Multi-scale space-variant FRep cellular structures

Existing mesh and voxel based modeling methods encounter difficulties when dealing with objects containing cellular structures on several scale levels and varying their parameters in space. We describe an alternative approach based on using real functions evaluated procedurally at any given point. This allows for modeling fully parameterized, nested and multi-scale cellular structures with dynamic variations in geometric and cellular properties. The geometry of a base unit cell is defined using Function Representation (FRep) based primitives and operations. The unit cell is then replicated in space using periodic space mappings such as sawtooth and triangle waves. While being replicated, the unit cell can vary its geometry and topology due to the use of dynamic parameterization. We illustrate this approach by several examples of microstructure generation within a given volume or along a given surface. We also outline some methods for direct rendering and fabrication not involving auxiliary mesh and voxel representations

Subdivision Surface based One-Piece Representation

Subdivision surfaces are capable of modeling and representing complex shapes of arbi-trary topology. However, methods on how to build the control mesh of a complex surfaceare not studied much. Currently, most meshes of complicated objects come from trian-gulation and simplification of raster scanned data points, like the Stanford 3D ScanningRepository. This approach is costly and leads to very dense meshes.Subdivision surface based one-piece representation means to represent the final objectin a design process with only one subdivision surface, no matter how complicated theobject\u27s topology or shape. Hence the number of parts in the final representation isalways one.In this dissertation we present necessary mathematical theories and geometric algo-rithms to support subdivision surface based one-piece representation. First, an explicitparametrization method is presented for exact evaluation of Catmull-Clark subdivisionsurfaces. Based on it, two approaches are proposed for constructing the one-piece rep-resentation of a given object with arbitrary topology. One approach is to construct theone-piece representation by using the interpolation technique. Interpolation is a naturalway to build models, but the fairness of the interpolating surface is a big concern inprevious methods. With similarity based interpolation technique, we can obtain bet-ter modeling results with less undesired artifacts and undulations. Another approachis through performing Boolean operations. Up to this point, accurate Boolean oper-ations over subdivision surfaces are not approached yet in the literature. We presenta robust and error controllable Boolean operation method which results in a one-piecerepresentation. Because one-piece representations resulting from the above two methodsare usually dense, error controllable simplification of one-piece representations is needed.Two methods are presented for this purpose: adaptive tessellation and multiresolutionanalysis. Both methods can significantly reduce the complexity of a one-piece represen-tation and while having accurate error estimation.A system that performs subdivision surface based one-piece representation was im-plemented and a lot of examples have been tested. All the examples show that our ap-proaches can obtain very good subdivision based one-piece representation results. Eventhough our methods are based on Catmull-Clark subdivision scheme, we believe they canbe adapted to other subdivision schemes as well with small modifications

GPU voxelization

Given a triangulated model, we want to identify which voxels of a voxel grid are intersected by the boundary of this model. There are other branch of implemented voxelizations, in which not only the boundary is detected, also the interior of the model. Often these voxels are cubes. But it is not a restriction, there are other presented techniques in which the voxel grid is the view frustum, and voxels are prisms. There are di erent kind of voxelizations depending on the rasterization behavior. Approximate rasterization is the standard way of rasterizing fragments in GPU. It means only those fragments whose center lies inside the projection of the primitive are identi ed. Conservative rasterization (Hasselgren et al. , 2005) involves a dilation operation over the primitive. This is done in GPU to ensure that in the rasterization stage all the intersected fragments have its center inside the dilated primitive. However, this can produce spurious fragments, non-intersected pixels. Exact voxelization detects only those voxels that we need.

Sweep encoding: Serializing space subdivision schemes for optimal slicing

Slicing a model (computing thin slices of a geometric or volumetric model with a sweeping plane) is necessary for several applications ranging from 3D printing to medical imaging. This paper introduces a technique designed to compute these slices efficiently, even for huge and complex models. We voxelize the volume of the model at a required resolution and show how to encode this voxelization in an out-of-core octree using a novel Sweep Encoding linearization. This approach allows for efficient slicing with bounded cost per slice. We discuss specific applications, including 3D printing, and compare these octrees’ performance against the standard representations in the literature.This work has been partially funded by the Spanish Ministry of Science and Innovation (MCIN / AEI / 10.13039/501100011033) and FEDER (‘‘A way to make Europe’’) under grant TIN2017- 88515-C2-1-R.Peer ReviewedPostprint (published version

Dynamic worlds in miniature

The World in Miniature (WIM) metaphor allows users to interact and travel efficiently in virtual environments. In addition to the first-person perspective offered by typical VR applications, the WIM offers a second dynamic viewpoint through a hand-held miniature copy of the virtual environment. In the original WIM paper the miniature was a scaled down replica of the whole environment, thus limiting the technique to simple models being manipulated at a single level of scale. Several WIM extensions have been proposed where the replica shows only a part of the virtual environment. In this paper we present an improved visualization of WIM that supports arbitrarily-complex, densely-occluded scenes. In particular, we discuss algorithms for selecting the region of the virtual environment which will be covered by the miniature copy and efficient algorithms for handling 3D occlusion from an exocentric viewpoint.Peer ReviewedPostprint (author’s final draft