{"responseHeader":{"status":0,"QTime":7,"params":{"q":"{!q.op=AND}id:\"103023\"","hl":"true","hl.simple.post":"","hl.fragsize":"5000","fq":"!embargo_tdt:[NOW TO *]","hl.fl":"ocr_t","hl.method":"unified","wt":"json","hl.simple.pre":""}},"response":{"numFound":1,"start":0,"docs":[{"file_name_t":"Yen-On_Representation.pdf","thumb_s":"/ed/1a/ed1adaea1b0df35718f9cd4099faf10cadc10921.jpg","oldid_t":"compsci 11136","setname_s":"ir_computersa","restricted_i":0,"format_t":"application/pdf","modified_tdt":"2016-05-26T00:00:00Z","file_s":"/06/95/0695b7df90649ade240f5af153beaf826133a30c.pdf","title_t":"Page 62","ocr_t":"51 A 8-spline curve -y(t) in parameter t can be expressed as: N 7{t)= ! P. B. k(t) i=O I I, where { Pi }~ 0 are N+ 1 vertices of the control polygon and Bi, k(t) are the basis functions. Each point on the B-spline curve is determined by blending the con-trol points using the basis functions as the weight. The basis functions are defined by the order k and the knot vectors. The order is the greatest degree of any of the polynomial piece plus one, e.g., a quadratic spline has order 3, a cubic spline has order 4. The knot vector is an ordered set of nondecreasing scalar values (the knots) which determines where and how those basis functions are tied together. Hence, a B-spline curve is completely determined by its or-der k, the knot vector and its control polygon. A proper refinement of the knot vector can force the control polygon to interpolate a particular point on the curve and thus to subdivide the curve into two curves each with its own control polygon. After the subdivision, the very same curve -y(t) can be written as: M -y(t)= ! j=O Q . B. k(t} J J, where { Qi }~ 0 are the M+ 1 vertices of the new control polygon and Bj, k(t} are the basis functions for the new knot vectors. Computationally, Q.'s can be exJ pressed as a function of the original Pi's and the discrete splines. A bivariate tensor product B-spline surface t3(u, v) in parameters u and v can be expressed as: N N u v t3(u, v)= ! ! Pi,i ~. k (v) ~. k (u) i=O j=O v u where { P .. I 0 ~ i ~ N and 0 ~ j ~ N } are vertices of the control mesh and I,J u v Bi,K (u) and B.\" (v) are the basis functions. It is completely determined by the u J, v orders ku and kv, the knot vectors and the control mesh. The control mesh consists of Nu + 1 * Nv + 1 points. Notice that it is inherently rectangular, i.e., it is","id":103023,"created_tdt":"2016-05-26T00:00:00Z","parent_i":103066,"_version_":1679953856823296000}]},"highlighting":{"103023":{"ocr_t":[]}}}