{"responseHeader":{"status":0,"QTime":6,"params":{"q":"{!q.op=AND}id:\"104046\"","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":"ADA004968.pdf","thumb_s":"/60/32/60325dfe3c959d9e7465dc9e8ae157daafa6eaf3.jpg","oldid_t":"compsci 12159","setname_s":"ir_computersa","restricted_i":0,"format_t":"application/pdf","creator_t":"Catmull, Edwin E.","modified_tdt":"2016-10-27T00:00:00Z","file_s":"/c2/40/c2408a68497255cf0df6215df5126bca1bab11b0.pdf","title_t":"Page 60","ocr_t":"■ l HI •mnin^t^m^^u^mmrmim''^'^-\"\" \"»i\" ' m^mmi^i^^^^r*~-r ^«a^«pm. ■■ i iin.i iiii.i>imi«^«wmOTv LUIU m ■. JUIHIU iia ^3 APPENDIX A THE BICUBIC EQUATION There are several different methods for generating bicubic patches. Each method is useful on different occasions. Bicubic equations are widely us-H in computer aided geometric design. Some good references are [11,12,13,14] with the article by George Peters in [11] being specially devoted to the bicubic patch. Consider the simple cubic: x(t) - •<» ♦ W» ♦ d ♦ d This can be expressed in matrix notation: x(t) - [t« l1 t 1] A curve in space can be represented by the parametric vector equation F(t) - [x(t) y(t) z(t)]. Since each component is a parametric function of t and is treated the same as the other components, it is only necessary for us to consider one component x(t). A patch is a function of »wo variables, u and v. F(u,v) - [x(u,v) y(u,v) z(u,v)]. Again only one component needs to be considered. The matrix notation for x(u,v) is: x(u,v) - [u3 u' u I] a,. ■it 3,3 a,. v» •> »22 a,. »a. v» ■tl a« a., a« V a.: a« a« a.« .1 -^_","id":104046,"created_tdt":"2016-10-27T00:00:00Z","parent_i":104071,"_version_":1642982555812626432}]},"highlighting":{"104046":{"ocr_t":[]}}}