Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Proceedings of the sixth ACM symposium on Solid modeling and applications
Detecting undersampling in surface reconstruction
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Geometric Data Analysis: An Empirical Approach to Dimensionality Reduction and the Study of Patterns
Geometric Data Analysis: An Empirical Approach to Dimensionality Reduction and the Study of Patterns
Modern Differential Geometry of Curves and Surfaces with Mathematica
Modern Differential Geometry of Curves and Surfaces with Mathematica
The Ball-Pivoting Algorithm for Surface Reconstruction
IEEE Transactions on Visualization and Computer Graphics
Estimating the Intrinsic Dimension of Data with a Fractal-Based Method
IEEE Transactions on Pattern Analysis and Machine Intelligence
Tight cocone: a water-tight surface reconstructor
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Manifold reconstruction from point samples
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Generalized Principal Component Analysis (GPCA)
IEEE Transactions on Pattern Analysis and Machine Intelligence
An incremental algorithm for reconstruction of surfaces of arbitrary codimension
Computational Geometry: Theory and Applications
An Algorithm for Finding Intrinsic Dimensionality of Data
IEEE Transactions on Computers
Geodesic entropic graphs for dimension and entropy estimation in manifold learning
IEEE Transactions on Signal Processing
Feature-Preserving Reconstruction of Singular Surfaces
Computer Graphics Forum
SMI 2013: Voronoi-based feature curves extraction for sampled singular surfaces
Computers and Graphics
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We present an algorithm capable of reconstructing a non-manifold surface embedded as a point cloud in a high-dimensional space. Our algorithm extends a previously developed incremental method and produces a non-optimal triangulation, but will work for non-orientable surfaces, and for surfaces with certain types of self-intersection. The self-intersections must be ordinary double curves and are fitted locally by intersecting planes using a degenerate quadratic surface. We present the algorithm in detail and provide many examples, including a dataset describing molecular conformations of cyclo-octane.