Lecture overview. Visualisatie BMT. Visualization pipeline. Data representation. Discrete data. Sampling. Data Datasets Interpolation

Transcription

1 Viualiatie BMT Lectue oveview Data Dataet Intepolation Data epeentation Ajan Kok 2 Viualization pipeline Raw Data Data Enichment/Enhancement Deived Data Data epeentation Viualization data ha eveal popetie: It i dicete It ha ome tuctue It ha a topological dimenion Viualization data Viualization Mapping Abtact Viualization Object Rendeing Diplaable Image 3 4 Dicete data Sampling Data toed in a compute i alwa dicete Infomation i meaued o ampled in a finite numbe of point Data i intepolated between the point continuou data ampling dicete data = f() ( 0, 0 ), (, ), ( 2, 2 ),, ( 8, 8 ) 5 6

2 Data tuctue Data ample ae oganized into ome tuctue The tuctue decibe how the ample elate to each othe Data tuctue Stuctue: Sample cone in (, ) pai Ode of pai = ode of ampling on -ai ampling ode ( 0, 0 ), (, ), ( 2, 2 ),, ( 8, 8 ) 7 8 Data deign citeia What fom of fom hould we ue to epeent data? Data deign citeia Compact Gigabte to toe, minimize toage equiement Efficient Data mut be quickl acceible Mappable Data mut be eail conveted fom etenal data to intenal viualization data tuctue Data mut efficientl map to gaphic pimitive Minimal coveage Need a minimal et of data epeentation that can decibe all eal-wold data tpe Simple Ea to undetand Optimization 9 0 The dataet The dataet i the compute epeentation of viualization data A dataet conit of: Oganizing tuctue The wa data ample elate to each othe (geometical, connection) Attibute The data ample (value) themelve The dataet TOPOLOGY STRUCTURE GEOMETRY DATASET Geomet The coodinate of the ample (node) Topolog Stuctue defined on thee point (cell) Attibute Sampled data at eve node o cell ATTRIBUTES 2 2

3 Dataet eample Dataet: ( 0, 0 ), (, ), ( 2, 2 ),, ( 8, 8 ) Node: 0,, 2,, 8 Cell: 0-, -2, 2-3,, 7-8 Attibute: 0,, 2,, 8 (cala, given pe node) 3D dataet eample The node (geomet) of a 3D dataet epeenting a teapot cell 0- cell D dataet eample The dataet Topolog (cell) => connectivit between the node Rendeed image of teapot STRUCTURE DATASET ATTRIBUTES TOPOLOGY GEOMETRY CELLS NODES 5 6 Cell Linea cell tpe Fundamental building block of data et Defined b Tpe Connectivit lit (odeed lit of point) 7 8 3

4 Non-linea cell tpe Dataet dimenion Topological dimenion (ndim) Gid dimenion The numbe of independent vaiable The numbe of coodinate pecifing the dataet Geometical dimenion (npace) Node dimenion The numbe of coodinate pecifing poition of each node 9 Flat page (2D, 2-pace) Bent page (2D, 3-pace) 20 Dataet dimenion Tpe of dataet Tpe of dataet pecifie the elationhip between cell and point Dataet chaacteization Topolog egula o iegula Geomet egula o iegula 2 22 Dataet chaacteization Regula geomet Poition of the node in pace i egula Iegula geomet Poition of the node in pace i not egula Coodinate of all point mut be toed eplicitl Data et chaacteization Regula topolog Regula elationhip between the node Can be toed in n-dimenional aa Node info acceed uing indice Iegula topolog No egula elationhip between the node All connectivit mut be toed eplicitl Fo comple geometie and adaptive gid

5 Tpe of dataet Stuctued point (image data) Rectilinea gid Stuctued gid Untuctued point Untuctued gid Polgonal data Stuctued point Regula geomet Regula topolog N-dimenional aa of node (-, -, z-ai aligned) Line (D), piel (2D) o voel (3D) cell tpe Defined b Topological dimenion Poition of node 0 Size of cell (ditance between node) Stuctued point Stuctued point DATASET STRUCTURED_POINTS DIMENSIONS 6 5 ORIGIN SPACING 0 Given Stuctued point gid dataet Dimenion (n, n, n z ) Spacing (,, z ) Oigin (o, o, o z ) 0 0 Quetion What i numbe of cell? What i poition of point (i, j, k)? What i id of node (i, j, k)? Rectilinea gid Rectilinea gid Regula topolog Patial egula geomet N-dimenional aa of node (-, -, z-ai aligned) Line (D), piel (2D) o voel (3D) cell tpe Defined b Topological dimenion Fo each dimenion an odeed lit with coodinate DATASET RECTILINEAR_GRID DIMENSIONS 6 5 X_XOORDINATES 6 float Y_XOORDINATES 5 float Z_COORDINATES float

6 Stuctued gid Stuctued gid eample Iegula geomet Regula topolog N-dimenional aa of node Line (D), quadilateal (2D) o heahedon (3D) cell tpe Defined b Topological dimenion Odeed lit with coodinate fo each node DATASET STRUCTURED_GRID DIMENSIONS 3 5 POINTS 5 float Untuctued point Iegula geomet No topolog Vete and polvete cell tpe Defined b Lit with coodinate fo each node Untuctued gid The mot geneal and fleible epeentation The mot memo conuming and comple implementation Iegula geomet Iegula topolog An cell tpe Defined b Lit with coodinate fo each node Fo each cell: tpe and odeed lit of node Untuctued gid eample Untuctued gid eample DATASET UNSTRUCTURED_GRID POINTS 9 float CELLS CELL_TYPES

7 Polgonal data Polgonal data eample Define geometic pimitive Iegula geomet Iegula topolog Vetice, polvetice, line, polline, polgon, tiangle tip cell tpe Defined b Odeed lit with coodinate fo each node Fo each cell: tpe and odeed lit of node DATASET POLYDATA POINTS 5 float LINES POLYGONS The dataet The dataet DATASET DATASET STRUCTURE ATTRIBUTES STRUCTURE ATTRIBUTES TOPOLOGY GEOMETRY TOPOLOGY GEOMETRY CELLS NODES CELLS NODES CELL DATA NODE DATA Node and cell data cell cell data value = 20 value = -0 value = 9 node data node value = -7 Data value can be povided fo each node in the data et, o fo each cell, o fo both Attibute data i optional Attibute data Attibute indicate the tpe of data ampled Scala ingle value Vecto tiplet of value (u,v,w) Nomal tiplet of value, nomalized Colo tiplet of value Teno (33) mati A dataet can contain eveal attibute et All node in a dataet have the ame attibute et All cell in a dataet have the ame attibute et

8 Attibute data eample Intepolation POINT_DATA 5 COLOR SCALARS node_colo CELL DATA 2 SCALARS cell_value float VECTORS cell_vecto float Intepolation Intepolation Compute deal with dicete data Data i eithe upplied: At a finite numbe of point B ampling continuou data at a finite numbe of point We need infomation at poition othe than thee dicete point location => intepolation function 45 We aume Data i defined at cell point (P i ) Unknown point P i inide the cell We need Data value at each cell point P Paametic coodinate of point P within the cell Cell tpe including intepolation function We compute Real coodinate of point P Attibute value at point P 46 Intepolation Intepolation D Intepolation i a linea combination of data value at the cell node d = n i= 0 W i d i d - data value at the deied cell location d i - data value at the i-th cell node W i - weight function fo the i-th cell node W i (p j ) = if i==j 0 othewie n W (p) i = in an point p in the cell i= d = n i= 0 W i d i d 0 d() = ( )d o + d - 0 d W 0 = ( ) W =

9 Intepolation Line intepolation Each cell tpe ha it own intepolation function Weight W i ae function of paametic coodinate, and t Compoite cell ue intepolation of compoing cell = 0 = Ue one paametic coodinate () W 0 = ( ) W = Piel intepolation Quadilateal intepolation = Two paametic coodinate (, ) = Two paametic coodinate (, ) = 0 = 0 = W 0 = ( ) ( ) W = ( ) W 2 = ( ) W 3 = = 0 = 0 = W 0 = ( ) ( ) W = ( ) W 2 = W 3 = ( ) 5 52 Tiangle intepolation Polgon intepolation = 0 + = p = 0 Two paametic coodinate (,) W 0 = ( ) W = W 2 = p 4 p 5 d 3 Two paametic coodinate (, ) Paameteization ectangle encloe polgon Weight baed on ditance to each polgon vete di Wi = n i= 0 di d = p i i

10 Tetahedon intepolation Heahedon intepolation t Thee paametic coodinate (,, t) W 0 = ( t) W = W 2 = W 3 = t p 4 t p 7 p6 p 5 Thee paametic coodinate (,,t) W 0 = ( ) ( ) ( t) W = ( ) ( t) W 2 = ( t) W 3 = ( ) ( t) W 4 = ( ) ( ) t W 5 = ( ) t W 6 = t W 7 = ( ) t Voel intepolation Heahedon intepolation t p 6 p 7 Thee paametic coodinate (,,t) t p 7 Thee paametic coodinate (,,t) p 4 p6 p 4 p 5 W 0 = ( ) ( ) ( t) W = ( ) ( t) W 2 = ( ) ( t) W 3 = ( t) W 4 = ( ) ( ) t W 5 = ( ) t W 6 = ( ) t W 7 = t p 5 W 0 = ( ) ( ) ( t) W = ( ) ( t) W 2 = ( t) W 3 = ( ) ( t) W 4 = ( ) ( ) t W 5 = ( ) t W 6 = t W 7 = ( ) t Viualization pipeline Raw Data Data Enichment/Enhancement Deived Data Viualization Mapping Abtact Viualization Object Rendeing Diplaable Image 59 0