{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:05:25Z","timestamp":1760148325761,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,21]],"date-time":"2023-04-21T00:00:00Z","timestamp":1682035200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004543","name":"Chinese Scholarship Council","doi-asserted-by":"publisher","award":["202007720052"],"award-info":[{"award-number":["202007720052"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computers"],"abstract":"<jats:p>Coarse meshes can be recursively subdivided into denser and denser meshes by dividing their faces into several smaller faces and repositioning the vertices according to carefully designed subdivision rules. This process leads to smooth surfaces, such as in the case of Catmull-Clark or Loop subdivision, but often suffers from shading artifacts near extraordinary points due to the lower quality of the normal field there, typically corresponding to only tangent-plane (and not higher) continuity at these points. The idea of subdivision shading is to apply the same subdivision rules that are used to subdivide geometry to also subdivide the normals associated with mesh vertices. This leads to smoother normal fields, which can be used for shading purposes, and this in turn removes the shading artifacts. However, the original subdivision shading method does not support sharp and semi-sharp creases, which are desired ingredients in subdivision surface modelling. We present two approaches to extending subdivision shading to work also on models with (semi-)sharp creases, and demonstrate this in the cases of Catmull-Clark as well as Loop subdivision.<\/jats:p>","DOI":"10.3390\/computers12040085","type":"journal-article","created":{"date-parts":[[2023,4,21]],"date-time":"2023-04-21T03:01:48Z","timestamp":1682046108000},"page":"85","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Subdivision Shading for Catmull-Clark and Loop Subdivision Surfaces with Semi-Sharp Creases"],"prefix":"10.3390","volume":"12","author":[{"given":"Jun","family":"Zhou","sequence":"first","affiliation":[{"name":"Bernoulli Institute, University of Groningen, 9712 Groningen, The Netherlands"}]},{"given":"Jan","family":"Boonstra","sequence":"additional","affiliation":[{"name":"Bernoulli Institute, University of Groningen, 9712 Groningen, The Netherlands"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8859-2586","authenticated-orcid":false,"given":"Ji\u0159\u00ed","family":"Kosinka","sequence":"additional","affiliation":[{"name":"Bernoulli Institute, University of Groningen, 9712 Groningen, The Netherlands"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/0010-4485(78)90110-0","article-title":"Recursively generated B-spline surfaces on arbitrary topological meshes","volume":"10","author":"Catmull","year":"1978","journal-title":"Comput.-Aided Des."},{"key":"ref_2","unstructured":"Loop, C. (1987). Smooth Subdivision for Surfaces Based on Triangles. [Master\u2019s Thesis, University of Utah]."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Alexa, M., and Boubekeur, T. (2008, January 10\u201313). Subdivision shading. Proceedings of the ACM Siggraph Asia, Singapore.","DOI":"10.1145\/1457515.1409095"},{"key":"ref_4","unstructured":"Bakker, J., Barendrecht, P., and Kosinka, J. (2018, January 16\u201320). Smooth Blended Subdivision Shading. Proceedings of the Eurographics (Short Papers), Delft, The Netherlands."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"DeRose, T., Kass, M., and Truong, T. (1998, January 19\u201324). Subdivision surfaces in character animation. Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques, Orlando, FL, USA.","DOI":"10.1145\/280814.280826"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1383","DOI":"10.1111\/j.1467-8659.2008.01278.x","article-title":"Fitting Sharp Features with Loop Subdivision Surfaces","volume":"27","author":"Ling","year":"2008","journal-title":"Comput. Graph. Forum"},{"key":"ref_7","unstructured":"Zhou, J., Boonstra, J., and Kosinka, J. (2022). Semi-Sharp Subdivision Shading, Eurographics Association."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Kovacs, D., Mitchell, J., Drone, S., and Zorin, D. (March, January 27). Real-time creased approximate subdivision surfaces. Proceedings of the 2009 Symposium on Interactive 3D Graphics and Games, New York, NY, USA.","DOI":"10.1145\/1507149.1507174"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2897824.2925874","article-title":"Efficient GPU rendering of subdivision surfaces using adaptive quadtrees","volume":"35","author":"Brainerd","year":"2016","journal-title":"ACM Trans. Graph."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1111\/cgf.12258","article-title":"Subdivision surfaces with creases and truncated multiple knot lines","volume":"33","author":"Kosinka","year":"2014","journal-title":"Comput. Graph. Forum"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Hoppe, H., DeRose, T., Duchamp, T., Halstead, M., Jin, H., McDonald, J., Schweitzer, J., and Stuetzle, W. (1994, January 24\u201329). Piecewise smooth surface reconstruction. Proceedings of the Computer Graphics and Interactive Techniques, Orlando, FL, USA.","DOI":"10.1145\/192161.192233"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1111\/cgf.12447","article-title":"Semi-sharp Creases on Subdivision Curves and Surfaces","volume":"33","author":"Kosinka","year":"2014","journal-title":"Comput. Graph. Forum"},{"key":"ref_13","unstructured":"McGuire, M. (2023, April 20). The Half-Edge Data Structure. Available online: https:\/\/www.flipcode.com\/archives\/The_Half-Edge_Data_Structure.shtml."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/S0167-8396(01)00038-3","article-title":"On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree","volume":"18","author":"Stam","year":"2001","journal-title":"Comput. Aided Geom. Des."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.cagd.2019.04.004","article-title":"A bivariate C1 subdivision scheme based on cubic half-box splines","volume":"71","author":"Barendrecht","year":"2019","journal-title":"Comput. Aided Geom. Des."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1111\/cgf.14381","article-title":"A Halfedge Refinement Rule for Parallel Catmull-Clark Subdivision","volume":"40","author":"Dupuy","year":"2021","journal-title":"Comput. Graph. 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