Related papers: Topological Offsets
Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…
Level set-based immersed boundary techniques operate on nonconforming meshes while providing a crisp definition of interface and external boundaries. In such techniques, an isocontour of a level set field interpolated from nodal level set…
To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…
Neural surface reconstruction has been dominated by implicit representations with marching cubes for explicit surface extraction. However, those methods typically require high-quality normals for accurate reconstruction. We propose…
In this paper we apply topology optimization to micro-structured superhydrophobic surfaces for the first time. It has been experimentally observed that a droplet suspended on a brush of micrometric posts shows a high static contact angle…
Offset surfaces, defined as the Minkowski sum of a base surface and a rolling ball, play a crucial role in geometry processing, with applications ranging from coverage motion planning to brush modeling. While considerable progress has been…
Unsigned distance fields (UDFs) offer broader modeling capabilities than signed distance fields (SDFs), enabling the representation of shapes with open boundaries, non-manifold structures or mixed curve and surface parts. However,…
With the increasing amount of data being visualized in large information spaces, methods providing data-driven context have become indispensable. Off-screen visualization techniques, therefore, have been extensively researched for their…
We present a topology-informed inverse rendering approach for reconstructing high-genus surface meshes from multi-view images. Compared to 3D representations like voxels and point clouds, mesh-based representations are preferred as they…
This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the topology of small regions around each point, one can…
We present an efficient, trivially parallelizable algorithm to compute offset surfaces of shapes discretized using a dexel data structure. Our algorithm is based on a two-stage sweeping procedure that is simple to implement and efficient,…
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…
We introduce a level set based approach to Bayesian geometric inverse problems. In these problems the interface between different domains is the key unknown, and is realized as the level set of a function. This function itself becomes the…
We explore offsets of Cayley ovals, by networking with different kinds of software. Using their specific abilities, algebraic, geometric, dynamic, we conjecture interesting properties of the offsets. For a given progenitor (the given plane…
This paper introduces progressive algorithms for the topological analysis of scalar data. Our approach is based on a hierarchical representation of the input data and the fast identification of topologically invariant vertices, which are…
We introduce a new technique to create a mesh of convex polyhedra representing the interior volume of a triangulated input surface. Our approach is particularly tolerant to defects in the input, which is allowed to self-intersect, to be…
This article introduces a novel approach to constructing a topometric map that allows for efficient navigation and decision-making in mobile robotics applications. The method generates the topometric map from a 2D grid-based map. The…
We propose a new approach for controlling the characteristics of certain mesh faces during optimization of high-order curved meshes. The practical goals are tangential relaxation along initially aligned curved boundaries and internal…
In a world abundant with diverse data arising from complex acquisition techniques, there is a growing need for new data analysis methods. In this paper we focus on high-dimensional data that are organized into several hierarchical datasets.…
In this paper, we present a novel workflow consisting of algebraic algorithms and data structures for fast and topologically accurate conversion of vector data models such as Boundary Representations into voxels (topological voxelization);…