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In these scenes, traditional path construction, which relies on local directional sampling, often fails to find intersections with the sparse geometry, and standard NEE also struggles as it typically connects vertices directly to emitters, failing when those connections are occluded or require intermediate bounces. We propose a novel approach that constructs paths via direct geometry sampling. Instead of relying on stochastic ray casting, we repurpose the scene's bounding volume hierarchy (BVH) as a hierarchical sampling structure. By performing a stochastic top\u2010down traversal, we transform the selection of the next path vertex into a hierarchical problem. To prioritize high\u2010throughput connections, the traversal is guided by a proxy contribution function evaluated at each internal node. This function leverages aggregated statistics of the geometry contained in the BVH nodes to efficiently estimate contribution during traversal. We demonstrate orders of magnitude improvements in complex scenarios such as indirect illumination from sparse geometry or rendering discrete scattering media.<\/jats:p>","DOI":"10.1111\/cgf.70539","type":"journal-article","created":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T11:30:13Z","timestamp":1786534213000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["One\u2010more\u2010vertex Next\u2010Event Estimation with Hierarchical Geometry Sampling"],"prefix":"10.1111","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6070-0509","authenticated-orcid":false,"given":"Jorge","family":"Garcia\u2010Pueyo","sequence":"first","affiliation":[{"name":"Universidad de Zaragoza, I3A  Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5323-3233","authenticated-orcid":false,"given":"Nestor","family":"Monzon","sequence":"additional","affiliation":[{"name":"Universidad de Zaragoza, I3A  Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9000-0466","authenticated-orcid":false,"given":"Adrian","family":"Jarabo","sequence":"additional","affiliation":[{"name":"Independent researcher, Zaragoza  Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8160-7159","authenticated-orcid":false,"given":"Adolfo","family":"Mu\u00f1oz","sequence":"additional","affiliation":[{"name":"Universidad de Zaragoza, I3A  Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,8,12]]},"reference":[{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12674"},{"key":"e_1_2_10_3_2","unstructured":"Burley BrentandWaltDisneyAnimationStudios. \u201cPhysically\u2010based shading at Disney\u201d.Proceedings of SIGGRAPH '12.2012 1\u201376."},{"issue":"2","key":"e_1_2_10_4_2","article-title":"Importance Sampling of Many Lights with Adaptive Tree Splitting","volume":"1","author":"Conty\u2010Estevez Alejandro","year":"2018","journal-title":"Proc. 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