Surface (topology)
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In topology and robotics, a **surface** refers to a two-dimensional manifold — a continuous geometric structure where every point has a neighborhood locally resembling a flat plane, which may be embedded in three-dimensional space. Surfaces can be smooth, curved, or irregular, and are foundational to how robots perceive, model, and interact with the physical world. In robotics and AI, surface representations are central to tasks such as 3D scene reconstruction, terrain mapping, path planning, object grasping, and tactile sensing. Techniques like signed distance functions, neural reconstruction, and multi-level surface maps allow robots to build accurate environmental models from sensor data, enabling navigation over uneven terrain or precise manipulation of complex objects. Surface topology also informs how robots climb walls, sample materials, or machine free-form parts along curved tool paths. Understanding surface geometry — including curvature, continuity, and defect detection — is critical for perception systems that must generalize across diverse real-world environments. As robotic applications demand greater physical autonomy and dexterity, robust surface modeling and analysis remain indispensable across both hardware design and intelligent software systems.
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Electrically driven directional motion of a four-wheeled molecule on a metal surface
Tibor Kudernác, Nopporn Ruangsupapichat, Manfred Parschau, Beatriz Maciá, Nathalie Katsonis, Syuzanna R. Harutyunyan, Karl‐Heinz Ernst, Ben L. Feringa
Citations: 762 • 2011
Image statistics and the perception of surface qualities
Isamu Motoyoshi, Shin’ya Nishida, Lavanya Sharan, Edward H. Adelson
Citations: 611 • 2007
Invariant surface characteristics for 3D object recognition in range images
Paul J. Besl, Ramesh Jain
Citations: 513 • 1986
Toward a Theory of Geometric Tolerancing
Aristides A. G. Requicha
Citations: 383 • 1983
Layered construction for deformable animated characters
Jason Chadwick, David Haumann, Richard E. Parent
Citations: 380 • 1989
Multi-Level Surface Maps for Outdoor Terrain Mapping and Loop Closing
Rudolph Triebel, Patrick Pfaff, Wolfram Burgard
Citations: 346 • 2006
Fully automated liquid extraction‐based surface sampling and ionization using a chip‐based robotic nanoelectrospray platform
Vilmos Kertész, Gary J. Van Berkel
Citations: 343 • 2009
Scaling Hard Vertical Surfaces with Compliant Microspine Arrays
Alan T. Asbeck, Sangbae Kim, Mark R. Cutkosky, William R. Provancher, Michele Lanzetta
Citations: 322 • 2006
Neural RGB-D Surface Reconstruction
Dejan Azinović, Ricardo Martin-Brualla, Dan B Goldman, Matthias NieBner, Justus Thies
Citations: 277 • 2022
Light-induced crawling of crystals on a glass surface
Emi Uchida, Reiko Azumi, Yasuo Norikane
Citations: 266 • 2015
DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation
Jeong Joon Park, Pete Florence, Julian Straub, Richard Newcombe, Steven Lovegrove
Citations: 259 • 2019
Clear Grasp: 3D Shape Estimation of Transparent Objects for Manipulation
Shreeyak S. Sajjan, Matthew R. Moore, Mike Pan, Ganesh Nagaraja, Johnny Lee, Andy Zeng, Shuran Song
Citations: 258 • 2020
Support-free volume printing by multi-axis motion
Chengkai Dai, Charlie C. L. Wang, Chenming Wu, Sylvain Lefèbvre, Guoxin Fang, Yong‐Jin Liu
Citations: 248 • 2018
Recovering the position and orientation of free-form objects from image contours using 3D distance maps
S. Lavallée, Richard Szeliski
Citations: 244 • 1995
How honeybees make grazing landings on flat surfaces
Mandyam V. Srinivasan, Shaowu Zhang, Javaan Chahl, Erhardt Barth, S. Venkatesh
Citations: 241 • 2000
Topography from Topology: Photoinduced Surface Features Generated in Liquid Crystal Polymer Networks
Michael E. McConney, Angel Martinez, Vincent P. Tondiglia, Kyung Min Lee, Derrick Langley, Ivan I. Smalyukh, Timothy J. White
Citations: 239 • 2013
Surface shape from the deformation of apparent contours
Roberto Cipolla, Andrew Blake
Citations: 237 • 1992
Microassembly of 3-D Microstructures Using a Compliant, Passive Microgripper
Nikolai Dechev, William L. Cleghorn, James K. Mills
Citations: 234 • 2004
Surface Optimal Path Planning Using an Extended Dijkstra Algorithm
Min Luo, Xiaorong Hou, Jing Yang
Citations: 224 • 2020
Ultra–Low Surface Brightness Imaging with the Dragonfly Telephoto Array
Citations: 215 • 2013