{"title":"Narrowing-Cascade splines for control nets that shed mesh lines","authors":"Serhat Cam , Erkan Gunpinar , Kȩstutis Karčiauskas , Jörg Peters","doi":"10.1016/j.cag.2025.104441","DOIUrl":null,"url":null,"abstract":"<div><div>Quad-dominant meshes are popular with animation designers and can efficiently be generated from point clouds. To join primary regions, quad-dominant meshes include non-4-valent vertices and non-quad regions. To transition between regions of rich detail and simple shape, quad-dominant meshes commonly use a cascade of <span><math><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></math></span> triangles that reduce the number of parallel quad strips from <span><math><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></math></span> to 2. For these cascades, the Narrowing-Cascade spline, short NC<span><math><msup><mrow></mrow><mrow><mi>n</mi></mrow></msup></math></span>, provides a new shape-optimized <span><math><msup><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> spline surface. NC<span><math><msup><mrow></mrow><mrow><mi>n</mi></mrow></msup></math></span> can treat cascade meshes as B-spline-like control nets. For <span><math><mrow><mi>n</mi><mo>></mo><mn>3</mn></mrow></math></span>, as opposed to <span><math><mrow><mi>n</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></math></span>, cascades have interior points that both guide and complicate the construction of the output tensor-product NC<span><math><msup><mrow></mrow><mrow><mspace></mspace></mrow></msup></math></span>spline. The NC<span><math><msup><mrow></mrow><mrow><mi>n</mi></mrow></msup></math></span> spline follows the input mesh, including interior points, and delivers a high-quality curved surface of low degree.</div></div>","PeriodicalId":50628,"journal":{"name":"Computers & Graphics-Uk","volume":"133 ","pages":"Article 104441"},"PeriodicalIF":2.8000,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computers & Graphics-Uk","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0097849325002821","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
引用次数: 0
Abstract
Quad-dominant meshes are popular with animation designers and can efficiently be generated from point clouds. To join primary regions, quad-dominant meshes include non-4-valent vertices and non-quad regions. To transition between regions of rich detail and simple shape, quad-dominant meshes commonly use a cascade of triangles that reduce the number of parallel quad strips from to 2. For these cascades, the Narrowing-Cascade spline, short NC, provides a new shape-optimized spline surface. NC can treat cascade meshes as B-spline-like control nets. For , as opposed to , cascades have interior points that both guide and complicate the construction of the output tensor-product NCspline. The NC spline follows the input mesh, including interior points, and delivers a high-quality curved surface of low degree.
期刊介绍:
Computers & Graphics is dedicated to disseminate information on research and applications of computer graphics (CG) techniques. The journal encourages articles on:
1. Research and applications of interactive computer graphics. We are particularly interested in novel interaction techniques and applications of CG to problem domains.
2. State-of-the-art papers on late-breaking, cutting-edge research on CG.
3. Information on innovative uses of graphics principles and technologies.
4. Tutorial papers on both teaching CG principles and innovative uses of CG in education.