Viewing/Projections IV. Week 4, Fri Feb 1

Transcription

1 Universit of British Columbia CPSC 314 Computer Graphics Jan-Apr 2008 Tamara Munzner Viewing/Projections IV Week 4, Fri Feb 1

2 News extra TA office hours in lab next week to answer questions Mon 1-3 Tue 2-4 Wed 1-3 reminder Wed 2/6: Homework 1 due 1pm sharp Wed 2/6: Project 1 due 6pm. 2

3 Review: View Volumes specifies field-of-view, used for clipping restricts domain of z stored for visibilit test perspective view volume orthographic view volume =top z VCS x x=left =bottom z=-near x=right z=-far z VCS x=left x =bottom =top x=right z=-near z=-far 3

4 Review: Understanding Z z axis flip changes coord sstem handedness RHS before projection ee/view coords) LHS after projection clip, norm device coords) VCS NDCS z x=left =top x=right -1,-1,-1) x z 1,1,1) x =bottom z=-near z=-far 4

5 Review: Projection Normalization warp perspective view volume to orthogonal view volume render all scenes with orthographic projection! aka perspective warp x x z=α z=d z=0 z=d 5

6 Review: 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 - normalized device coordinate sstem DCS - device/displa/screen coordinate sstem V2C projection transformation C2N perspective divide N2D viewport transformation clipping CCS normalized device NDCS device DCS 6

7 Review: Separate Warp From viewing VCS Homogenization V2C projection transformation alter w clipping CCS C2N perspective division / w normalized device NDCS warp requires onl standard matrix multipl distort such that orthographic projection of distorted objects is desired persp projection w is changed clip after warp, before divide division b w: homogenization 7

8 Reading for Viewing FCG Chapter 7 Viewing FCG Section Windowing Transforms RB rest of Chap Viewing RB rest of App Homogeneous Coords 8

9 RB Chap Color Reading for Next Time FCG Sections FCG Chap 20 Color FCG Chap Visual Perception Color) 9

10 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 - normalized device coordinate sstem DCS - device/displa/screen coordinate sstem V2C projection transformation C2N perspective divide N2D viewport transformation clipping CCS normalized device NDCS device DCS 10

11 NDC to Device Transformation map from NDC to pixel coordinates on displa NDC range is x = , = , z = tpical displa range: x = , = maximum is size of actual screen z range max and default is 0, 1), use later for visibilit -1 glviewport0,0,w,h); gldepthrange0,1); // depth = 1 b default NDC 1 x x 500 viewport 11

12 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 x NDC 1 x 300 viewport 12

13 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 pixel centers at.5,.5) instead of 0,0) x 500 height 1-1 NDC 1 x 300 width viewport 13

14 N2D Transformation " width %" width % " widthx " x D % N +1) 1 % height D " % " x height N % 2 = height N +1) 1 N z D = depth # depth z N depthz N +1) & 2 2 # & # 1 & 2 # & # & # 1 & x 500 height 1-1 NDC 1 x 300 width viewport 14

15 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... 0 x x offset 0 x offset viewport viewport displa displa width displa height 15

16 Projective Rendering Pipeline glvertex3fx,,z) object world viewing O2W OCS WCS W2V VCS modeling transformation gltranslatefx,,z) glulookat...) C2N / w glrotatefa,x,,z)... perspective division OCS - object coordinate sstem glutinitwindowsizew,h) N2D WCS - world coordinate sstem glviewportx,,a,b) VCS - viewing coordinate sstem viewport transformation CCS - clipping coordinate sstem NDCS - normalized device coordinate sstem DCS - device coordinate sstem viewing transformation V2C alter w projection transformation glfrustum...) clipping CCS normalized device NDCS device DCS 16

17 Coordinate Sstems viewing 4-space, W=1) projection matrix clipping 4-space parallelepiped, with COP moved backwards to infinit divide b w normalized device 3-space parallelepiped) scale & translate device 3-space parallelipiped) framebuffer 17

18 Perspective To NDCS Derivation VCS =top NDCS x=left 1,1,1) z x =bottom z=-near x=right z=-far -1,-1,-1) x z 18

19 Perspective Derivation simple example earlier: " x % " % " x% = z z # w & # 0 0 1/d 0& # 1& complete: shear, scale, projection-normalization " x % " E 0 A 0% " x% F 1 B 0 = z 0 0 C D z # w & # & # 1& 19

20 Perspective Derivation earlier: " x % " % " x% = z z # w & # 0 0 1/d 0& # 1& complete: shear, scale, projection-normalization " x % " E 0 A 0% " x% F 1 B 0 = z 0 0 C D z # w & # & # 1& 20

21 Perspective Derivation earlier: " x % " % " x% = z z # w & # 0 0 1/d 0& # 1& complete: shear, scale, projection-normalization " x % " E 0 A 0% " x% F 1 B 0 = z 0 0 C D z # w & # & # 1& 21

22 Perspective Derivation " x % " E 0 A 0% " x% 0 F B 0 = z 0 0 C D z # w & # & # 1& x= Ex + Az = F + Bz z= Cz + D w= "z x = left " x/w=1 x = right " x/w= #1 = top " /w=1 = bottom " /w= #1 z = #near " z/w=1 z = # far " z/w= #1 = F + Bz, w = F + Bz w, 1 = F + Bz w, 1= 1= F "z + B z "z, 1 = F "z " B, 1= F top ""near) " B, 1 = F top near " B F + Bz "z, 22

23 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 % 0 0 "1 0 "2 fn f " n & 23

24 Perspective Example tracks in VCS: left x=-1, =-1 right x=1, =-1 view volume left = -1, right = 1 bot = -1, top = 1 near = 1, far = 4 x=-1 x=1 1 max-1 z=-4 z=-1 real midpoint x NDCS DCS xmax-1 z VCS top view z not shown) z not shown) 24

25 Perspective Example # 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 % 0 0 "1 0 view volume left = -1, right = 1 bot = -1, top = 1 near = 1, far = 4 # & % % % 0 0 "5 /3 "8 /3 % 0 0 "1 0 25

26 Perspective Example # 1 & % % "1 %"5z VCS /3" 8 /3 % "z VCS # 1 % = % % % 1 &# % % "5 /3 "8 /3% % "1 1 & "1 1 z VCS / w x NDCS = "1/z VCS NDCS =1/z VCS z NDCS = z VCS 26

27 OCS2 OpenGL Example object world viewing O2W W2V OCS WCS VCS CCS VCS WCS OCS1 modeling transformation glmatrixmode GL_PROJECTION ); glloadidentit); gluperspective 45, 1.0, 0.1, ); glmatrixmode GL_MODELVIEW ); glloadidentit); gltranslatef 0.0, 0.0, -5.0 ); glpushmatrix) gltranslate 4, 4, 0 ); glutsolidteapot1); glpopmatrix); gltranslate 2, 2, 0); glutsolidteapot1); viewing transformation W2O W2O V2C projection transformation clipping CCS transformations that are applied first are specified last 27

28 perspective: 1,2,3-point planar projections parallel Projection Taxonom perspective: projectors converge orthographic, axonometric: projectors parallel and perpendicular to projection plane oblique: projectors parallel, but not perpendicular to projection plane oblique orthographic cabinet cavalier top, front, side axonometric: isometric dimetric trimetric 28

29 Perspective Projections projectors converge on image plane select how man vanishing points one-point: projection plane parallel to two axes two-point: projection plane parallel to one axis three-point: projection plane not parallel to an axis one-point perspective two-point perspective three-point perspective Tuebingen demo: vanishingpoints 29

30 Orthographic Projections projectors parallel, perpendicular to image plane image plane normal parallel to one of principal axes select view: top, front, side ever view has true dimensions, good for measuring 30

31 Axonometric Projections projectors parallel, perpendicular to image plane image plane normal not parallel to axes select axis lengths can see man sides at once 31

32 Oblique Projections projectors parallel, oblique to image plane select angle between front and z axis lengths remain constant both have true front view cavalier: distance true cabinet: distance half d / 2 z d d cavalier! x Tuebingen demo: oblique projections z d cabinet! x 32