Planar Shape Interpolation Based On Teichmüller Mapping

2016 ◽  
Vol 35 (7) ◽  
pp. 43-56 ◽  
Author(s):  
Xianshun Nian ◽  
Falai Chen
Keyword(s):  
Planar Shape ◽  
Shape Interpolation ◽  
Teichmüller Mapping

Planar shape interpolation with bounded distortion

2013 ◽  
Vol 32 (4) ◽  
pp. 1-12 ◽  
Author(s):  
Renjie Chen ◽  
Ofir Weber ◽  
Daniel Keren ◽  
Mirela Ben-Chen
Keyword(s):  
Planar Shape ◽  
Shape Interpolation ◽  
Bounded Distortion

Planar shape interpolation using relative velocity fields

2013 ◽  
Vol 37 (5) ◽  
pp. 364-375 ◽  
Author(s):  
Guiqing Li ◽  
Liang Yang ◽  
Shihao Wu ◽  
Wenshuang Tan ◽  
Xinyu Chen ◽  
...  
Keyword(s):  
Relative Velocity ◽  
Velocity Fields ◽  
Planar Shape ◽  
Shape Interpolation

Teichmuller Geometry

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Uniqueness Theorem ◽  
Existence Theorems ◽  
Quadratic Differentials ◽  
Complex Structures ◽  
Metric Geometry ◽  
Quasiconformal Maps ◽  
Hyperbolic Structures ◽  
Teichmüller Metric ◽  
Uniqueness And Existence ◽  
Teichmüller Mapping

This chapter focuses on the metric geometry of Teichmüller space. It first explains how one can think of Teich(Sɡ) as the space of complex structures on Sɡ. To this end, the chapter defines quasiconformal maps between surfaces and presents a solution to the resulting Teichmüller's extremal problem. It also considers the correspondence between complex structures and hyperbolic structures, along with the Teichmüller mapping, Teichmüller metric, and the proof of Teichmüller's uniqueness and existence theorems. The fundamental connection between Teichmüller's theorems, holomorphic quadratic differentials, and measured foliations is discussed as well. Finally, the chapter describes the Grötzsch's problem, whose solution is tied to the proof of Teichmüller's uniqueness theorem.

Part-based data-driven 3D shape interpolation

2021 ◽  
Vol 136 ◽  
pp. 103027
Author(s):  
Melike Aydınlılar ◽  
Yusuf Sahillioğlu
Keyword(s):  
Data Driven ◽  
3D Shape ◽  
Shape Interpolation

scholarly journals Active palpation underlying shape perception is shaped by physiological thresholds and experience

2020 ◽  
Author(s):  
Neomi Mizrachi ◽  
Guy Nelinger ◽  
Ehud Ahissar ◽  
Amos Arieli
Keyword(s):  
High Speed ◽  
Shape Perception ◽  
Tactile Perception ◽  
Hand Movements ◽  
Hand Tracking ◽  
Experimental Session ◽  
Temporal Adaptation ◽  
Planar Shape ◽  
Contour Following ◽  
Human Participants

ABSTRACTHand movements are essential for tactile perception of objects. However, why different individuals converge on specific movement patterns is not yet clear. Focusing on planar shape perception, we tracked the hands of 11 participants while they practiced shape recognition. Our results show that planar shape perception is mediated by contour-following movements, either tangential to the contour or spatially-oscillating perpendicular to it, and by scanning movements, crossing between distant parts of the shapes’ contour. Both strategies exhibited non-uniform coverage of the shapes’ contours. We found that choice of strategy during the first experimental session was strongly correlated with two idiosyncratic parameters: participants with lower tactile resolution tended to move faster; and faster-adapting participants tended to employ oscillatory movements more often. In addition, practicing on isolated geometric features increased the tendency to use the contour-following strategy. These results provide insights into the processes of strategy selection in tactile perception.SIGNIFICANCE STATMENTHand movements are integral components of tactile perception. Yet, the specific motion strategies used to perceive specific objects and features, and their dependence on physiological features and on experience, are understudied. Focusing on planar shape perception and using high-speed hand tracking we show that human participants employ two basic palpation strategies: Contour-following and scanning. We further show that the strategy chosen by each participant and its kinematics depend strongly on the participant’s physiological thresholds – indicative of spatial resolution and temporal adaptation - and on their perceptual experience.

scholarly journals Kinematic synthesis of planar, shape-changing, rigid body mechanisms for design profiles with significant differences in arc length

2013 ◽  
Vol 70 ◽  
pp. 425-440 ◽  
Author(s):  
Shamsul A. Shamsudin ◽  
Andrew P. Murray ◽  
David H. Myszka ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Arc Length ◽  
Kinematic Synthesis ◽  
Planar Shape

scholarly journals Interactive Shape Interpolation through Controllable Dynamic Deformation

2011 ◽  
Vol 17 (7) ◽  
pp. 983-992 ◽  
Author(s):  
Jin Huang ◽  
Yiying Tong ◽  
Kun Zhou ◽  
Hujun Bao ◽  
Mathieu Desbrun
Keyword(s):  
Dynamic Deformation ◽  
Shape Interpolation

A multiobjective sensor placement optimization for SHM systems considering Fisher information matrix and mode shape interpolation

2018 ◽  
Vol 35 (2) ◽  
pp. 519-535 ◽  
Author(s):  
Guilherme Ferreira Gomes ◽  
Fabricio Alves de Almeida ◽  
Patricia da Silva Lopes Alexandrino ◽  
Sebastiao Simões da Cunha ◽  
Bruno Silva de Sousa ◽  
...  
Keyword(s):  
Fisher Information ◽  
Mode Shape ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Sensor Placement ◽  
Placement Optimization ◽  
Sensor Placement Optimization ◽  
Shape Interpolation
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