Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
A volumetric method for building complex models from range images
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Using generic programming for designing a data structure for polyhedral surfaces
Computational Geometry: Theory and Applications - Special issue on applications and challenges
Geometric structures for three-dimensional shape representation
ACM Transactions on Graphics (TOG)
Proceedings of the sixth ACM symposium on Solid modeling and applications
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
The Ball-Pivoting Algorithm for Surface Reconstruction
IEEE Transactions on Visualization and Computer Graphics
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics)
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Poisson surface reconstruction
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Voronoi-based variational reconstruction of unoriented point sets
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Moving parabolic approximation of point clouds
Computer-Aided Design
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We use a moving parabolic approximation (MPA) to reconstruct a triangular mesh that approximates the underlying surface of a point cloud from closed objects. First, an efficient strategy is presented for constructing a hierarchical grid with adaptive resolution and generating an initial mesh from point clouds. By implementing the MPA algorithm, we can estimate the differential quantities of the underlying surface, and subsequently, we can obtain the local quadratic approximants of the squared distance function for any point in the vicinity of the target shape. Thus, second, we adapt the mesh to the target shape by an optimization procedure that minimizes a quadratic function at each step. With the objective of determining the geometrical features of the target surface, we refine the approximating mesh selectively for the non-flat regions by comparing the estimated curvature from the point clouds and the estimated curvatures computed from the current mesh. Finally, we present various examples that demonstrate the robustness of our method and show that the resulting reconstructions preserve geometric details.