Related papers: Simplification of Indoor Space Footprints
As an important practice of map generalization, the aim of line simplification is to reduce the number of points without destroying the essential shape or the salient character of a cartographic curve. This subject has been well-studied in…
This paper describes a general-purpose programming technique, called the Simulation of Simplicity, which can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task to provide a…
We give necessary and sufficient criteria for elementary operations in a two-dimensional terrain to preserve the persistent homology induced by the height function. These operations are edge flips and removals of interior vertices,…
As modeling and visualization applications proliferate, there arises a need to simplify large polygonal models at interactive rates. Unfortunately existing polygon mesh simplification algorithms are not well suited for this task because…
We describe how to implement Simulation of Simplicity (SoS). SoS removes geometric degeneracies in point-in-polygon queries, polyhedron intersection, map overlay, and other 2D and 3D geometric and spatial algorithms by determining the…
Polytope complexes are the generalisation of polygon meshes in geo-information systems (GIS) to arbitrary dimension, and a natural concept for accessing spatio-temporal information. Complexes of each dimension have a straight-forward…
The rapidly evolving field of engineering design of functional surfaces necessitates sophisticated tools to manage the inherent complexity of high-dimensional design spaces. This survey paper offers a scoping review, i.e., a literature…
Polygons are a paramount data structure in computational geometry. While the complexity of many algorithms on simple polygons or polygons with holes depends on the size of the input polygon, the intrinsic complexity of the problems these…
We present semisimp, a tool for semiautomatic simplification of three dimensional polygonal models. Existing automatic simplification technology is quite mature, but is not sensitive to the heightened importance of distinct semantic model…
Multidimensional scaling (MDS) is a dimensionality reduction tool used for information analysis, data visualization and manifold learning. Most MDS procedures embed data points in low-dimensional Euclidean (flat) domains, such that…
Interpolation methodologies have been widely used within the domain of indoor positioning systems. However, existing indoor positioning interpolation algorithms exhibit several inherent limitations, including reliance on complex…
In this paper we present some new, practical, geometric optimization techniques for computing polygon partitions, 1D and 2D point, interval, square and rectangle covers, as well as 1D and 2D interval and rectangle K-centers. All the…
This paper describes a method for fast simplification of surface meshes. Whereas past methods focus on visual appearance, our goal is to solve equations on the surface. Hence, rather than approximate the extrinsic geometry, we construct a…
Multidimensional scaling (MDS) is a family of methods that embed a given set of points into a simple, usually flat, domain. The points are assumed to be sampled from some metric space, and the mapping attempts to preserve the distances…
With the development of cheap image sensors, the amount of available image data have increased enormously, and the possibility of using crowdsourced collection methods has emerged. This calls for development of ways to handle all these…
We present a novel methodology based on geometric approach to simulate magnification lens effects. Our aim is to promote new applications of powerful geometric modeling techniques in visual computing. Conventional image…
Geometry processing of 3D objects is of primary interest in many areas of computer vision and graphics, including robot navigation, 3D object recognition, classification, feature extraction, etc. The recent introduction of cheap range…
In many applications, maintaining a consistent map of the environment is key to enabling robotic platforms to perform higher-level decision making. Detection of already visited locations is one of the primary ways in which map consistency…
This paper presents a novel approach for structure-preserving planar simplification of indoor scene point clouds for both simulated and real-world environments. Initially, the scene point cloud undergoes preprocessing steps, including noise…
3D Gaussian Splatting (3DGS) has recently gained popularity for efficient scene rendering by representing scenes as explicit sets of anisotropic 3D Gaussians. However, most existing work focuses primarily on modeling external surfaces. In…