Continuity and Interpolation Techniques for Computer Graphics
González García, Francisco
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In Computer Graphics applications, it is a common practice to texture 3D models to applymaterial properties to them. Then, once the models are textured, they are deformedto create new poses that can be more appropriate for the needs of a certain scene andfinally, those models are visualized with a rendering algorithm. So, it is evident that meshtexturing, mesh deformation and rendering are still key parts of Computer Graphics. Inthese fields much research has been done, resulting in methods that allow to create acomputer-aided images in a more flexible, robust and efficient way. Despite this, thereexist improvements to be done, as many of those approaches suffer from continuity problemsthat dumper interpolation procedures. Thus, in this thesis we present algorithms thataddress continuity in key areas of Computer Graphics.In the field of mesh texturing, we introduce a new algorithm, called Continuity Mapping,that allows a continuous mapping of multi-chart textures on 3D models. This type ofparameterizations break a continuous model into a set of disconnected charts in texturespace, making discontinuities appear and causing serious problems for common applicationslike texture filtering and continuous simulations in texture space. Our approachmakes any multi-chart parameterization seamless by the use of a bidirectional mappingbetween areas outside the charts and areas inside, as well as the usage of a set of virtualtriangles that sew the charts for addressing the sampling mismatch produced at chartboundaries. Continuity Mapping does not require any modification of the artist-providedtextures, it is fully automatic and has small memory and computational costs.To deform a model and create new poses, we propose a novel cage-based deformationapproach. Up to now, cage-based deformation techniques were limited to the usage of singlecages because of the presence of continuity problems existing at cage boundaries. Asa consequence, they cannot locally deform a region of a model and the time and memoryconsumption is increased. We introduce *Cages a technique which allows the usage ofmultiple cages enclosing the model, at multiple levels of details for easier and faster meshdeformation. The proposed approach solves the discontinuities of previous approaches bysmoothly blending each cage deformation and allowing the usage of heterogeneous setsof coordinates, giving more flexibility to the final user.Finally, we propose a new rendering acceleration technique, called I-Render, for fast andapproximate Ray Tracing. First, we perform a pre-processing clustering on the input mesh,that builds upon information theoretic tools to group triangles by their similar features.These clusters define regions of smooth variation, as well as regions of sharp transitions(discontinuities). Then, we introduce a new multi-pass rendering algorithm that uses thatinformation to decide which areas of the final image could be interpolated and whichrequire more involved calculations. All this process is carried out completely in screenspace and, as a consequence, our approach can be used in addition to common accelerationspatial data structures. I-Render also supports animated models.