Construction and smoothing of triangular Coons patches with geodesic boundary curves

2010 ◽  
Vol 27 (4) ◽  
pp. 301-312 ◽  
Author(s):  
R.T. Farouki ◽  
N. Szafran ◽  
L. Biard
Keyword(s):  
Geodesic Boundary ◽  
Boundary Curves

Existence conditions for Coons patches interpolating geodesic boundary curves

2009 ◽  
Vol 26 (5) ◽  
pp. 599-614 ◽  
Author(s):  
R.T. Farouki ◽  
N. Szafran ◽  
L. Biard
Keyword(s):  
Geodesic Boundary ◽  
Existence Conditions ◽  
Boundary Curves

Derivation of Decision Boundaries for Left-Turn Treatments at Signalized Intersections

2017 ◽  
Vol 2620 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Andrew Raessler ◽  
Jidong J. Yang
Keyword(s):  
Decision Making ◽  
Signalized Intersections ◽  
Maintenance Costs ◽  
Left Turn ◽  
Practical Guidelines ◽  
Decision Boundaries ◽  
Boundary Curves ◽  
Benefits And Costs

A new methodology is proposed to establish practical guidelines for four incremental left-turn treatments: ( a) permissive single left-turn lane, ( b) protected–permissive single left-turn lane, ( c) protected dual left-turn lanes with equal lane use, and ( d) protected dual left-turn lanes with unequal lane use. Decision boundaries were derived from the equilibrium at which the delays of two incremental treatments were equal. The benefits and costs associated with different left-turn treatments—including safety impact and construction and maintenance costs—also were considered. These benefits and costs effectually shift the boundary curves for more realistic decision making.

scholarly journals Edge detection with trigonometric polynomial shearlets

2021 ◽  
Vol 47 (1) ◽  
Author(s):  
Kevin Schober ◽  
Jürgen Prestin ◽  
Serhii A. Stasyuk
Keyword(s):  
Edge Detection ◽  
Trigonometric Polynomial ◽  
Two Dimensions ◽  
Characteristic Functions ◽  
Numerical Examples ◽  
Special Cases ◽  
Periodic Characteristic ◽  
Boundary Curves ◽  
Theoretical Results ◽  
De La Vallée Poussin

AbstractIn this paper, we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vallée Poussin-type wavelets are able to detect step discontinuities along boundary curves of periodic characteristic functions. Motivated by recent results for discrete shearlets in two dimensions, we provide lower and upper estimates for the magnitude of the corresponding inner products. In the proof, we use localization properties of trigonometric polynomial shearlets in the time and frequency domain and, among other things, bounds for certain Fresnel integrals. Moreover, we give numerical examples which underline the theoretical results.

Approximate Degree Reduction of NURBS Curves and Surfaces: An Integrated Approach

1994 ◽  
Author(s):  
Srinivasa P. Varanasi ◽  
Athamaram H. Soni
Keyword(s):  
Shape Control ◽  
Data Exchange ◽  
Data Transfer ◽  
Integrated Approach ◽  
Free Form ◽  
Aircraft Industry ◽  
Trimmed Surfaces ◽  
Curves And Surfaces ◽  
High Degree ◽  
Boundary Curves

Abstract Data exchange between different CAD systems usually requires conversion between different representations of free-form curves and surfaces. Also, trimmed surfaces give rise to high degree boundary curves. Accurate conversion of these forms becomes necessary for reliable data transfer. Also important is the issue of shape control, specially in the aircraft industry. The objective of this paper is to investigate conversion methods and effect of shape control on the design and choice of such methods.

Constrained Shape Scaling of Trimmed NURBS Surfaces

1999 ◽  
Author(s):  
Pifu Zhang ◽  
Caiming Zhang ◽  
Fuhua (Frank) Cheng
Keyword(s):  
Data Exchange ◽  
Surface Deformation ◽  
Current Data ◽  
Free Form ◽  
Test Results ◽  
Nurbs Surface ◽  
Curvature Distribution ◽  
The Given ◽  
Boundary Curves

Abstract A method to scale and deform a trimmed NURBS surface while holding the shape and size of specific features (trimming curves) unchanged is presented. The new surface is formed by scaling the given surface according to the scaling requirement first; and then attaching the (original) features to the scaled NURBS surface at appropriate locations. The attaching process requires several geometric operations and constrained free-form surface deformation. The resulting surface has the same features as the original surface and same boundary curves as the scaled surface while reflecting the shape and curvature distribution of the scaled surface. This is achieved by minimizing a shape-preserving objective function which covers all the factors in the deformation process such as bending, stretching and spring effects. The resulting surface maintains a NURBS representation and, hence, is compatible with most of the current data-exchange standards. Test results on several car parts with trimming curves are included. The, quality of the resulting surfaces is examined using the highlight line model.

Scattering of a Plane Elastic Wave From Objects Near an Interface

1972 ◽  
Vol 39 (4) ◽  
pp. 1019-1026 ◽  
Author(s):  
Stephen B. Bennett
Keyword(s):  
Elastic Wave ◽  
Electromagnetic Waves ◽  
Three Dimensions ◽  
Circular Cylinders ◽  
Scattering Problems ◽  
Reflection And Refraction ◽  
Time Harmonic ◽  
Incident Plane ◽  
Boundary Curves ◽  
Consistent Formulation

The displacement field generated by the reflection and refraction of plane (time harmonic) elastic waves by finite obstacles of arbitrary shape, in the neighborhood of a plane interface between two elastic media, is investigated. The technique employed allows a consistent formulation of the problem for both two and three dimensions, and is not limited either to boundary shapes which are level surfaces in appropriate coordinate systems, i.e., circular cylinders, spheres, etc., or to closed boundary curves or surfaces. The approach is due to Twersky, and has been applied to many problems of the scattering of electromagnetic waves. The method consists of expressing the net field due to all multiple scattering in terms of the field reflected from each boundary in isolation when subjected to an incident plane elastic wave. Thus the technique makes use of more elemental scattering problems whose solutions are extant. By way of illustration, a numerical solution to the scattering of a plane elastic wave by a rigid circular cylindrical obstacle adjacent to a plane free surface is considered.

scholarly journals Using Dielectric Relaxation Spectroscopy to Characterize the Glass Transition and Onset of Crystallinity of Skim-Milk Powder

2018 ◽  
Author(s):  
Martin G. Buehler
Keyword(s):  
Glass Transition ◽  
Shelf Life ◽  
Dielectric Relaxation ◽  
Loss Tangent ◽  
Milk Powder ◽  
Skim Milk ◽  
Skim Milk Powder ◽  
Dielectric Relaxation Spectroscopy ◽  
Scanning Calorimetry ◽  
Boundary Curves

This paper describes the dielectric relaxation spectroscopy (DRS) method for obtaining glass transition temperature and the onset of crystallinity of skim milk powder (SMP). The methodology consists of exposing SMP samples to numerous constant temperatures, T, and water activities, aw, and measuring the relaxation time. Measurements are based on changes in the loss-tangent height at its peak frequency. Glass transition times are identified at peaks in the loss-tangent height versus time curve and the onset of crystallinity times are identified when the loss-tangent height collapses. The analysis leads to two boundary curves: glass transition Tg, aw curve and the onset of crystallinity Tc, aw curve. They separate the SMP stable (long shelf life) and unstable (short shelf life) regions. Two curve fitting algorithms were developed for (a) aw2, tg curve where tg is the time to glass transition and aw2, tc curve where time tc is the time to onset of crystallinity and (b) Tg, aw and Tc, aw boundary curves. Finally, the DRS data are compared to differential scanning calorimetry (DSC) results.

Smooth geometry generation in additive manufacturing file format: problem study and new formulation

2017 ◽  
Vol 23 (1) ◽  
pp. 34-43 ◽  
Author(s):  
Kai-Ming Yu ◽  
Yu Wang ◽  
Charlie C.L. Wang
Keyword(s):  
Additive Manufacturing ◽  
Design Methodology ◽  
Hermite Interpolation ◽  
File Format ◽  
Opposite Edge ◽  
Standard Specification ◽  
Content Type ◽  
New Formulation ◽  
Boundary Curves ◽  
Boolean Sum

Purpose In the newly released ASTM standard specification for additive manufacturing file (AMF) format – version 1.1 – Hermite curve-based interpolation is used to refine input triangles to generate denser mesh with smoother geometry. This paper aims to study the problems of constructing smooth geometry based on Hermite interpolation on curves and proposes a solution to overcome these problems. Design/methodology/approach A formulation using triangular Bézier patch is proposed to generate smooth geometry from input polygonal models. Different configurations on the boundary curves in the formulation are analyzed to further enrich this formulation. Findings The study shows that the formulation given in the AMF format (version 1.1) can lead to the problems of inconsistent normals and undefined end-tangents. Research limitations/implications The scheme has requirements on the input normals of a model, only C0 interpolation can be generated on those cases with less-proper input. Originality/value To overcome the problems of smooth geometry generation in the AMF format, the authors propose an enriched scheme for computing smooth geometry by using triangular Bézier patch. For the configurations with less-proper input, the authors adopt the Boolean sum and the Nielson’s point-opposite edge interpolation for triangular Coons patch to generate the smooth geometry as a C0 interpolant.

scholarly journals The simplicial volume of hyperbolic manifolds with geodesic boundary

2010 ◽  
Vol 10 (2) ◽  
pp. 979-1001 ◽  
Author(s):  
Roberto Frigerio ◽  
Cristina Pagliantini
Keyword(s):  
Hyperbolic Manifolds ◽  
Geodesic Boundary ◽  
Simplicial Volume
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