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To achieve a desired effect one is typically interested in smoothly varying fields that satisfy a sparse set of user-provided constraints. Using tools from Discrete Exterior Calculus, we present a simple and efficient algorithm for designing such fields over arbitrary triangle meshes. By representing the field as scalars over mesh edges (<jats:italic>i.e.<\/jats:italic>, discrete 1-forms), we obtain an intrinsic, coordinate-free formulation in which field smoothness is enforced through discrete Laplace operators. Unlike previous methods, such a formulation leads to a linear system whose sparsity permits efficient pre-factorization. Constraints are incorporated through weighted least squares and can be updated rapidly enough to enable interactive design, as we demonstrate in the context of anisotropic texture synthesis.<\/jats:p>","DOI":"10.1145\/1276377.1276447","type":"journal-article","created":{"date-parts":[[2007,9,14]],"date-time":"2007-09-14T13:44:55Z","timestamp":1189777495000},"page":"56","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":112,"title":["Design of tangent vector fields"],"prefix":"10.1145","volume":"26","author":[{"given":"Matthew","family":"Fisher","sequence":"first","affiliation":[{"name":"Caltech"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Schr\u00f6der","sequence":"additional","affiliation":[{"name":"Caltech"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mathieu","family":"Desbrun","sequence":"additional","affiliation":[{"name":"Caltech"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hugues","family":"Hoppe","sequence":"additional","affiliation":[{"name":"Microsoft Research"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2007,7,29]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"crossref","unstructured":"Arnold D. 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