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We introduce the notion of low-discrepancy curves as an extension of the notion of low-discrepancy sequences\u2014such that sufficiently smooth curves with low-discrepancy properties can be defined and generated. We then devise a procedure for lifting these curves, that efficiently cover the unit cube, to abstract surfaces, such as nonlinear manifolds. We present algorithms that yield suitable <jats:italic>fair<\/jats:italic> mappings between the unit cube and the abstract surface. We demonstrate the application of these ideas using some concrete examples of interest in robotics.<\/jats:p>","DOI":"10.1017\/s0263574707004067","type":"journal-article","created":{"date-parts":[[2008,1,22]],"date-time":"2008-01-22T10:03:27Z","timestamp":1200996207000},"page":"503-512","source":"Crossref","is-referenced-by-count":1,"title":["Efficient, incremental coverage of space with a continuous curve"],"prefix":"10.1017","volume":"26","author":[{"given":"Subramanian","family":"Ramamoorthy","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ram","family":"Rajagopal","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lothar","family":"Wenzel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2008,7,1]]},"reference":[{"key":"S0263574707004067_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/S0010-4655(96)00108-7"},{"key":"S0263574707004067_ref14","unstructured":"14. Richtmyer R. D. , \u201cA Non-random Sampling Method, Based on Congruences for Monte Carlo Problems,\u201d Rep. NYO-8674. Institute of Mathematical Sciences, New York University, New York, 1958)."},{"key":"S0263574707004067_ref18","volume-title":"An Introduction to the Theory of Numbers","author":"Hardy","year":"1980"},{"key":"S0263574707004067_ref12","first-page":"784","article-title":"The distribution of points in a cube and the approximate evaluation of integrals","volume":"7","author":"Sobol","year":"1967","journal-title":"Zh. Vychisl. Mat. i Mat. Fiz. USSR Comput. Math. Math. Phys."},{"key":"S0263574707004067_ref13","doi-asserted-by":"crossref","unstructured":"13. Richtmyer R. D. , \u201cThe evaluation of definite integrals, and quasi-Monte Carlo method based on the properties of algebraic numbers,\u201d Rep. 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Niederreiter H. , Random Number Generation and Quasi-Monte Carlo Methods, CBMS-NSF Regional Conference Series in Applied Mathematics, No. 63 (SIAM, Philadelphia, PA, 1992).","DOI":"10.1137\/1.9781611970081"},{"key":"S0263574707004067_ref23","volume-title":"Handbook of Differential Equations","author":"Zwillinger","year":"1997"},{"key":"S0263574707004067_ref1","volume-title":"Hamiltonian Chaos and Fractional Dynamics","author":"Zaslavsky","year":"2005"},{"key":"S0263574707004067_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-03942-3"},{"key":"S0263574707004067_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511626371"},{"key":"S0263574707004067_ref5","first-page":"2920","volume-title":"Proceedings of the IEEE International Conference on Robotics and Automation","author":"Lindemann","year":"2003"},{"key":"S0263574707004067_ref6","first-page":"297","volume-title":"Algorithmic Foundations of Robotics VI","author":"Lindemann","year":"2005"},{"key":"S0263574707004067_ref7","doi-asserted-by":"publisher","DOI":"10.1109\/70.163777"},{"key":"S0263574707004067_ref10","first-page":"813","article-title":"Vereilungsfunktionen 1,11","volume":"38","author":"Corput","year":"1935","journal-title":"Nederl. 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