Viewing/Projection IV. Week 4, Fri Jan 29

Transcription

1 Universit of British Columbia CPSC 314 Computer Graphics Jan-Apr 2010 Tamara Munner Viewing/Projection IV Week 4, Fri Jan 29

2 News etra TA office hours in lab 005 Fri 2-4 Garrett) Tamaras usual office hours in lab Fri 4-5 hand in H1 here/now or in bo net to 005 lab b 5pm correction: problem 6 worth 54 not 60 marks 2

3 Review: Basic Perspective Projection similar triangles P,,) d = = # d /d /d # d P,, ) =d homogeneous coords # /d = d = d # 0 0 1/d 1 3

4 Review: View Volumes specifies field-of-view, used for clipping restricts domain of stored for visibilit test perspective view volume orthographic view volume =top VCS =left =bottom =-near =right =-far VCS =left =bottom =top =right =-near =-far 4

5 Review: Understanding Z ais flip changes coord sstem handedness RHS before projection ee/view coords) LHS after projection clip, norm device coords) VCS NDCS =left =top =right -1,-1,-1) 1,1,1) =bottom =-near =-far 5

6 Review: Orthographic Derivation scale, translate, reflect for new coord ss VCS =left =bottom =top =right =-near # # e 0 0 f # 0 a 0 b = 0 0 c d NDCS -1,-1,-1) =-far = a! + b a = top = 1 = bot =! 1 b = 2 top! bot top =! top +! bot bot 1,1,1) 6

7 Review: Orthographic Derivation scale, translate, reflect for new coord ss 2 right left 0 P = 0 0 top 0 2 bot 0 0 far near 0 right right top top far far left # left!!!! bot bot! P near!! near!!! 7

8 Demo Robins demo: projection orthographic perspective 8

9 Projections II 9

10 Asmmetric Frusta our formulation allows asmmetr wh bother? right left Frustum - right left Frustum - =-n =-f 10

11 Asmmetric Frusta our formulation allows asmmetr wh bother? binocular stereo view vector not perpendicular to view plane Left Ee Right Ee 11

12 Simpler Formulation left, right, bottom, top, near, far nonintuitive often overkill look through window center smmetric frustum constraints left = -right, bottom = -top 12

13 Field-of-View Formulation FOV in one direction + aspect ratio w/h) determines FOV in other direction also set near, far reasonabl intuitive) w α Frustum - fov/2 fov/2 h =-n =-f 13

14 Perspective OpenGL glmatrimodegl_projection); glloadidentit); glfrustumleft,right,bot,top,near,far); or glperspectivefov,aspect,near,far); 14

15 Demo: Frustum vs. FOV Nate Robins tutorial take 2): projection frustum vs perspective 15

16 Projective Rendering Pipeline object world viewing O2W OCS WCS W2V VCS modeling transformation OCS - object/model coordinate sstem WCS - world coordinate sstem viewing transformation VCS - viewing/camera/ee coordinate sstem CCS - clipping coordinate sstem NDCS - normalied device coordinate sstem DCS - device/displa/screen coordinate sstem V2C projection transformation C2N perspective divide N2D viewport transformation clipping CCS normalied device NDCS device DCS 16

17 Perspective Warp warp perspective view volume to orthogonal view volume render all scenes with orthographic projection! aka perspective normaliation =α =d =0 =d 17

18 Perspective Warp perspective viewing frustum transformed to cube orthographic rendering of warped objects in cube produces same image as perspective rendering of original frustum 18

19 Predistortion 19

20 Projective Rendering Pipeline object world viewing O2W OCS WCS W2V VCS modeling transformation OCS - object/model coordinate sstem WCS - world coordinate sstem viewing transformation VCS - viewing/camera/ee coordinate sstem CCS - clipping coordinate sstem NDCS - normalied device coordinate sstem DCS - device/displa/screen coordinate sstem V2C projection transformation C2N perspective divide N2D viewport transformation clipping CCS normalied device NDCS device DCS 20

21 Separate Warp From Homogeniation viewing VCS V2C projection transformation alter w clipping CCS C2N perspective division / w normalied device NDCS warp requires onl standard matri multipl distort such that orthographic projection of distorted objects shows desired perspective projection w is changed clip after warp, before divide division b w: homogeniation 21

22 Perspective Divide Eample specific eample assume image plane at = -1 a point [,,,1] T projects to [-/,-/,-/,1] T [,,,-] T # # 1-22

23 + * - T * - * - * - )# 1, Perspective Divide Eample / = / = =. / # # 1 #. # 1 after homogeniing, once again w=1 projection transformation alter w perspective division / w 23

24 Perspective Normaliation matri formulation warp and homogeniation both preserve relative depth coordinate) d d a a # d d a d 0 ) ) ) ) ) # 1 ) ) ) ) = a) # d d a d ) ) ) ) ) ) p p p # = /d /d d 2 d a 1 a ) * +, -. #

25 Demo Brown applets: viewing techniques parallel/orthographic cameras projection cameras /viewing_techniques.html 25

26 Perspective To NDCS Derivation VCS =top NDCS =left 1,1,1) =bottom =-near =right =-far -1,-1,-1) 26

27 27 Perspective Derivation simple eample earlier: simple eample earlier: complete: shear, scale, projection-normaliation complete: shear, scale, projection-normaliation w # = /d 0 # 1 # w # = E 0 A 0 0 F B C D 0 0 )1 0 # 1 #

28 28 Perspective Derivation earlier: earlier: complete: shear, scale, projection-normaliation complete: shear, scale, projection-normaliation w # = /d 0 # 1 # w # = E 0 A 0 0 F B C D 0 0 )1 0 # 1 #

29 29 Perspective Derivation earlier: earlier: complete: shear, scale, projection-normaliation complete: shear, scale, projection-normaliation w # = /d 0 # 1 # w # = E 0 A 0 0 F B C D 0 0 )1 0 # 1 #

30 Perspective Derivation E 0 A 0 0 F B 0 = 0 0 C D # w # # 1 = E + A = F + B = C + D w= = left /w=1 = right /w= #1 = top /w=1 = bottom /w= #1 = #near /w=1 = # far /w= #1 = F + B, w = F + B w, 1= F + B w, 1= 1 = F + B, 1= F B, 1= F top near) B, 1 = F top near B F + B, 30

31 Perspective Derivation similarl for other 5 planes 6 planes, 6 unknowns # 2n r + l 0 0 r l r l 2n t + b 0 0 t b t b f + n) 0 0 f n fn f n 31

32 Projective Rendering Pipeline object world viewing O2W OCS WCS W2V VCS modeling transformation OCS - object/model coordinate sstem WCS - world coordinate sstem viewing transformation VCS - viewing/camera/ee coordinate sstem CCS - clipping coordinate sstem NDCS - normalied device coordinate sstem DCS - device/displa/screen coordinate sstem V2C projection transformation C2N perspective divide N2D viewport transformation clipping CCS normalied device NDCS device DCS 32

33 NDC to Device Transformation map from NDC to piel coordinates on displa NDC range is = , = , = tpical displa range: = , = maimum is sie of actual screen range ma and default is 0, 1), use later for visibilit -1 glviewport0,0,w,h); gldepthrange0,1); // depth = 1 b default NDC viewport 33

34 Origin Location et more possibl confusing) conventions OpenGL origin: lower left most window sstems origin: upper left then must reflect in when interpreting mouse position, have to flip our coordinates NDC viewport 34

35 general formulation N2D Transformation reflect in for upper vs. lower left origin scale b width, height, depth translate b width/2, height/2, depth/2 FCG includes additional translation for piel centers at.5,.5) instead of 0,0) height 1-1 NDC width viewport 35

36 N2D Transformation width width width D N +1) 1 height D height N 2 = height N +1) 1 N D = depth # depth N depth N +1) 2 2 # # 1 2 # # # height 1-1 NDC width viewport 36

37 Device vs. Screen Coordinates viewport/window location wrt actual displa not available within OpenGL usuall don t care use relative information when handling mouse events, not absolute coordinates could get actual displa height/width, window offsets from OS loose use of terms: device, displa, window, screen offset 0 offset viewport viewport displa displa width displa height 37

38 Projective Rendering Pipeline glverte3f,,) object world viewing O2W OCS WCS W2V VCS modeling transformation gltranslatef,,) glulookat...) C2N / w glrotatefa,,,)... perspective division OCS - object coordinate sstem glutinitwindowsiew,h) N2D WCS - world coordinate sstem glviewport,,a,b) VCS - viewing coordinate sstem viewport transformation CCS - clipping coordinate sstem NDCS - normalied device coordinate sstem DCS - device coordinate sstem viewing transformation V2C alter w projection transformation glfrustum...) clipping CCS normalied device NDCS device DCS 38

39 Coordinate Sstems viewing 4-space, W=1) projection matri clipping 4-space parallelepiped, with COP moved backwards to infinit divide b w normalied device 3-space parallelepiped) scale translate device 3-space parallelipiped) framebuffer 39

40 Perspective Eample tracks in VCS: left =-1, =-1 right =1, =-1 view volume left = -1, right = 1 bot = -1, top = 1 near = 1, far = 4 =-1 =1 1 ma-1 =-4 =-1 real midpoint NDCS DCS ma-1 VCS top view not shown) not shown) 40

41 Perspective Eample # 2n r + l 0 0 r l r l 2n t + b 0 0 t b t b f + n) 2 fn 0 0 f n f n view volume left = -1, right = 1 bot = -1, top = 1 near = 1, far = 4 # /3 8/

42 Perspective Eample # VCS /3 8/3 VCS # 1 = 1 # 5 /3 8/ VCS / w NDCS = 1/ VCS NDCS =1/ VCS NDCS = VCS 42

43 OCS2 OpenGL Eample object world viewing OCS O2W W2V WCS VCS CCS VCS WCS OCS1 modeling transformation glmatrimode GL_PROJECTION ); glloadidentit); gluperspective 45, 1.0, 0.1, ); glmatrimode GL_MODELVIEW ); glloadidentit); gltranslatef 0.0, 0.0, -5.0 ); glpushmatri) gltranslate 4, 4, 0 ); glutsolidteapot1); glpopmatri); gltranslate 2, 2, 0); glutsolidteapot1); viewing transformation W2O W2O V2C projection transformation clipping CCS transformations that are applied to object first are specified last 43

44 RB Chap Color Reading for Net Time FCG Sections FCG Chap 20 Color FCG Chap Visual Perception Color) 44