{"responseHeader":{"status":0,"QTime":6,"params":{"q":"{!q.op=AND}id:\"95850\"","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":"/0b/59/0b597401b8edd28ae451ee4a5809d3cf2e6defb9.jpg","oldid_t":"compsci 3668","setname_s":"ir_computersa","file_s":"/a2/ce/a2ce5b6b933c6797d7850fefeb19d9f6dd997c48.pdf","title_t":"Page 18","ocr_t":"7 Th omponents of matrix R and v ctor d an b cal ulat d b equations: lving th f 11 wing [ X1 Yl Z1 X2 Y2 Z2 X3 Y3 Z3 x4 Y4 z4 r31 l [ U1 VI WI l r32 _ u2 v2 w2 - ' r33 U3 V3 W3 d3 u4 v4 W4 where ( Ui, Vi, wi), 1 :::; i :::; 4, are the vector field values in the four vertices of the cell. By differentiating the components of ii with respect to the world coordinates, we have: [au] ax = R. (2.1) 2.2 The Canonical Coordinate System The interpolation functions described in the previous section are polynomials of the world coordinates. Since the shapes and positions of cells are not fixed in the world coordinate system, these functions vary from one cell to another. Therefore function value calculations are cell-dependent. In FEA computations, usually a standard cell is designated as the template for all cells. Calculations are carried out in the standard cell and transformed back to the original cells. Consequently all formulations are the same for all cells. A popular standard cell is shown in Figure 2.2. This cell is constructed in a coordinate system which is different from the world coordinate system. This coordinate system is called the canonical coordinate system. The three coordinates of this system are denoted as ~' ry, and (. In the canonical coordinate system, the first vertex of the standard cell is located at the origin, and the other three vertices are separately located at the three axes with a unit distance from the origin. 2.2.1 Coordinate Transformation In order to carry out calculation in the standard cell, coordinate transformation between the world coordinate system and the canonical coordinate system is required. An example of the coordinate transformation is shown in Figure 2.3. As shown in this example, when the standard cell is mapped onto a cell in the world coordinate system, the origin of the canonical coordinate system are mapped onto the first vertex of the cell, and the three axes of the canonical coordinate system coincide with the three edges emitting from the first vertex of the cell. Therefore, in the world coordinate system, the","restricted_i":0,"id":95850,"created_tdt":"2015-11-02T00:00:00Z","format_t":"application/pdf","parent_i":95941,"_version_":1642982571740495873}]},"highlighting":{"95850":{"ocr_t":[]}}}