Form-factors Josef Pelikán CGG MFF UK Praha.

Transcription

1 Form-factors Josef Pelkán CGG MFF UK Praha FormFactor 2016 Josef Pelkán, 1 / 23

2 Form-factor F It ndcates the proporton of energy emtted from the surface whch wll ht the the surface key value when creatng a system of lnear equatons (searchng for ndvdual area radostes) frst calculaton (physcs): Lambert 1760 t depends only on the geometry of the scene dstance, nclnaton and slope of the areas F s a dmensonless number from the nterval 0,1 for a convex polygon s F = 0 FormFactor 2016 Josef Pelkán, 2 / 23

3 Form-factor F N y y d N x r x FormFactor 2016 Josef Pelkán, 3 / 23

4 FormFactor 2016 Josef Pelkán, 4 / 23 F G y x d d x y V x y d d 1 1 2, cos cos, B B B G y x d d e, N 1 1, Form-factor Radosty equaton (wth constant elements):

5 Dfferental form-factor df d d cos cos r 2 N y y d N x r x FormFactor 2016 Josef Pelkán, 5 / 23

6 Dfferental form-factor F d cos cos r 2 d N y y d N x r x FormFactor 2016 Josef Pelkán, 6 / 23

7 verage form-factor F 1 cos r cos 2 d d N y y d N x r x FormFactor 2016 Josef Pelkán, 7 / 23

8 Calculaton of form-factors analytcal methods numercal methods hemcube (Nusselt analogue), proecton nto one plane, curve ntegral (accordng to Stokes' theorem) numercal stochastc methods (Monte-Carlo) samplng of a spatal angle or an area that receves energy FormFactor 2016 Josef Pelkán, 8 / 23

9 Nusselt analogue N r1 F d FormFactor 2016 Josef Pelkán, 12 / 23

10 Nusselt analogue F F d d B F d C C B FormFactor 2016 Josef Pelkán, 13 / 23

11 Hemcube Regular cell network: delta form-factors F q FormFactor 2016 Josef Pelkán, 14 / 23

12 Hemcube calculaton of all F d for gven we proect all other faces on the hemcube bult around we calculate the vsblty of the ndvdual faces on the surface of the hemcube (Z-buffer method) the surface of the hemcube s dvded nto a regular network of cells Cq for each cell we have calculated delta form-factor F q n advance FormFactor 2016 Josef Pelkán, 15 / 23

13 Hemcube confguraton factor s estmated by cells that were covered by ts proecton: F dvdng the cube affects the accuracy of the estmaton of the confguraton factors n practce from64 64 to 2k 2k cells were used F d q qj FormFactor 2016 Josef Pelkán, 16 / 23

14 Delta form-factors F 2 z x 1 z F 1 x y x 1 y 1 z 2 x 2 FormFactor 2016 Josef Pelkán, 17 / 23

15 Sllon hemplane method F q 1 h FormFactor 2016 Josef Pelkán, 18 / 23

16 Hemplane method faster mplementaton (proecton, trmmng) part of the spatal angle s neglected the heght of the proecton plane should be maxmum 0.1 vsblty s calculated by dvde and conquer Warnock algortm analogue method adaptve proecton plane dvson better effcency delta form-factor are precalculated for dfferent levels of dvson FormFactor 2016 Josef Pelkán, 19 / 23

17 Monte-Carlo methods usng the ray tracng method t s possble to use more complex scene geometry classc acceleraton calculaton methods samplng of the obect surfaces calculaton of ndvdual form-factor easy calculaton for area area form-factor (ndependent samplng) samplng of the sold angle all form-factors from one pont at a tme FormFactor 2016 Josef Pelkán, 20 / 23

18 Samplng on the hemsphere Unform samplng of the sold angle wth cos pdf k FormFactor 2016 Josef Pelkán, 21 / 23

19 Samplng on the source Non-unform samplng of the sold angle all rays have the same mportaton! FormFactor 2016 Josef Pelkán, 22 / 23

20 Lterature. Glassner: Prncples of Dgtal Image Synthess, Morgan Kaufmann, 1995, M. Cohen, J. Wallace: Radosty and Realstc Image Synthess, cadem. Press, 1993, J. Foley,. van Dam, S. Fener, J. Hughes: Computer Graphcs, Prncples and Practce, FormFactor 2016 Josef Pelkán, 23 / 23