{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T13:32:04Z","timestamp":1774877524573,"version":"3.50.1"},"reference-count":21,"publisher":"Wiley","license":[{"start":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T00:00:00Z","timestamp":1774828800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T00:00:00Z","timestamp":1774828800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Computer Graphics Forum"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We investigate the evaluation of points and derivatives of B\u00e9zier curves and surfaces on modern architectures, focusing on performance and guided by numerical error bounds. While the de Casteljau algorithm remains the reference for numerical robustness, its linear working\u2010set size imposes substantial register pressure on GPUs. We introduce a linear\u2010time, constant\u2010storage evaluation framework derived from the ladder algorithm that attains de Casteljau\u2010level robustness and demonstrate that it outperforms other methods both on the GPU and CPU. Our analysis provides backward\u2010error bounds for points and derivatives and it is also supported by empirical tests across degrees commonly used in rendering of curves and surfaces. Moreover, we show that fused multiply\u2010add (FMA) instructions, now ubiquitous in hardware, can improve robustness even for linear interpolation. We advocate a nested FMA formulation that reconstructs endpoints exactly, in contrast to the subtraction\u2010and\u2010FMA pattern prevalent in shader compilers. Together, these results yield reduced memory bandwidth and register pressure, and improved performance.<\/jats:p>","DOI":"10.1111\/cgf.70403","type":"journal-article","created":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T12:35:21Z","timestamp":1774874121000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Register\u2010Efficient Linear\u2010Time Evaluation in the Bernstein Basis"],"prefix":"10.1111","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0007-8647","authenticated-orcid":false,"given":"G\u00e1bor","family":"Valasek","sequence":"first","affiliation":[{"name":"E\u00f6tv\u00f6s Lor\u00e1nd University  Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-2956-9227","authenticated-orcid":false,"given":"Anna Lili","family":"Horv\u00e1th","sequence":"additional","affiliation":[{"name":"E\u00f6tv\u00f6s Lor\u00e1nd University  Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2026,3,30]]},"reference":[{"key":"e_1_2_9_2_2","volume-title":"RDNA4 Instruction Set Architecture: Reference Guide","year":"2025"},{"key":"e_1_2_9_3_2","unstructured":"Advanced Micro Devices Inc.half: Half-precision Floating Point Library.https:\/\/github.com\/ROCm\/half. 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