A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2010; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Embeddings of Surfaces, Curves, and Moving Points in Euclidean Space

2013
*
SIAM journal on computing (Print)
*

*In*this paper we show that dimensionality reduction (i.e., Johnson-Lindenstrauss lemma) preserves not only the distances between static

*points*, but also between

*moving*

*points*,

*and*more generally between ... low-dimensional flats, polynomial

*curves*,

*curves*with low winding degree,

*and*polynomial

*surfaces*. ... The authors thank Sayan Mukherjee, Piotr Indyk, Assaf Naor, Kasturi Varadarajan,

*and*Yusu Wang for helpful discussions concerning the problems studied

*in*this paper. ...

##
###
Embeddings of surfaces, curves, and moving points in euclidean space

2007
*
Proceedings of the twenty-third annual symposium on Computational geometry - SCG '07
*

*In*this paper we show that dimensionality reduction (i.e., Johnson-Lindenstrauss lemma) preserves not only the distances between static

*points*, but also between

*moving*

*points*,

*and*more generally between ... low-dimensional flats, polynomial

*curves*,

*curves*with low winding degree,

*and*polynomial

*surfaces*. ... The authors thank Sayan Mukherjee, Piotr Indyk, Assaf Naor, Kasturi Varadarajan,

*and*Yusu Wang for helpful discussions concerning the problems studied

*in*this paper. ...

##
###
CurvedLand: An Applet for Illustrating Curved Geometry without Embedding
[article]

2010
*
arXiv
*
pre-print

The underlying two-dimensional

arXiv:1010.1426v1
fatcat:cxvh3coxxbembbwlf6ns3gav4y
*space*has a constant, positive curvature, which causes the apparent paths*and*shapes*of*the objects*in*the map to appear distorted*in*ways that change as you view them from ... We have written a Java applet to illustrate the meaning*of**curved*geometry. ... ACKNOWLEDGEMENTS We would like to thank the students who helped contribute to the writing*of*the program: Lauren Barth-Cohen, Dooshaye Moonshiram,*and*Nicole Brynes. ...##
###
Page 1592 of Mathematical Reviews Vol. , Issue 86d
[page]

1986
*
Mathematical Reviews
*

A motion

*in**Euclidean*3-*space*is a Darboux motion if the tra- jectory*of*any*point**in*the*moving**space*is a plane*curve*. ... Motions*in**Euclidean*kinematics such that the trajectory*of*any*point**in*the*moving**space*is a plane*curve*were studied by Dar- boux. The author considers the analogous problem*in*hyperbolic*space*. ...##
###
Curvature Regularization to Prevent Distortion in Graph Embedding
[article]

2020
*
arXiv
*
pre-print

ambient

arXiv:2011.14211v1
fatcat:ng7ixm3zdvcyvl3qecm435nxa4
*embedding**Euclidean**space*,*and*hence to detect them becomes difficult for machine learning models. ... Recent research on graph*embedding*has achieved success*in*various applications. Most graph*embedding*methods preserve the proximity*in*a graph into a manifold*in*an*embedding**space*. ... Recall that*curve*curvature is modeled as the rate*of*change*of*direction*of*tangent at a*point*that*moves*on the*curve*. ...##
###
Page 4756 of Mathematical Reviews Vol. , Issue 95h
[page]

1995
*
Mathematical Reviews
*

*and*related questions, projective arc length

*and*projective curvature); (3) Applications

*of*the projective theory

*of*

*curves*(

*moving*frame, rational

*curves*, ruled

*surfaces*); (4)

*Surfaces*

*in*

*space*(type ...

*of*conjugate nets

*and*congruences, La- place sequences, conjugate normal congruences

*and*connection with theory

*of*

*surfaces*

*in*

*Euclidean*

*space*);

*and*(6) Perspectives (tangency invariants for

*curves*, projective ...

##
###
Page 6460 of Mathematical Reviews Vol. , Issue 88m
[page]

1988
*
Mathematical Reviews
*

By means

*of*the*moving*frame for a*point*x € V, (p vectors*of*this frame lie*in*the tangent*space*7,*of*V,*in*x), the author constructs for each direction*in*7,, a normal direction*in*the*space*completely ... Let V, be a p-dimensional*surface**in**Euclidean*n-*space*E.,. ...##
###
Differential Geometry and Relativity Theory: An Introduction

1986
*
American Journal of Physics
*

A parametric

doi:10.1119/1.14853
fatcat:nyqiwkbinzbvhpkwind43h6nye
*surface*is the image*of*an open subset*of*the*Euclidean*plane by a continuous function,*in*a topological*space*, generally a*Euclidean**space**of*dimension at least three. ...*space*such that every*point*has a neighborhood which is homeomorphic to an open subset*of*the*Euclidean*plane. ...*Of*course, all these*surfaces*can be thought*of*as*embedded**in**Euclidean**space*E 3 . ...##
###
Page 2066 of Mathematical Reviews Vol. , Issue 93d
[page]

1993
*
Mathematical Reviews
*

be a regular /-dimensional submanifold

*in*an n-dimensional*Euclidean**space*E”. Taking the tangent subspace To F ! at a*point*Q € F;*and**moving*this subspace to the origin, one can consider TgF! ... Summary: “Let ® be a nonplanar minimal*surface**in**Euclidean**space*E>. ...##
###
Sector models—A toolkit for teaching general relativity: I. Curved spaces and spacetimes

2014
*
European journal of physics
*

Sector models describe

doi:10.1088/0143-0807/35/5/055020
fatcat:iwfykq4hb5ejhgxu4r6hwyetbq
*curved**spaces*the Regge calculus way by subdivision into blocks with*euclidean*geometry. This procedure is similar to the approximation*of*a*curved**surface*by flat triangles. ... We outline a workshop for high school*and*undergraduate students that introduces the notion*of**curved**space*by means*of*sector models*of*black holes. ... Gaps appear whenever the pieces*of*a*curved**surface*are laid out*in*a plane or the blocks*of*a*curved**space*are assembled*in**euclidean**space*. ...##
###
Embedding Spacetime via a Geodesically Equivalent Metric of Euclidean Signature

2001
*
General Relativity and Gravitation
*

This geodesically equivalent, or dual, metric can be

doi:10.1023/a:1012037418513
fatcat:6m3iv4wxvfgxveyiqzuvxzbgqa
*embedded**in*ordinary*Euclidean**space*. On the*embedded**surface*freely falling particles*move*on the shortest path. ... Thus one can visualize how acceleration*in*a gravitational field is explained by particles*moving*freely*in*a*curved*spacetime. ... When we create the*embedding*diagram for the*space**of*a symmetry plane through a star, we make a mapping from our spatial plane onto a*curved**surface**embedded**in**Euclidean**space*. ...##
###
Delaunay triangulations and Voronoi diagrams for Riemannian manifolds

2000
*
Proceedings of the sixteenth annual symposium on Computational geometry - SCG '00
*

For a sufficiently dense set

doi:10.1145/336154.336221
dblp:conf/compgeom/LeibonL00
fatcat:7z4taevduzehthikoufhif3vo4
*of**points**in*any closed Riemannian manifold, we prove that a unique Delannay triangulation exists. This triangulation has the same properties as*in**Euclidean**space*. ... ACKNOWLEDGEMENTS We would like to thank Herbert Edelsbrunner for helpful discussions about the algorithms, Hyam Rubinstein for his suggestions for dealing with normal submanifolds*of**Euclidean**space**and*... SUBMANIFOLDS*OF**EUCLIDEAN**SPACE*Any manifold*embedded**in**Euclidean**space*inherits a Riemannian structure where the lengths*of**curves*on the manifold are the*Euclidean*lengths*of*the*curves*. ...##
###
Embedding the Reissner–Nordström spacetime in Euclidean and Minkowski spaces

2006
*
Classical and quantum gravity
*

These

doi:10.1088/0264-9381/23/12/003
fatcat:mwrymfzqmbfcbi2dghtko7xugu
*embedding*diagrams serve as useful tools to visualize the geometry*of*the hypersurfaces*and**of*the whole spacetime*in*general. ... We examine*embedding*diagrams*of*hypersurfaces*in*the Reissner-Nordstrom black hole spacetime. ... This research was supported by the ISF center*of*excellence for High Energy Astrophysics*and*by the Schwartzmann University Chair (TP). ...##
###
Weighted averages on surfaces

2013
*
ACM Transactions on Graphics
*

Abstract We consider the problem

doi:10.1145/2461912.2461935
fatcat:f3vy7xtgsvhhxkjkh63jd7ubga
*of*generalizing affine combinations*in**Euclidean**spaces*to triangle meshes: computing weighted averages*of**points*on*surfaces*. ... We demonstrate that anchor*points**in*the above applications can be added/removed*and**moved*around on the meshes at interactive framerates, giving the user an immediate result as feedback. ... This work was supported*in*part by the ERC grant iModel (StG-2012-306877), by an SNF award 200021 137879*and*a gift from Adobe Research. ...##
###
A Riemannian Self-Organizing Map
[chapter]

2009
*
Lecture Notes in Computer Science
*

We generalize the classic self-organizing map (SOM)

doi:10.1007/978-3-642-04146-4_26
fatcat:6zqqgclmi5bjnjonybnoqmoaem
*in*flat*Euclidean**space*(linear manifold) onto a Riemannian manifold. ... We here compared the performance*of*the generalized SOM*and*the classical SOM using real 3-Dimensional facial*surface*normals data. ... Under the*embedding*Φ,*points*on M can be depicted by corresponding vectors*in*the*Euclidean**space*R d . ...
« Previous

*Showing results 1 — 15 out of 26,475 results*