Related papers: Optimizing Mesh to Improve the Triangular Expansio…
Shape is a powerful tool to understand point sets. A formal notion of shape is given by $\alpha$-shapes, which generalize the convex hull and provide adjustable level of detail. Many real-world point sets have an inherent temporal property…
We describe an algorithm to construct an intrinsic Delaunay triangulation of a smooth closed submanifold of Euclidean space. Using results established in a companion paper on the stability of Delaunay triangulations on $\delta$-generic…
Delaunay flip is an elegant, simple tool to convert a triangulation of a point set to its Delaunay triangulation. The technique has been researched extensively for full dimensional triangulations of point sets. However, an important case of…
Effective query expansion for web search benefits from promoting both exploration and result diversity to capture multiple interpretations and facets of a query. While recent LLM-based methods have improved retrieval performance and…
High-quality observations of the real world are crucial for a variety of applications, including producing 3D printed replicas of small-scale scenes and conducting inspections of large-scale infrastructure. These 3D observations are…
Estimating the location where an image was taken based solely on the contents of the image is a challenging task, even for humans, as properly labeling an image in such a fashion relies heavily on contextual information, and is not as…
Anytime heuristic search algorithms try to find a (potentially suboptimal) solution as quickly as possible and then work to find better and better solutions until an optimal solution is obtained or time is exhausted. The most widely-known…
Surveying 3D scenes is a common task in robotics. Systems can do so autonomously by iteratively obtaining measurements. This process of planning observations to improve the model of a scene is called Next Best View (NBV) planning. NBV…
Most of the existing point-to-mesh distance query solvers, such as Proximity Query Package (PQP), Embree and Fast Closest Point Query (FCPW), are based on bounding volume hierarchy (BVH). The hierarchical organizational structure enables…
The necessary decarbonization efforts in energy sectors entail the integration of flexibility assets, as well as increased levels of uncertainty for the planning and operation of power systems. To cope with this in a cost-effective manner,…
Adaptive spatial meshing has proven invaluable for the accurate, efficient computation of solutions of time dependent partial differential equations. In a DA context the use of adaptive spatial meshes addresses several factors that place…
This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…
For explicit interface tracking in three dimensions, we propose a linear MARS method that (a) represents the interface by a partially ordered set of glued surfaces and approximates each glued surface with a triangular mesh, (b) maintains an…
We study the accuracy of triangulation in multi-camera systems with respect to the number of cameras. We show that, under certain conditions, the optimal achievable reconstruction error decays quadratically as more cameras are added to the…
Data augmentation serves as a popular regularization technique to combat overfitting challenges in neural networks. While automatic augmentation has demonstrated success in image classification tasks, its application to time-series…
Mesh plays an indispensable role in dense real-time reconstruction essential in robotics. Efforts have been made to maintain flexible data structures for 3D data fusion, yet an efficient incremental framework specifically designed for…
Mesh processing pipelines are mature, but adapting them to newer non-mesh surface representations -- which enable fast rendering with compact file size -- requires costly meshing or transmitting bulky meshes, negating their core benefits…
Computational mathematics plays an increasingly important role in computational fluid dynamics (CFD). The aeronautics and aerospace re- search community is working on next generation of CFD capacity that is accurate, automatic, and fast. A…
Divide-and-conquer is a central paradigm for the design of algorithms, through which some fundamental computational problems, such as sorting arrays and computing convex hulls, are solved in optimal time within $\Theta(n\log{n})$ in the…
Textured meshes significantly enhance the realism and detail of objects by mapping intricate texture details onto the geometric structure of 3D models. This advancement is valuable across various applications, including entertainment,…