We introduce a new biorthogonal wavelet approach to creating a water-tight surface defined by an implicit function, from a finite set of oriented points. Our approach aims at addressing problems with previous wavelet ...
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We introduce a new biorthogonal wavelet approach to creating a water-tight surface defined by an implicit function, from a finite set of oriented points. Our approach aims at addressing problems with previous wavelet methods which are not resilient to missing or nonuniformly sampled data. To address the problems, our approach has two key elements. First, by applying a three-dimensional partial integration, we derive a new integral formula to compute the wavelet coefficients without requiring the implicit function to be an indicator function. It can be shown that the previously used formula is a special case of our formula when the integrated function is an indicator function. Second, a simple yet general method is proposed to construct smooth wavelets with small support. With our method, a family of wavelets can be constructed with the same support size as previously used wavelets while having one more degree of continuity. Experiments show that our approach can robustly produce results comparable to those produced by the Fourier and Poisson methods, regardless of the input data being noisy, missing or nonuniform. Moreover, our approach does not need to compute global integrals or solve large linear systems.
We present a novel method to construct subdivision stencils near extraordinary vertices with limit surfaces having optimal bounded curvature at extraordinary positions. With the proposed method, subdivision stencils f...
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We present a novel method to construct subdivision stencils near extraordinary vertices with limit surfaces having optimal bounded curvature at extraordinary positions. With the proposed method, subdivision stencils for newly inserted and updated vertices near extraordinary vertices are first constructed to ensure subdivision with G1 continuity and bounded curvature at extraordinary positions. The remaining degrees of freedom of the constructed subdivision stencils are further used to optimize the eigenbasis functions corresponding to the subsubdominant eigenvalues of the subdivision with respect to G2 continuity constraints. We demonstrate the method by replacing subdivision stencils near extraordinary vertices for Catmull-Clark subdivision and compare the results with the original Catmull-Clark subdivision and previous tuning schemes known with small curvature variation near extraordinary positions. The results show that the proposed method produces subdivision schemes with better or comparable curvature behavior around extraordinary vertices with comparatively simple subdivision stencils.
We propose a novel method for interactive design of well-fitting body-supporting surfaces that is driven by the pressure distribution on the body's surface. Our main contribution is an interactive modeling system ...
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We propose a novel method for interactive design of well-fitting body-supporting surfaces that is driven by the pressure distribution on the body's surface. Our main contribution is an interactive modeling system that utilizes captured body poses and computes an importance field that is proportional to the pressure distribution on the body for a given pose. This distribution indicates where the body should be supported in order to easily hold a particular pose, which is one of the measures of comfortable sitting. Using our approximation, we propose the entire workflow for interactive design of C-2 smooth surfaces which serve as seats, or generally, as body supporting furniture for comfortable sitting. Finally, we also provide a design tool for Rhinoceros/Grasshopper that allows for interactive creation of single designs or entire multi-person sitting scenarios. We also test the tool with design students and present several results. Our method aims at interactive design in order to help designers to create appropriate surfaces digitally without additional empirical design passes.
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