Automatic geometric transformations over the input domain to produce abetter mesh with an Octree-based technique.

CIMNE 2015

The Octree [1] technique is one of the most popular methods to produce hex-dominantmeshes. It starts by computing the Bounding Box (Bbox) of the input domain; anhexahedron that will define the root Octant. Then, this Octant is recursively split into newOctants until a given constraint is fulfilled.The Octree is not sensitive to some aspects of the input mesh. For instance if the input is asurface mesh defining a cube with 12 triangles or it is the same cube defined by 1000triangles, this should not produce any difference in the output. Probably it will only takemore time. However if we now consider a cube perfectly aligned with the reference axes andthe same cube slightly rotated in one of the axes, the output will certainly be different.One natural solution to overcome this issue would be to apply geometric transformationsover the input domain in order to align it with the reference axes. Then execute the meshingalgorithm and finally, apply the reverse transformations to the output mesh.The most important application of this work is in the medical field. Many simulations mustbe performed on patient-specific meshes. Consider the following workflow: acquire medicalimages, achieve proper segmentation, build a surface model and finally build a volume meshfor simulation with a numerical method.Now, it is clear that most of soft and hard tissues do not count with dominant directions.However, if we consider the problem of mesh adaptation, where the idea is to concentratemore nodes in a given region important for the simulation, our algorithm could be veryuseful. For instance, consider the simulation of brain tumor resection. It is clear that moreprecision is needed in the region of the tumor. Normally the Octree can be modified to refinemore the elements over this region and leave a coarse mesh elsewhere. This Region ofInterest (RoI) is defined regularly with a cube that intersects the brain. Now we can apply thetransformations to align the cube defining the RoI with refe

Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits; Finite element method; Digital computer simulation; Simulació per ordinador digital; Conference report

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Lobos, C.; Durán, S. Automatic geometric transformations over the input domain to produce abetter mesh with an Octree-based technique. A: ADMOS 2015. CIMNE, 2015, p. 34.
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