Slide 1 Lecture 18 Copyright

Transcription

1 MI (Georges de a Tour) Side 1 Lecture 18 9DO 5D=@ MI Shadows give us important visua cues about 3D object pacement and motion Movies are from: /users/kersten/kerstenab/demos/shadows.htm Side 2 Lecture 18 1

2 Aso, reaism 9DO MI Image courtesy, Codemasters Game: Bade of Darkness Side 3 Lecture 18 Shadows just ook coo Side 4 Lecture 18 2

3 Cast Shadows Attached shadows are easy to render Because they are oca. We aready have discussed this. Cast shadows require us to determine whether the surface is visibe to the ight. Attached Shadows Side 5 Lecture 18 0=H@ 5 BJ 5D=@ MI point source area source umbra penumbra umbra Images courtesy, Eric Haines and Tomas Moeer Side 6 Lecture 18 3

4 4A= JE A 5D=@ MI Assumptions: hard shadows from point ight sources onto panar surfaces Let the ight source be at infinity in the direction L(x, y, z ), and we want to compute the shadow S(x w, y w, z w ) of the point P(x p, y p, z p ), on the pane z = 0 It is easy to see that S ies on the ine defined by P and L or S = P L Since the shadow is on the pane z = 0, z w = 0 =z p /z, and x w = x p - (z p / z ) x y w = y p - (z p / z ) y Side 7 Lecture 18 4A= JE A 5D=@ MI Restating the equations from previous side in a matrix form: x w 1 0 x z 0 x p y w 0 1 y z 0 y p z p Shadows on arbitrary panes can be performed by prefixing the above matrix by a suitabe transformation that transforms that pane to z = 0 Side 8 Lecture 18 4

5 4A= JE A 5D=@ MI Remember to set the right shadow coor before drawing the shadow Z-conficts can ruin shadows, so remember to sighty offset the shadows to ie above the surface: genabe(gl_polygon_offset_fill) gpoygonoffset(glfoat factor, GLfoat units) // dispay the poygon here gdisabe(gl_polygon_offset_fill) Aternativey if the scene geometry is we understood the foowing might be possibe and simper: Render the pane, turn off the depth test, render the shadows, turn the depth test back on, and render the rest of the scene. Side 9 Lecture 18 4A= JE A 5D=@ MI We assumed ight source at infinity. If the ight source is oca at L(x, y, z ), we can use the foowing matrix [Binn 88]: x z 0 x 0 x w y w z 0 0 y y p 0 z z 1 0 p p Side 10 Lecture 18 5

6 Why is this the right matrix? Let s just work through the x coordinate. To project the point onto the z = 0 pane as a shadow, we need to move it in the direction from the ight to the point, and to move it far enough so that it s on the z = 0 pane. That means we need to add a scaed version of (xp-x,yp-y,zp-z) to the point (xp,yp,zp). Our projected point wi be (xp,yp,zp) + a(xp-x,yp-y,zp-z) where we choose a so that the resuting z coordinate wi be 0. That is, zp + a(zp-z) = 0, or a = zp(z-zp). The x coordinate that we wind up with, then wi be xp + zp(xp-x)/(z-zp). We can rewrite this as: (xp(z-zp) + zp(xp-x))/(z-zp) = (xp*z zp*x)/(z-zp). Notice that if we appy our matrix to (xp,yp,zp,1), we get (xp*z zp*x,?, 0, z-zp), where we haven t cacuated the y coordinate yet. This is in homogenous coordinates, but if we divide by the fourth coordinate, we get the correct x coordinate that we have just cacuated. We can check the y coordinate in the same way. Side 11 Lecture 18 ECDJ =FI Idea is to store the view-independent ighting of a scene as a 2D texture map Light maps are reasonaby effective even when used at ow resoutions (since they usuay don t have high frequency detai) Efficiency invoves custering simiary ighted poygona patches (Zhukov et a. 1998) Side 12 Lecture 18 6

7 6ANJKHA 5?A A Images courtesy, 3D Games by Watt and Poicarpo Side 13 Lecture 18 ECDJ =FFA@ 5?A A No fitering of the ight map Images courtesy, 3D Games by Watt and Poicarpo Side 14 Lecture 18 7

8 Light map with inear fitering ECDJ 5?A A Images courtesy, 3D Games by Watt and Poicarpo Side 15 Lecture 18 6ANJKHA ECDJ =FFA@ 5?A A Texture mapped * Fitered Light Mapped Images courtesy, 3D Games by Watt and Poicarpo Side 16 Lecture 18 8

9 ECDJ =FI Texture mapped Texture + Fitered Light Mapped Images courtesy, 3D Games by Watt and Poicarpo Side 17 Lecture 18 5D=@ M )KC A JA@ ECDJ =FI If ight sources and scene objects are static then the shadows wi be static. Precompute the shadows as a part of the ight map and appy as a texture (The word) saw shadows back unti Monet discovered they were cooured, Maugham, Of Human Bondage Images from 3D Games by Watt and Poicarpo Side 18 Lecture 18 9

10 M *KBBAH Proposed by Wiiams 1978 Render the scene from the ight s point of view and store the resut in a shadow z-buffer Then render the scene from the user s view point and for each pixe that overwrites a previousy written pixe: Transform the pixe s screen space coordinates into the ight source s coordinate frame Index into the shadow z-buffer to see whether the rendered point s depth is greater than the depth for the corresponding pixe in the shadow z-buffer If the depth is greater point is in shadow and use the shadow coor, otherwise render normay Side 19 Lecture 18 5D=@ M >KBBAH Low resoution shadow map Higher resoution shadow map Side 20 Lecture 18 Images from 3D Computer Graphics by Watt 10

11 M >KBBAH Images from 3D Computer Graphics by Watt Depth map from User s View Point Shadow Environment Z-buffer from Light s View Point Side 21 Lecture 18 11