Increase in the measurement of the normal vectors of an aspherical surface used in deflectometry

2017 ◽  
Author(s):  
Diana Castán-Ricaño ◽  
Fermín S. Granados-Agustín ◽  
E. Percino-Zacarías ◽  
A. Cornejo-Rodríguez
Keyword(s):  
Aspherical Surface ◽  
Normal Vectors

scholarly journals Elastic deformation of the mandibular jaw revisited—a clinical comparison between digital and conventional impressions using a reference

2021 ◽  
Author(s):  
Alexander Schmidt ◽  
Leona Klussmann ◽  
Maximiliane A. Schlenz ◽  
Bernd Wöstmann
Keyword(s):  
Statistical Analysis ◽  
Elastic Deformation ◽  
Clinical Relevance ◽  
Mouth Opening ◽  
Reference Structure ◽  
Intraoral Scanner ◽  
Digital Impressions ◽  
Normal Vectors ◽  
Mandibular Deformation ◽  
Conventional Impression

Abstract Objectives Due to the partly strongly differing results in the literature, the aim of the present study was to investigate a possible deformation of the mandible during mouth opening using an intraoral scanner (IOS) and a conventional impression for comparison with a reference aid. Materials and methods Four steel spheres were reversibly luted in the mandibular (n = 50) with a metallic reference aid at maximum mouth opening (MMO). Two digital impressions (Trios3), at MMO and at slightly mouth opening SMO and a conventional impression (Impregum), were taken as the measuring accuracy of the reference structure was already known. Difference between MMO-SMO for digital impressions and deviations between digital and conventional (SMO) were calculated. Furthermore, the angle between the normal vectors of two constructed planes was measured. Statistical analysis was performed with SPSS25. Results Deviations for linear distances ranged from −1 ± 3 μm up to 17 ± 78 μm (digital impressions, MMO-SMO), from 19 ± 16 μm up to 132 ± 90 μm (digital impressions, SMO), and from 28 ± 17 μm up to 60 ± 52 μm (conventional impressions, SMO). There were no significant differences for digital impressions (MMO-SMO), and there were significant differences between the conventional and digital impressions at SMO. Conclusions Based on the results of the present study, no mandibular deformation could be detected during mouth opening with regard to the digital impressions. The results were rather within the measuring tolerance of the intraoral scanner. Clinical relevance Based on the present study, no deformation of the mandibular during mouth opening could be observed at the level previously assumed. Therewith related, dental techniques related to a possible mandibular deformation therefore should be reconsidered.

A Fast and Rigorously Parallel Surface Voxelization Technique for GPU-Accelerated CFD Simulations

2015 ◽  
Vol 17 (5) ◽  
pp. 1246-1270 ◽  
Author(s):  
C. F. Janßen ◽  
N. Koliha ◽  
T. Rung
Keyword(s):  
Graphics Processing Units ◽  
Parallel Implementation ◽  
Parallel Execution ◽  
Time Step ◽  
Cfd Simulations ◽  
Performance Loss ◽  
Neighbor Search ◽  
Body Shell ◽  
Normal Vectors ◽  
Grid Nodes

AbstractThis paper presents a fast surface voxelization technique for the mapping of tessellated triangular surface meshes to uniform and structured grids that provide a basis for CFD simulations with the lattice Boltzmann method (LBM). The core algorithm is optimized for massively parallel execution on graphics processing units (GPUs) and is based on a unique dissection of the inner body shell. This unique definition necessitates a topology based neighbor search as a preprocessing step, but also enables parallel implementation. More specifically, normal vectors of adjacent triangular tessellations are used to construct half-angles that clearly separate the per-triangle regions. For each triangle, the grid nodes inside the axis-aligned bounding box (AABB) are tested for their distance to the triangle in question and for certain well-defined relative angles. The performance of the presented grid generation procedure is superior to the performance of the GPU-accelerated flow field computations per time step which allows efficient fluid-structure interaction simulations, without noticeable performance loss due to the dynamic grid update.

A Local Approach for Computing Smooth B-spline Surfaces for Arbitrary Quadrilateral Base Meshes

2021 ◽  
pp. 1-28
Author(s):  
Dennis Mosbach ◽  
Katja Schladitz ◽  
Bernd Hamann ◽  
Hans Hagen
Keyword(s):  
Degrees Of Freedom ◽  
Tangent Plane ◽  
Local Approach ◽  
Approximation Process ◽  
Surface Approximation ◽  
B Spline ◽  
Spline Surfaces ◽  
Continuous Surface ◽  
Normal Vectors ◽  
The Individual

Abstract We present a method for approximating surface data of arbitrary topology by a model of smoothly connected B-spline surfaces. Most of the existing solutions for this problem use constructions with limited degrees of freedom or they address smoothness between surfaces in a post-processing step, often leading to undesirable surface behavior in proximity of the boundaries. Our contribution is the design of a local method for the approximation process. We compute a smooth B-spline surface approximation without imposing restrictions on the topology of a quadrilateral base mesh defining the individual B-spline surfaces, the used B-spline knot vectors, or the number of B-spline control points. Exact tangent plane continuity can generally not be achieved for a set of B-spline surfaces for an arbitrary underlying quadrilateral base mesh. Our method generates a set of B-spline surfaces that lead to a nearly tangent plane continuous surface approximation and is watertight, i.e., continuous. The presented examples demonstrate that we can generate B-spline approximations with differences of normal vectors along shared boundary curves of less than one degree. Our approach can also be adapted to locally utilize other approximation methods leading to higher orders of continuity.

Cusping, capture, and breakup of interacting drops by a curvatureless boundary-integral algorithm

1999 ◽  
Vol 391 ◽  
pp. 249-292 ◽  
Author(s):  
ALEXANDER Z. ZINCHENKO ◽  
MICHAEL A. ROTHER ◽  
ROBERT H. DAVIS
Keyword(s):  
Three Dimensional ◽  
Adaptive Mesh ◽  
Boundary Integral ◽  
Small Surface ◽  
Low Viscosity ◽  
Primary Breakup ◽  
Dimensional Boundary ◽  
Normal Vectors ◽  
Passive Technique ◽  
Line Singularities

A three-dimensional boundary-integral algorithm for interacting deformable drops in Stokes flow is developed. The algorithm is applicable to very large deformations and extreme cases, including cusped interfaces and drops closely approaching breakup. A new, curvatureless boundary-integral formulation is used, containing only the normal vectors, which are usually much less sensitive than is the curvature to discretization errors. A proper regularization makes the method applicable to small surface separations and arbitrary λ, where λ is the ratio of the viscosities of the drop and medium. The curvatureless form eliminates the difficulty with the concentrated capillary force inherent in two-dimensional cusps and allows simulation of three-dimensional drop/bubble motions with point and line singularities, while the conventional form can only handle point singularities. A combination of the curvatureless form and a special, passive technique for adaptive mesh stabilization allows three-dimensional simulations for high aspect ratio drops closely approaching breakup, using highly stretched triangulations with fixed topology. The code is applied to study relative motion of two bubbles or drops under gravity for moderately high Bond numbers [Bscr ], when cusping and breakup are typical. The deformation-induced capture efficiency of bubbles and low-viscosity drops is calculated and found to be in reasonable agreement with available experiments of Manga & Stone (1993, 1995b). Three-dimensional breakup of the smaller drop due to the interaction with a larger one for λ=O(1) is also considered, and the algorithm is shown to accurately simulate both the primary breakup moment and the volume partition by extrapolation for moderately supercritical conditions. Calculations of the breakup efficiency suggest that breakup due to interactions is significant in a sedimenting emulsion with narrow size distribution at λ=O(1) and [Bscr ][ges ]5–10. A combined capture and breakup phenomenon, when the smaller drop starts breaking without being released from the dimple formed on the larger one, is also observed in the simulations. A general classification of possible modes of two-drop interactions for λ=O(1) is made.

scholarly journals Stereo Camera Head-Eye Calibration Based on Minimum Variance Approach Using Surface Normal Vectors

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 3706 ◽  
Author(s):  
Joong-Jae Lee ◽  
Mun-Ho Jeong
Keyword(s):  
Vision System ◽  
Real Data ◽  
Humanoid Robots ◽  
Calibration Method ◽  
Minimum Variance ◽  
Kinematic Data ◽  
Stereo Camera ◽  
Surface Normal ◽  
Normal Vectors ◽  
Variance Approach

This paper presents a stereo camera-based head-eye calibration method that aims to find the globally optimal transformation between a robot’s head and its eye. This method is highly intuitive and simple, so it can be used in a vision system for humanoid robots without any complex procedures. To achieve this, we introduce an extended minimum variance approach for head-eye calibration using surface normal vectors instead of 3D point sets. The presented method considers both positional and orientational error variances between visual measurements and kinematic data in head-eye calibration. Experiments using both synthetic and real data show the accuracy and efficiency of the proposed method.

Extracting Geometric Edges from 3D Point Clouds Based on Normal Vector Change

2014 ◽  
Vol 571-572 ◽  
pp. 729-734
Author(s):  
Jia Li ◽  
Huan Lin ◽  
Duo Qiang Zhang ◽  
Xiao Lu Xue
Keyword(s):  
Point Clouds ◽  
Detection Algorithm ◽  
Growth Strategy ◽  
Normal Vector ◽  
Geometric Morphometric ◽  
3D Point Clouds ◽  
Real Scene ◽  
Edge Points ◽  
Normal Vectors ◽  
Change Intensity

Normal vector of 3D surface is important differential geometric property over localized neighborhood, and its abrupt change along the surface directly reflects the variation of geometric morphometric. Based on this observation, this paper presents a novel edge detection algorithm in 3D point clouds, which utilizes the change intensity and change direction of adjacent normal vectors and is composed of three steps. First, a two-dimensional grid is constructed according to the inherent data acquisition sequence so as to build up the topology of points. Second, by this topological structure preliminary edge points are retrieved, and the potential directions of edges passing through them are estimated according to the change of normal vectors between adjacent points. Finally, an edge growth strategy is designed to regain the missing edge points and connect them into complete edge lines. The results of experiment in a real scene demonstrate that the proposed algorithm can extract geometric edges from 3D point clouds robustly, and is able to reduce edge quality’s dependence on user defined parameters.

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