Hierarchical volumetric object representations for digital fabrication workflows

With the rise of of desktop 3D printers, hackerspaces, and fab labs, more and more individuals are engaging in personal-scale digital fabrication. For historical reasons, fabrication workflows are often based on triangulated meshes. Meshes are easy to render, but cannot guarantee physical feasibility -- holes, zero-area faces, incorrect normals, and other flaws can make them nonsensical descriptions of physical objects.

[1]  Ronald N. Perry,et al.  Kizamu: a system for sculpting digital characters , 2001, SIGGRAPH.

[2]  Ronald N. Perry,et al.  Adaptively sampled distance fields: a general representation of shape for computer graphics , 2000, SIGGRAPH.

[3]  Xin-She Yang,et al.  Introduction to Algorithms , 2021, Nature-Inspired Optimization Algorithms.

[4]  A. Ricci,et al.  A Constructive Geometry for Computer Graphics , 1973, Computer/law journal.

[5]  Pere Brunet,et al.  Solid representation and operation using extended octrees , 1990, TOGS.

[6]  P.-C. Hsu,et al.  The Scale Method for Blending Operations in Functionally‐Based Constructive Geometry , 2003, Comput. Graph. Forum.

[7]  I. C. Braid,et al.  Designing with volumes , 1973 .

[8]  Robert B. Jerard,et al.  Comparison of discretization algorithms for surfaces with application to numerically controlled machining , 1997, Comput. Aided Des..

[9]  Eva Dyllong,et al.  A Reliable Extended Octree Representation of CSG Objects with an Adaptive Subdivision Depth , 2007, PPAM.

[10]  Donald Meagher,et al.  Geometric modeling using octree encoding , 1982, Comput. Graph. Image Process..

[11]  Irina Voiculescu,et al.  Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms , 2009 .

[12]  Madhu Sudan.  The P vs. NP problem , 2010 .

[13]  Yuan-Jye Tseng.  Machining of free-form solids using an octree volume decomposition approach , 1999 .

[14]  Alexander A. Pasko,et al.  Function-Based Shape Modeling: Mathematical Framework and Specialized Language , 2002, Automated Deduction in Geometry.

[15]  Alan Sullivan,et al.  High accuracy NC milling simulation using composite adaptively sampled distance fields , 2012, Comput. Aided Des..

[16]  John C. Hart,et al.  Sphere tracing: a geometric method for the antialiased ray tracing of implicit surfaces , 1996, The Visual Computer.

[17]  Martin Held,et al.  VRONI: An engineering approach to the reliable and efficient computation of Voronoi diagrams of points and line segments , 2001, Comput. Geom..

[18]  Andreas Nüchter,et al.  Efficient processing of large 3D point clouds , 2011, 2011 XXIII International Symposium on Information, Communication and Automation Technologies.

[19]  Tom Duff,et al.  Interval arithmetic recursive subdivision for implicit functions and constructive solid geometry , 1992, SIGGRAPH.

[20]  Lu Wu,et al.  Real-time collision-free path planning for robot manipulator based on octree model , 2006, 9th IEEE International Workshop on Advanced Motion Control, 2006..

[21]  Steve Maddock,et al.  Implicit Surfaces: Appearance, Blending and Consistency , 2005 .

[22]  D. Jung,et al.  Octree-based hierarchical distance maps for collision detection , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[23]  Martin Held,et al.  Voronoi diagrams and offset curves of curvilinear polygons , 1998, Comput. Aided Des..

[24]  Alexander A. Pasko,et al.  Procedural function-based modelling of volumetric microstructures , 2011, Graph. Model..

[25]  Bing-Yu Chen,et al.  Cubical Marching Squares: Adaptive Feature Preserving Surface Extraction from Volume Data , 2005, Comput. Graph. Forum.

[26]  Andreas Pommert,et al.  3D visualization of tomographic volume data using the generalized voxel model , 1990, VVS '89.

[27]  Alan H. Barr,et al.  Global and local deformations of solid primitives , 1984, SIGGRAPH.

[28]  W. Lorensen,et al.  System and method for the display of surface structures contained within the interior region of a solid body , 1988 .

[29]  Luiz Velho,et al.  Revisiting adaptively sampled distance fields , 2001, Proceedings XIV Brazilian Symposium on Computer Graphics and Image Processing.

[30]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[31]  Wim H. Hesselink,et al.  A General Algorithm for Computing Distance Transforms in Linear Time , 2000, ISMM.

[32]  Samuli Laine,et al.  Efficient Sparse Voxel Octrees , 2011, IEEE Trans. Vis. Comput. Graph..

[33]  Bernd Hamann,et al.  The asymptotic decider: resolving the ambiguity in marching cubes , 1991, Proceeding Visualization '91.

[34]  Brian Wyvill,et al.  Interactive techniques for implicit modeling , 1990, I3D '90.

[35]  Jakob Andreas Bærentzen,et al.  MANIPULATION OF VOLUMETRIC SOLIDS WITH APPLICATIONS TO SCULPTING , 2002 .

[36]  Waldemar Celes Filho,et al.  GPU-accelerated Adaptively Sampled Distance Fields , 2008, 2008 IEEE International Conference on Shape Modeling and Applications.

[37]  Thomas Lewiner,et al.  Efficient Implementation of Marching Cubes' Cases with Topological Guarantees , 2003, J. Graphics, GPU, & Game Tools.

[38]  Heinrich Müller,et al.  Visualization of Implicit Surfaces Using Adaptive Tetrahedrizations , 1997, Scientific Visualization Conference (dagstuhl '97).

[39]  Alexei Sourin,et al.  Function representation in geometric modeling: concepts, implementation and applications , 1995, The Visual Computer.