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Because our new form of the collision test is also a smooth inequality, it can be used as a holonomic unilateral constraint in many applications, such as path planning, rigid body dynamics, nesting or tool placement, replacing the need for more ad-hoc normal\/contact-based constraint solvers. Moreover, we also show how this constraint can be directly differentiated via Fourier multipliers with only a constant factor overhead, which leads to a simple method for constructing a Jacobian for both normal forces and rotational torques.<\/jats:p>","DOI":"10.1177\/0278364913477165","type":"journal-article","created":{"date-parts":[[2013,2,25]],"date-time":"2013-02-25T22:35:52Z","timestamp":1361831752000},"page":"483-503","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":8,"title":["Fourier collision detection"],"prefix":"10.1177","volume":"32","author":[{"given":"Mikola","family":"Lysenko","sequence":"first","affiliation":[{"name":"Spatial Automation Lab, University of Wisconsin\u2013Madison, Madison, WI, USA."}]}],"member":"179","published-online":{"date-parts":[[2013,2,25]]},"reference":[{"key":"bibr1-0278364913477165","volume-title":"VRIC","author":"Avril Q","year":"2009"},{"key":"bibr2-0278364913477165","doi-asserted-by":"publisher","DOI":"10.1145\/357306.357310"},{"key":"bibr3-0278364913477165","doi-asserted-by":"publisher","DOI":"10.1145\/91385.91427"},{"key":"bibr4-0278364913477165","doi-asserted-by":"publisher","DOI":"10.1145\/359046.359048"},{"key":"bibr5-0278364913477165","doi-asserted-by":"publisher","DOI":"10.1201\/9781420041767"},{"key":"bibr6-0278364913477165","doi-asserted-by":"publisher","DOI":"10.1145\/321466.321468"},{"key":"bibr7-0278364913477165","doi-asserted-by":"publisher","DOI":"10.1680\/geot.1979.29.1.47"},{"key":"bibr8-0278364913477165","doi-asserted-by":"publisher","DOI":"10.1109\/70.988971"},{"key":"bibr9-0278364913477165","doi-asserted-by":"publisher","DOI":"10.1145\/1060244.1060266"},{"key":"bibr10-0278364913477165","volume-title":"Realtime Collision Detection","author":"Ericson C","year":"2005","edition":"1"},{"key":"bibr11-0278364913477165","doi-asserted-by":"publisher","DOI":"10.1137\/S1111111102406038"},{"key":"bibr12-0278364913477165","first-page":"249","volume-title":"Proceedings of 27th annual conference on computer graphics and interactive techniques","author":"Frisken S","year":"2009"},{"key":"bibr13-0278364913477165","doi-asserted-by":"publisher","DOI":"10.1109\/MCG.2006.17"},{"key":"bibr14-0278364913477165","first-page":"58","author":"Fuhrmann A","year":"2003","journal-title":"Proceedings of GraphiCon 2003"},{"key":"bibr15-0278364913477165","doi-asserted-by":"publisher","DOI":"10.1115\/1.3258768"},{"key":"bibr16-0278364913477165","doi-asserted-by":"publisher","DOI":"10.1109\/JRA.1985.1087003"},{"key":"bibr17-0278364913477165","doi-asserted-by":"publisher","DOI":"10.1109\/56.2083"},{"key":"bibr18-0278364913477165","doi-asserted-by":"publisher","DOI":"10.1145\/282918.282923"},{"key":"bibr19-0278364913477165","volume-title":"Marker layout problem via graph theory: An attempt for optimal layout of irregular patterns","author":"Gurel O","year":"1968"},{"key":"bibr20-0278364913477165","doi-asserted-by":"publisher","DOI":"10.1007\/BF01582255"},{"key":"bibr21-0278364913477165","unstructured":"Karush W (1939) Minima of Functions of Several variables with Inequalities with Side Constraints. 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