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Despite still being an important criterion, other geometric properties also play critical roles in different applications, such as triangle quality for computations. This motivates our work to stay under the umbrella of the popular quadric error mesh simplification, while proposing different ways to control the simplified mesh to possess other geometric properties. The key ingredient of our work is another quadric error, called <jats:italic>line quadrics<\/jats:italic>, which can be seamlessly added to the vanilla quadric error metric. We show that, theoretically and empirically, adding our line quadrics can improve the numerics and encourage the simplified mesh to have uniformly distributed vertices. If we spread the line quadric adaptively to different regions, it can easily lead to soft preservation of feature vertices and edges. Our method is simple to implement, requiring only a few lines of code change on top of the original quadric error simplification, and can lead to a variety of user controls.<\/jats:p>","DOI":"10.1111\/cgf.70184","type":"journal-article","created":{"date-parts":[[2025,8,28]],"date-time":"2025-08-28T15:25:12Z","timestamp":1756394712000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Controlling Quadric Error Simplification with Line Quadrics"],"prefix":"10.1111","volume":"44","author":[{"given":"Hsueh\u2010Ti Derek","family":"Liu","sequence":"first","affiliation":[{"name":"Roblox  USA"}]},{"given":"Mehdi","family":"Rahimzadeh","sequence":"additional","affiliation":[{"name":"Roblox  USA"}]},{"given":"Victor","family":"Zordan","sequence":"additional","affiliation":[{"name":"Roblox  USA"}]}],"member":"311","published-online":{"date-parts":[[2025,8,28]]},"reference":[{"issue":"48","key":"e_1_2_7_2_2","doi-asserted-by":"crossref","first-page":"4864","DOI":"10.1016\/j.cma.2004.11.016","article-title":"Simplification of surface mesh using hausdorff envelope","volume":"194","author":"Borouchaki H.","year":"2005","journal-title":"Computer methods in applied mechanics and engineering"},{"key":"e_1_2_7_3_2","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/0024-3795(94)90493-6","article-title":"Numerics of gram-schmidt orthogonalization","volume":"197","author":"Bj\u00f6rck \u00c5.","year":"1994","journal-title":"Linear Algebra and Its Applications"},{"key":"e_1_2_7_4_2","doi-asserted-by":"crossref","unstructured":"BotschM. 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