{"responseHeader":{"status":0,"QTime":5,"params":{"q":"{!q.op=AND}id:\"104049\"","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":"/28/0f/280f511a13f884a751b5273e4577c0d8a78973d5.jpg","oldid_t":"compsci 12162","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":"/10/17/10170bfc84ce4a0e5c8b42b25083049362a9e868.pdf","title_t":"Page 63","ocr_t":"-\">• m\" 'ii - -i'i ■ m^nm^^mmmi i, i n ■ « i n.« i \\\\mvmmm**W ^PII pii^iiMfn M 56 2. THE BEZIER OR BERNSTEIN CUBIC Consider the four points P,, P„ P,, and P,. The curve will pass through P, and Pa. The line from P, to P? is tangent to the curve at P, and the line from P, to Pa is tangent at P,,. The length of the tangent vector at P, is three times the length of the line from P, to P,. S^.iilarly the length of the tangent vector at Pa it three t.me the length of the line i'Om Pj to P,. The curve is constrained to lie with the convex hull of the defining points. P, xm-tt* t» t I]M. where M2- -13-3 1 3-630 -3300 10 0 0 Two cubics can be joined with C, continuity if the control points at the joint are the same (quite obviously) and the two control points of both connecting ends are all colinear, ie., in the following diagram P3, P,-Q„ and Q, are colinear. IM mm Maah-a^---. ___^^Mfl","id":104049,"created_tdt":"2016-10-27T00:00:00Z","parent_i":104071,"_version_":1679953243556282368}]},"highlighting":{"104049":{"ocr_t":[]}}}