{"responseHeader":{"status":0,"QTime":6,"params":{"q":"{!q.op=AND}id:\"104015\"","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":"/0d/1a/0d1aba7dd2ea71bf743e81d9652bdd60e54b785a.jpg","oldid_t":"compsci 12128","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":"/5b/52/5b52ffe02417452a9b3c4e2816bda2a968caa15a.pdf","title_t":"Page 29","ocr_t":"»3Pwa«w\"»\",w\"i\"»i»»™*^w>wRi»i»^p!ii«»p^»«iF»«»w^i «WM\" i W^WPHF\"\"»*1 \" ■ ■,,l \"■• ni\"\"w^Bp»w^j«.i.»,Pnii«-«p»w»>w^Bpww»fPipn\"nii Jin ■w^mmFmmm Sl^ CHAPTER FOUR EXTENSION OF CUBIC SUBDIVISION TO SURFACES The method of subdivioing cubic curves can be extended to bicubic surfaces. With a cubic curve there is a value and a correction term at each end; with a bicubic patch there is a value '..nd three correction terms at each corner. Subdivision of the patch into four pieces means finding the midpoint of each of the sides and the midpoint of the patch. There may be several components to the vector that describes a t^-ee dimensional patch. The surface has three purely geometric components X(u(v), Y(u,v), and Z(uIv). There may be additional components for other information such as shading and color. Each component is treated the same so we need only consider one component of the patch here. Since we are considering only one component of the surface let that component be: f(u,v) - [u5 u7 U I] b7 a, b, C, c7 d, d? a. a« M b^ b« V2 C3 c« V d3 d4J 1 If we multiply the u matrix by the coefficient matrix this equation becomes ^M* - Mil-IIII ' - ' - ■• ■ IT ■■-\"-'- - ■ OMMMMMikiMti","id":104015,"created_tdt":"2016-10-27T00:00:00Z","parent_i":104071,"_version_":1679953243545796608}]},"highlighting":{"104015":{"ocr_t":[]}}}