Signed distance fields (SDFs) have emerged as an alternative shape representation for real-time collision detection and lighting effects. Computing these for complex models can be expensive, so one ...popular approach is to prepare an approximation via sampling and interpolation. Then, these may be rendered using sphere marching, which gets close to the surface quickly, but needs several iterations to converge to it. In this paper, we propose an alternative that computes the intersection of a given ray and the surface analytically at a narrow band. This may be combined with other enhancements like having variable error for the approximation depending on the distance to the surface and skipping regions that do not contain the surface to accelerate the outer band ray traversal while reducing the required memory. To achieve smoother representations with minimal computational cost, we propose a method for computing surface intersections and normals from separate interpolants. We evaluate all these to find the optimal combination improving the rendering performance and memory consumption of these SDF approximations.
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•Enhancements for rendering SDF piecewise approximations.•Solving narrow band intersections using analytical methods.•Reducing SDF approximations for improving required memory and outer band ray traversal.
The objective of this paper is to learn dense 3D shape correspondence for topology-varying generic objects in an unsupervised manner. Conventional implicit functions estimate the occupancy of a 3D ...point given a shape latent code. Instead, our novel implicit function produces a probabilistic embedding to represent each 3D point in a part embedding space. Assuming the corresponding points are similar in the embedding space, we implement dense correspondence through an inverse function mapping from the part embedding vector to a corresponded 3D point. Both functions are jointly learned with several effective and uncertainty-aware loss functions to realize our assumption, together with the encoder generating the shape latent code. During inference, if a user selects an arbitrary point on the source shape, our algorithm can automatically generate a confidence score indicating whether there is a correspondence on the target shape, as well as the corresponding semantic point if there is one. Such a mechanism inherently benefits man-made objects with different part constitutions. The effectiveness of our approach is demonstrated through unsupervised 3D semantic correspondence and shape segmentation.
Semantic scene completion is the task of jointly estimating 3D geometry and semantics of objects and surfaces within a given extent. This is a particularly challenging task on real-world data that is ...sparse and occluded. We propose a scene segmentation network based on local Deep Implicit Functions as a novel learning-based method for scene completion. Unlike previous work on scene completion, our method produces a continuous scene representation that is not based on voxelization. We encode raw point clouds into a latent space locally and at multiple spatial resolutions. A global scene completion function is subsequently assembled from the localized function patches. We show that this continuous representation is suitable to encode geometric and semantic properties of extensive outdoor scenes without the need for spatial discretization (thus avoiding the trade-off between level of scene detail and the scene extent that can be covered). We train and evaluate our method on semantically annotated LiDAR scans from the Semantic KITTI dataset. Our experiments verify that our method generates a powerful representation that can be decoded into a dense 3D description of a given scene. The performance of our method surpasses the state of the art on the Semantic KITTI Scene Completion Benchmark in terms of geometric completion intersection-over-union (IoU).
A formulation for the optimization of index-1 differential algebraic equation systems (DAEs) is described that uses implicit functions to remove algebraic variables and equations from the ...optimization problem. The formulation uses the implicit function theorem to calculate derivatives of functions that remain in the optimization problem in terms of a reduced space of variables, allowing it to be solved with second-order nonlinear optimization algorithms. The formulation is shown to lead to more reliable solver convergence when compared with a full-space simultaneous formulation in challenging case studies involving a chemical looping combustion reactor. In a steady state simulation problem, the implicit function formulation solves 82 out of 100 instances, while the full space formulation solves only 42 out of 100 instances. In a dynamic optimization problem, the implicit function formulation solves 189 out of 200 instances, while the full space formulation solves only 152 out of 200 instances.
•A formulation for differential–algebraic equation optimization is proposed.•The formulation uses an implicit function for the algebraic equations and variables.•Convergence reliability is an issue for some dynamic optimization problems.•The implicit function formulation improves convergence reliability.
We prove that constant scalar curvature Kähler metric “adjacent” to a fixed Kähler class is unique up to isomorphism. The proof is based on the study of a fourth order evolution equation, namely, the ...Calabi flow, from a new geometric perspective, and on the geometry of the space of Kähler metrics.
Generalized Derivatives for Hybrid Systems Khan, Kamil A.; Barton, Paul I.
IEEE transactions on automatic control,
2017-July, 2017-7-00, Letnik:
62, Številka:
7
Journal Article
Recenzirano
Odprti dostop
Established sensitivity results for hybrid discrete/continuous dynamic systems are generalized by relaxing smoothness assumptions on the functions governing the systems' continuous evolution and ...discrete event handling. The new results only require L-smoothness of these functions in the sense of Nesterov, instead of continuous differentiability. Parametric lexicographic derivatives for such a hybrid system provide useful local first-order sensitivity information, and are described as the unique solutions of auxiliary hybrid systems. This sensitivity analysis framework permits generalized derivative evaluation even for certain hybrid systems in which small changes in parameters can change the sequence of discrete modes visited. To handle parametric sensitivities of event times that are not known explicitly, conditions are provided under which a local inverse function or implicit function is L-smooth, with lexicographic derivatives that are described as the unique solutions of certain equation systems. These equation systems are readily solved when the functions involved are piecewise differentiable.
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