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My Research Story - Implicit Representations and Evolving Surface Remeshing
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This is my lecture presentation I've given to the Department of Applied Informatics at Commenius University in Bratislava (in December 13th 2021). It outlines my research story which includes a research project at a company I worked for, my master's thesis, and my current line of research for my dissertation.
Enjoy.
00:00 - 00:33 Intro
00:33 - 4:26 The "Gentle" Introduction
4:26 - 8:45 The Rough Timeline of This Project
8:45 - 27:03 Part I. - Introduction to Signed Distance Fields of Polygonal Meshes
27:03 - 38:18 Part II. - Evolving Surface Shrink-Wrapping of Polygonal Meshes
38:18 - 38:56 New Insights from This Project
38:56 - 43:11 What's Next?
43:11 Acknowledgements
Known Errors:
1.) At 22:20 - The dmin value should be the sqrt of the minimum squared distance. Computing square root is expensive, so it should only be done once the minimum squared distance is found.
2.) At 22:50 - The mapping formulas from x,y,z Euclidean coordinates to grid index space should be of form:
ix = floor( ( 0.5*(C.min.x + C.max.x) - g_min,x)/s)
because the centroid x-coordinate of cube voxel C is: 0.5*(C.min.x + C.max.x)
3.) At 22:20 - The first if should take place when the box size is larger than minimum cell size.
Presentation Abstract:
Implicit representations of 3D objects find their applications in many areas of CAD geometry. It is often easier for users to generate an "outline" (e.g.: a contour rendering of a volumetric representation) of their desired shape, and modify its topological properties after conversion to a polygonal representation. Combining pre-existing polygonal meshes into an implicit object requires high computational efficiency for computing their signed distance fields (SDF). We deal with this problem using a three step approach with hierarchical volume subdivision followed by applying a numerical Eikonal solver. Furthermore, we test and analyze an experimental approach to triangular remeshing using an SDF-based advection onto a mesh obstacle.
Enjoy.
00:00 - 00:33 Intro
00:33 - 4:26 The "Gentle" Introduction
4:26 - 8:45 The Rough Timeline of This Project
8:45 - 27:03 Part I. - Introduction to Signed Distance Fields of Polygonal Meshes
27:03 - 38:18 Part II. - Evolving Surface Shrink-Wrapping of Polygonal Meshes
38:18 - 38:56 New Insights from This Project
38:56 - 43:11 What's Next?
43:11 Acknowledgements
Known Errors:
1.) At 22:20 - The dmin value should be the sqrt of the minimum squared distance. Computing square root is expensive, so it should only be done once the minimum squared distance is found.
2.) At 22:50 - The mapping formulas from x,y,z Euclidean coordinates to grid index space should be of form:
ix = floor( ( 0.5*(C.min.x + C.max.x) - g_min,x)/s)
because the centroid x-coordinate of cube voxel C is: 0.5*(C.min.x + C.max.x)
3.) At 22:20 - The first if should take place when the box size is larger than minimum cell size.
Presentation Abstract:
Implicit representations of 3D objects find their applications in many areas of CAD geometry. It is often easier for users to generate an "outline" (e.g.: a contour rendering of a volumetric representation) of their desired shape, and modify its topological properties after conversion to a polygonal representation. Combining pre-existing polygonal meshes into an implicit object requires high computational efficiency for computing their signed distance fields (SDF). We deal with this problem using a three step approach with hierarchical volume subdivision followed by applying a numerical Eikonal solver. Furthermore, we test and analyze an experimental approach to triangular remeshing using an SDF-based advection onto a mesh obstacle.
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