Polygon
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Related Articles from SNS
Zero-Shot Polygon Matching with Pre-trained Models for Pose Estimation and Polygon Cloud from Challenging Stereo
Announce Type: replace Abstract: While stereo matching has achieved maturity for 0D point and 1D line primitives, establishing correspondences for 2D polygons remains largely unexplored due to challenges including disparity discontinuity, scale variation, training dependency, and poor generalization, limiting downstream tasks such as pose estimation and 3D reconstruction. To address these issues, we are the first to propose a Zero-shot Polygon Matching paradigm with Pre-trained Models (i.e.,...
Optimal error estimates for a discontinuous Galerkin method on curved boundaries with polygonal meshes
Announce Type: replace Abstract: We consider a discontinuous Galerkin method for the numerical solution of boundary value problems in two-dimensional domains with curved boundaries. A key challenge in this setting is the potential loss of convergence order due to approximating the physical domain by a polygonal mesh. Unless boundary conditions can be accurately transferred from the true boundary to the computational one, such geometric approximation errors generally lead to suboptimal...
PolyBuild: An End-to-End Method for Polygonal Building Contour Extraction from High-Resolution Remote Sensing Images
arXiv:2606.08920v1 Announce Type: new Abstract: Extracting building polygon contours from high-resolution remote sensing images is a fundamental task for various mapping applications. However, the presence of varying imaging conditions and complex building structures, makes automatic contour extraction extremely challenging. Mainstream approaches for building extraction often rely on pixel-level segmentation followed by multiple post-processing steps to produce building contour, which can be...
A Linear Time Algorithm for the Maximum Overlap of Two Convex Polygons Under Translation
arXiv:2504.18352v2 Announce Type: replace Abstract: Given two convex polygons $P$ and $Q$ with $n$ and $m$ edges, the maximum overlap problem is to find a translation of $P$ that maximizes the area of its intersection with $Q$. We give the first randomized algorithm for this problem with linear running time. Our result improves the previous two-and-a-half-decades-old algorithm by de Berg, Cheong, Devillers, van Kreveld, and Teillaud (1998), which ran in $O((n+m)\log(n+m))$ time, as well as...
Show HN: Formally verified polygon intersection – Opus 4.8 oneshots, prev failed
To my knowledge, this is the first formally verified implementation of an intersection algorithm for polygons. The experience of working with AI agents on this project changed a lot with recent model releases, as I describe in the readme. Opus 4.8 is able to provide algorithm implementation with formal proof in one shot, whereas previous models required me to provide proof strategies in multiple steps.
A Mixed Extended Virtual Element Method for Elliptic Interface Problems on Polygonal Meshes
arXiv:2606.08526v1 Announce Type: new Abstract: We propose a lowest-order \(H(\operatorname{div})\)-conforming mixed extended virtual element method for elliptic interface problems on interface-unfitted polygonal meshes. The flux and pressure are approximated by subdomain-wise extended \(H(\operatorname{div})\)-VEM spaces and by piecewise constants, respectively. On cut elements, the computable polynomial projection is defined on the whole background element and then restricted to the two...
A Geometric Gaussian Mixture Representation of Plane Curves
Announce Type: new Abstract: We introduce a user defined probabilistic polygonal representation for plane curves. Given a curve, we select vertices on the curve and connect consecutive vertices by line segments to obtain a polygonal approximation. Each segment is equipped with a user defined uncertainty parameter in the normal direction.
Show HN: A CSS 3D Engine (no WebGL)
A CSS polygon mesh library. A 3D engine for the DOM. Renders OBJ/MTL, GLB and VOX as real HTML elements transformed with CSS matrix3d(...) .
Sibley's Guard-Point Convexity Measure: A Perimeter Counterexample and a Dominance Bound
Announce Type: new Abstract: We study Sibley's guard-point convexity measure for simple polygons and compare it with the exterior and perimeter convexity measures. We prove the exterior inequality G(F) <= E(F) and disprove the pointwise perimeter inequality G(F)
Hierarchical Space Partition for Surface Reconstruction
arXiv:2606.04891v1 Announce Type: new Abstract: Generating compact polygonal models from point clouds is a key problem in 3D vision and computer graphics. However, due to inherent limitations of LiDAR scanning (e.g. range constraints and occlusions), critical scene information is often missing, leading to degraded reconstruction accuracy. To address this, we propose a plane assembling strategy that effectively recovers missing details while maintaining model compactness.