CS 475 / CS 675 Computer Graphics. Lecture 7 : The Modeling-Viewing Pipeline

Transcription

1 CS 475 / CS 675 Computer Graphics Lecture 7 : The Modeling-Viewing Pipeline

2 Taonom Planar Projections Parallel Perspectie Orthographic Aonometric Oblique Front Top Side Trimetric Dimetric Isometric Caalier Cabinet One Point Two Point Three Point

3 The Modeling-Viewing Pipeline Modelling Transformations Viewing Transformation Object Coordinates World Coordinates View Coordinates Projection Transformation Deice Coordinates Normalied Deice Coordinates Clip Coordinates Viewport Transform Perspectie Diision

4 Viewing Transformation up o WCS View Direction Gien: 1.In the World Coordinate Sstem (WCS): a)position of the Ee (E) b)the lookat point (A) c)the up ector,. up A E

5 Viewing Transformation up o WCS T Near Plane Far Clipping Plane L R VCS Gien: 1.In the View Coordinate Sstem (VCS): a)the distance of near and far clipping planes. b)etents of the near plane L, R, T, B. B Ee u

6 Defining the VCS A E n= A E u= up n up n =n u A up E n u

7 From WCS to VCS The iewing transformation should: u n Map the origin of the WCS, O to the Ee, E. P O E n u If the point P has coordinates,, in WCS a, b, c in VCS then

8 From WCS to VCS The iewing transformation should: u n Map the origin of the WCS, O to the Ee, E. P O E n u [ ]=[ u n ].[a b c ] [e e e ]

9 From WCS to VCS The iewing transformation should: u n Map the origin of the WCS, O to the Ee, E. P O E n u [ ]=[u n ].[a u n b u n c ] [e e e ]

10 From WCS to VCS The iewing transformation should: u n Map the origin of the WCS, O to the Ee, E. P O E n [a b c u ]=[u n u n u n ] 1 [ ] [e e e ]

11 From WCS to VCS The iewing transformation should: u n Map the origin of the WCS, O to the Ee, E. P O E n [a b c u ]=[u n u n u n ]T [ ] e ] [e e

12 From WCS to VCS The iewing transformation should: u n Map the origin of the WCS, O to the Ee, E. P O E [a b c n u ]=[u u u ] [ n n n u ] [u u e n n n ] [e ] e

13 From WCS to VCS The iewing transformation should: u n Map the origin of the WCS, O to the Ee, E. P O E n u [a]=[ u.. OE b. c n. OP] [ u ]. OE n. OE

14 From WCS to VCS The iewing transformation should: u n Map the origin of the WCS, O to the Ee, E. P O E n u [a b c ]=[ u. OP ' ]. e ' n. OP] [e e '

15 From WCS to VCS The iewing transformation should: u n Map the origin of the WCS, O to the Ee, E. P A WV O E n u [a u u e ' b e ' c n n n e ' 1]=[u ].[ 1]

16 From WCS to VCS - OpenGL glmatrimode(gl_modelview); glloadidentit(); glulookat(e, E, E, A, A, A, Vup, Vup, Vup); O P A WV o E n u [a u u e ' b e ' c n n n e ' 1]=[u ].[ 1]

17 From WCS to VCS Far clipping plane Near clipping plane Let the Near clipping plane be at 0, 0, N and Far clipping plane be at 0, 0, F Ee u n

18 From VCS to CCS n n We shear the frustum so that the direction of projection aligns with the n ais and frustum becomes smmetricall aligned about it. If the etents of the near plane are gien b L, R, T, B then: [ 0 0 N 1 ]=[1 0 Sh Sh 0 T B / N ][ R L /2 1 ]

19 From VCS to CCS n n We shear the frustum so that the direction of projection aligns with the n ais and frustum becomes smmetricall aligned about it. If the etents of the near plane are gien b L, R, T, B then: 0= R L /2 Sh. N Sh = R L R L 1] 0 0 2N 2N Sh=[1 0= T B /2 Sh. N Sh = T B T B N 2N

20 From VCS to CCS Now we scale along u and so that we get u=±n,=±n as the top side faces of the frustum. n n After shearing the point L, B, N becomes R L 2, T B 2, N After shearing the point R,T, N becomes R L 2, T B 2, N

21 From VCS to CCS =n Now we scale along u and so that we get u=±n,=±n as the side faces of the frustum. n n = n So the scaling matri should map ± R L 2, ± T B 2, N to ±N,±N, N Sc=[ 2N 1] R L 2N T B

22 From VCS to CCS n' '=1 Now we transform the frustum to a canonical frustum. n'=1 F n This is equialent to n= N n'= 1 N doing a perspectie n= F '= 1 transform. It is called a projection u,, N should map to u/ N, / N, 1 normaliation. u,, F should map to u/ F,/ F, Nm=[1 ] 0 0 F N 2FN F N F N '

23 Projection Normaliation Projection Normaliation An Orthographic projection of a distorted object can be the same as a Perspectie projection of the undistorted object.

24 From VCS to CCS So the complete transformation is: A c =Nm.Sc. Sh ].[ 2N R L 1] R L 2N =[1 0 0 F N 2N T B 2FN T B 2N F N F N ].[

25 From VCS to NDCS So the complete transformation is: A c =[ =Nm.Sc. Sh ] 2N R L 0 0 R L R L 2N T B 0 0 T B T B F N 2FN 0 0 F N F N CCS coordinates retain the homogenous coordinate. This is follwed b a perspectie diide stage where the coordinates are diided b the 'w' coordinate. That puts all the coordinates within the normalied +/ 1 cube. This is called the Normalied Deice Coordinate Sstem.

26 From VCS to NDCS - OpenGL glmatrimode(gl_projection); glloadidentit(); glfrustum(l, R, B, T, N, F); or glmatrimode(gl_projection); glloadidentit(); gluperspectie(fo, aspect, N, F); N and F gie the distance of Near and Far clipping planes from the Ee and must be positie numbers and must not be equal.

27 From NDCS to DCS Now we need to map the NDCs to Deice or Window coordinates. This is done b the iewport transformation. If the aspect of the iewport is not the same as that of the iew frustum then the image is distorted. w = 1. R L w w L 2 w w = 1. T B w w B 2 w w = 1 2 w =T w w =B w w =L w w =R w

28 From NDCS to DCS- OpenGL gldepthrange(n f, F f ); : Default range is 0 to 1 glviewport(,, width, height);

29 From VCS to NDCS - Orthographic An Orhographic frustum is full specified b L, R, T, B, N and F as well. Here there is no need to shear the frustum to make it smmetric a translation can center it on the n ais. This is followed b a scaling to transform the frustum to the canonical frustum. No projection normaliation is required. A c =[ =Sc.T ] 2 R L 0 0 R L R L 2 T B 0 0 T B T B 2 F N 0 0 F N F N glortho(l, R, B, T, N, F) or gluortho2d(l, R, B, T)

30 Wh carr the depth through? Intuition: Visibilit computation or Hidden Surface Remoal Algorithm: The Z Buffer Algorithm OpenGL: glclear(gl_depth_buffer_bit); glenable(gl_depth_test);