano 2016-04-08 16:47:20 2017-04-03 08:11:13 2024-03-01 13:33:26 0000-00-00 00:00:00 2014 0 0 str. 65-78 Vol. 257 2014 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 0377-0427 519.65 27496960 16726361 http://dx.doi.org/10.1016/j.cam.2013.08.007 1 https://repozitorij.upr.si/Dokument.php?lang=slv&id=7739 Inštitut Andrej Marušič 0 0 0