CREATIVE FREEDOM FOR COMPUTATIONAL MESH GENERATION IN DEAL.II Nicola - PowerPoint PPT Presentation

CREATIVE FREEDOM FOR COMPUTATIONAL MESH GENERATION IN DEAL.II Nicola Giuliani , Luca Heltai (ngiuliani@sissa.it) Sixth deal.II Users and Developers Workshop

MESH GENERATION Mesh generation … a secret of the darkest arts ▸ An accurate mesh is a prerogative require of an accurate simulation ▸ Mesh generator gets very expensive very quickly ▸ CAD files: engineeringly accurate and engineeringly limited Let’s look somewhere else… N.Giuliani Creative Freedom in deal.II � 2

3D MODELLING TOOLS 3D modelling tools offer the possibility of creating complex geometries in a very straightforward way (relative definition). ▸ Used in computer graphics (video-gaming, animation studios), enormous users community and opportunities ▸ Produce smooth surfaces exploiting the subdivision surface algorithm (Catmull-Clark 1978) ▸ The algorithm is a generalisation of bi-cubic uniform B- spline surfaces to arbitrary topology Bridge computer graphics and scientific computing may not be such a bad idea… N.Giuliani Creative Freedom in deal.II � 3

CATMULL CLARK SUBDIV ▸ Recursive algorithm ▸ Refinement based on neighbouring faces/edges/ vertices ▸ Each new point is created using an “average” of face points and edges. ▸ The limit surface of Catmull–Clark subdivision surfaces can also be evaluated directly, without any recursive refinement. ▸ Little scientific literature (opportunities) N.Giuliani Creative Freedom in deal.II � 4

LET’S SEE IT … “Know averaging? You know enough to work at Pixar” 
 Tony De Rose Ted-ED talk N.Giuliani Creative Freedom in deal.II � 5

CLICK BAITS AND APPETISERS Foobar Yorozuya (https://www.youtube.com/watch?v=dY0K65eXhkA ) Now version 2.79b (23rd July 12.00) N.Giuliani Creative Freedom in deal.II � 6

BLENDER PROS ▸ Free open-source software (GPL license) ▸ Straightforward mesh generation using a GUI ▸ Developed and scriptable in Python 3 ▸ Constantly increasing users’ community (2017: +6.5 millions downloads) ▸ Reasonably good documentation ▸ BlenderStackExchange ▸ Youtube channels: at least three are official ▸ Very catchy results (made for artists and small teams) N.Giuliani Creative Freedom in deal.II � 7

BLENDER AND DEAL.II NOW ▸ Readable geometries using the Open-Asset-IMPorter-Lib (ASSIMP), introduced by deal2lkit and now in deal.II ▸ Blender generates surface geometries and those can be imported in deal.II ▸ Codimension zero/one problem with Blender geometries solvable in deal.II, dim = 1,2 spacedim = 2, 3 ▸ Possibility of non trivial geometries for scientific computing N.Giuliani Creative Freedom in deal.II � 8

CREATE A NOT SO STUPID MESH N.Giuliani Creative Freedom in deal.II � 9

STEP-38 MONKEY CODE N.Giuliani Creative Freedom in deal.II � 10

STEP-38 MONKEY RESULTS N.Giuliani Creative Freedom in deal.II � 11

REAL WORKING EXAMPLE 1/2 N.Giuliani Creative Freedom in deal.II � 12

REAL WORKING EXAMPLE 2/2 N.Giuliani Creative Freedom in deal.II � 13

CATCHY RESULTS (NICOLA LEVEL) N.Giuliani Creative Freedom in deal.II � 14

CATCHY RESULTS (LUCA LEVEL) We are just scratching the surface N.Giuliani Creative Freedom in deal.II � 15

PRESENT SITUATION SUMMARY ▸ Generation of complex geometry using Blender ▸ Import of the geometries directly in deal.II ▸ Creation of codim-1 surfaces in 3D ▸ Creation of codim-0/1 surfaces in 2D Blender only creates curves and surfaces so only those can be imported directly in deal.II N.Giuliani Creative Freedom in deal.II � 16

DEAL.II AND BLENDER IN THE FUTURE We need to overcome the codim-1 limitation in 3D ▸ Definition and implementation of new Manifold using the geometry exported from Blender (interpolating polynomials) ▸ Introduction of the Catmull-Clark algorithm in the library to have a high order mapping capable of smooth surfaces ▸ Expand the connections between deal.II and the 3D modelling world We can look beyond Blender to search for something more deal.II oriented N.Giuliani Creative Freedom in deal.II � 17

LET’S LOOK BIG N.Giuliani Creative Freedom in deal.II � 18

OPENSUBDIV OpenSubdiv is a set of open source libraries that implement high performance subdivision surface (subdiv) evaluation on massively parallel CPU and GPU architectures. ▸ Massively parallel implementation of Catmull-Clark algorithm ▸ Developed and freely available in C++ ▸ Released under Apache license ▸ Fairly reliable developers (Pixar Animation studios) http://graphics.pixar.com/opensubdiv/docs/intro.html https://github.com/PixarAnimationStudios/OpenSubdiv N.Giuliani Creative Freedom in deal.II � 19


 REFERENCES • N. Giuliani. Modelling Fluid Structure Interaction problems using Boundary Element Method. PhD thesis, SISSA, Scuola Internazionale Superiore di Studi Avanzati, 2017. • https://www.blender.org/ • https://www.youtube.com/ Questions? Curiosities? Feel free to ask anything (ngiuliani@sissa.it, heltai@sissa.it) N.Giuliani Creative Freedom in deal.II � 20