{"responseHeader":{"status":0,"QTime":7,"params":{"q":"{!q.op=AND}id:\"95852\"","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":[{"modified_tdt":"2015-11-02T00:00:00Z","thumb_s":"/86/e5/86e5e24644286c66766bc00c214a50020910d2d7.jpg","oldid_t":"compsci 3670","setname_s":"ir_computersa","file_s":"/46/a1/46a1e75857c179e7ea020bab69caef2ffe6966a0.pdf","title_t":"Page 20","ocr_t":"(2. ) 2.2.2 Interpolation Since the coordinate transformation function from the world coordinate system to the canonical coordinate system is linear, the interpolation of the scalar field f is a lin ar polynomial of the canonical coordinates. It can be formulated as: where ai, 1 ::; i ::; 4, are the coefficients of the polynomial. Assume that the scalar field values at the four vertices of the standard cell are fi, 1 ::; i ::; 4,. By substituting the canonical coordinates and the scalar field values at the vertices of the standard cell into the above equation, these coefficients ai can be solved as: a1 !2-!I, a2 !3- !I, a3 !4- !I, a4 fi. Therefore the interpolation function can be expressed as: f(~,ry,() (h - !I)~+ (!3 - !I)TJ + (!4 - !I)(+ !I' ( 1 - ~ - 7] - ()!I + ~ h + 7] !3 + ( !4. (2.4) The components of the vector field i1 are linear polynomials of the canonical coordinates in the standard cell. Based on Equation 2.4, the interpolation function of i1 can be written as: (2.5) where iii, 1 ::; i ::; 4, are the vector field values at the four vertices of the standard cell. The world coordinate vector x can be regarded as a vector field in the standard cell. Therefore, the world coordinates of a canonical coordinate vector [can be computed by using the above interpolation function. Assume the world coordinate vectors of the","restricted_i":0,"id":95852,"created_tdt":"2015-11-02T00:00:00Z","format_t":"application/pdf","parent_i":95941,"_version_":1642982571740495875}]},"highlighting":{"95852":{"ocr_t":[]}}}