Surface Remeshing on Triangular Domain for CAD Applications

Four new quartic rational Said-Ball-like basis functions, which include the cubic Said-Ball basis functions as a special case, are constructed in this paper. The new basis is applied to generate a class ofC1continuous quartic rational Hermite interpolation splines with local tension shape parameters. The error estimate expression of the proposed interpolant is given and the sufficient conditions are derived for constructing aC1positivity- or monotonicity- preserving interpolation spline. In addition, we extend the quartic rational Said-Ball-like basis to a triangular domain which has three tension shape parameters and includes the cubic triangular Said-Ball basis as a special case. In order to compute the corresponding patch stably and efficiently, a new de Casteljau-type algorithm is developed. Moreover, theG1continuous conditions are deduced for the joining of two patches.

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High precision calibration of line structured light sensors based on linear transformation over triangular domain

10.1117/12.2242945 ◽

2016 ◽

Cited By ~ 1

Author(s):

Yuehua Li ◽

Jingbo Zhou ◽

Fengshan Huang

Keyword(s):

High Precision ◽

Linear Transformation ◽

Structured Light ◽

Triangular Domain

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Hexagonal pyramid algorithm over a triangular domain

Graphical Models ◽

10.1016/j.gmod.2018.10.001 ◽

2018 ◽

Vol 100 ◽

pp. 51-60

Author(s):

Wanqiang Shen ◽

Guozhao Wang ◽

Yang Yang ◽

Aihua Hu

Keyword(s):

Triangular Domain ◽

Hexagonal Pyramid

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REFLECTIONS ON THE HYPERBOLIC PLANE

International Journal of Modern Physics D ◽

10.1142/s0218271813500855 ◽

2013 ◽

Vol 22 (14) ◽

pp. 1350085

Author(s):

ORCHIDEA MARIA LECIAN

Keyword(s):

Physical Interpretation ◽

Hyperbolic Plane ◽

Einstein Equations ◽

Billiard Table ◽

Billiard Ball ◽

Cosmological Singularity ◽

Triangular Domain ◽

Quantum Properties ◽

Poincaré Return Map

The most general solution to the Einstein equations in 4 = 3 + 1 dimensions in the asymptotic limit close to the cosmological singularity under the BKL (Belinskii–Khalatnikov–Lifshitz) hypothesis can be visualized by the behavior of a billiard ball in a triangular domain on the Upper Poincaré Half Plane (UPHP). The billiard system (named "big billiard") can be schematized by dividing the successions of trajectories according to Poincaré return map on the sides of the billiard table, according to the paradigms implemented by the BKL investigation and by the CB–LKSKS (Chernoff–Barrow–Lifshitz–Khalatnikov–Sinai–Khanin–Shchur) one. Different maps are obtained, according to different symmetry-quotienting mechanisms used to analyze the dynamics. In the inhomogeneous case, new structures have been uncovered, such that, in this framework, the billiard table (named "small billiard") consists of 1/6 of the previous one. The connections between the symmetry-quotienting mechanisms are further investigated on the UPHP. The relation between the complete billiard and the small billiard are also further explained according to the role of Weyl reflections. The quantum properties of the system are sketched as well, and the physical interpretation of the wave function is further developed. In particular, a physical interpretation for the symmetry-quotienting maps is proposed.

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Valence optimization and angle improvement for molecular surface remeshing

The Visual Computer ◽

10.1007/s00371-020-01967-6 ◽

2020 ◽

Vol 36 (10-12) ◽

pp. 2355-2368

Author(s):

Dawar Khan ◽

Alexander Plopski ◽

Yuichiro Fujimoto ◽

Masayuki Kanbara ◽

Zhanglin Cheng ◽

...

Keyword(s):

Molecular Surface ◽

Surface Remeshing

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An improved implementation of triangular-domain basis functions for the analysis of microstrip interconnects

Journal of Electromagnetic Waves and Applications ◽

10.1163/156939394x00560 ◽

1994 ◽

Vol 8 (6) ◽

pp. 779-795 ◽

Cited By ~ 2

Author(s):

C.H. Chan ◽

R.A. Kipp

Keyword(s):

Basis Functions ◽

Triangular Domain

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Triangular Surface Patch Based on Bivariate Meyer-König-Zeller Operator

Open Mathematics ◽

10.1515/math-2019-0021 ◽

2019 ◽

Vol 17 (1) ◽

pp. 282-296 ◽

Cited By ~ 2

Author(s):

Guorong Zhou ◽

Qing-Bo Cai

Keyword(s):

Convex Hull ◽

Curve Surface ◽

Surface Modeling ◽

Modeling Method ◽

Basis Functions ◽

Surface Patch ◽

Affine Invariance ◽

Triangular Domain ◽

Probability Operators ◽

The Relationship

Abstract Based on the relationship between probability operators and curve/surface modeling, a new kind of surface modeling method is introduced in this paper. According to a kind of bivariate Meyer-König-Zeller operator, we study the corresponding basis functions called triangular Meyer-König-Zeller basis functions which are defined over a triangular domain. The main properties of the basis functions are studied, which guarantee that the basis functions are suitable for surface modeling. Then, the corresponding triangular surface patch called a triangular Meyer-König-Zeller surface patch is constructed. We prove that the new surface patch has the important properties of surface modeling, such as affine invariance, convex hull property and so on. Finally, based on given control vertices, whose number is finite, a truncated triangular Meyer-König-Zeller surface and a redistributed triangular Meyer-König-Zeller surface are constructed and studied.

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Spin lattices, state transfer, and bivariate Krawtchouk polynomials

Canadian Journal of Physics ◽

10.1139/cjp-2014-0568 ◽

2015 ◽

Vol 93 (9) ◽

pp. 979-984 ◽

Cited By ~ 2

Author(s):

Vincent X. Genest ◽

Hiroshi Miki ◽

Luc Vinet ◽

Alexei Zhedanov

Keyword(s):

Three Dimensional ◽

Rotation Group ◽

Matrix Elements ◽

Quantum State Transfer ◽

Krawtchouk Polynomials ◽

Triangular Domain ◽

State Transfer ◽

Exactly Solvable ◽

Spin Lattices ◽

Transfer Properties

The quantum state transfer properties of a class of two-dimensional spin lattices on a triangular domain are investigated. Systems for which the 1-excitation dynamics is exactly solvable are identified. The exact solutions are expressed in terms of the bivariate Krawtchouk polynomials that arise as matrix elements of the unitary representations of the rotation group on the states of the three-dimensional harmonic oscillator.

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