1. OpenGL Shadow

2. Content Shadowing using Stencil Buffer Shadowing using Projective Texture Shadow map Shadow volume

3. Shadows are important … It is usually better to have an inaccurate shadow than none at all

5. Terminology (area) light source receiver shadow occluder umbra penumbra Hard ShadowSoft Shadow Occludee (receiver)

6. Soft Shadows (Ref)Ref –Point light generates hard shadows only –Soft shadows are NOT generated by low pass filters –Soft shadows are generally preferable, if possible.

7. Planar Projection Shadow (xz plane) x v l y p shadow v: any pt on model

8. Planar Projection (general) l v p  :nx+d=0 n

9. Planar Projection Shadow Problems [& Solutions] Z-fighting [polygon offset, stencil] Shadow fall outside of the receiver [stencil] Semi-transparent shadows [blending + stencil, ensuring each pixel is drawn at most once] Planar receiver only Need to render each frame (But for static objects, the shadows are view-independent) [render the shadow into texture]

10. Remark Shadow polygons are blended with the floor, one-by-one Repetitive blending … To prevent this from happening, use stencil buffer When a polygon is drawn, increment the stencil count (therefore, the area is not drawn again) glStencilFunc(GL_EQUAL, 1, 0xFF); glStencilOp (GL_KEEP, GL_KEEP, GL_INCR); glStencilFunc(GL_EQUAL, 1, 0xFF); glStencilOp (GL_KEEP, GL_KEEP, GL_INCR);

11. Stencil Setting

12. Projective Texture Shadow

13. Overview In the display callback  Render occluders to projective shadow texture (with FBO)  Set up texture unit 1 for projective (shadow) texture; render receiver  Render occluder to complete the scene

14. Steps Terrain: triangle strip FBO for render to shadow texture Render projective (shadow) texture

15. Terrain (trianglestrip) 01 234 4 0 1 2 3 x z [0,0] [0,1] [1,0] [1,1] [2,0] [2,1] …[4,0] [4,1] [i-1,j] [i,j] [i-1,j+1] [i,j+1] [i,j] [i-1,j+1] Set normal at

16. Render to Shadow Texture Render occluder (unlit) as black objects Clear color set to (1,1,1)

17. Projective Shadow Texture Set texture environment to modulate Shadowed part: dark (modulated by GREY) Unshadowed part: unchanged (modulated by WHITE) Use the same projective parameters (fovy, …) as in render to texture

18. Tricks This is normal! If you see something like this, the artifact comes from projective texture clamping: the shadow touches the texture border. It can be alleviated by increasing the fov or raising the light position

19. Shadow Map Primer Image-based technique by Lance Williams (1978) Amenable to h/w implementation

26. Coordinate Transformation World Space Note the convention on X and X -1

27. E e : transformed plane equations P light : projection matrix for light frustum [s,t,r,q] T is actually [x,y,z,w] T (scale-biased clip coordinates) Texgen (eye-linear) We do not use texture matrix T for now S: scale-bias matrix from [-1,1] to [0,1]

28. Depth Map Comparison Render from eye ’ s point of view “ Convert ” the eye coordinates to light space via texgen facility Object  Light Eye  Light

29. Summary Eye  Light

30. After converting to light space Compare with depth texture: Use comparison result (0 or 1) in fragment shading (can be bilinearly filtered): use the result directly to modulate the diffuse and specular intensity Z ls > Z sm : in shadow

31. GL_ARB_shadow (ref)ref Require depth texture extension Enable shadow comparison glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_COMPARE_MODE_ARB, GL_COMPARE_R_TO_TEXTURE); Not in shadow if r<=texture glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_COMPARE_FUNC_ARB, GL_LEQUAL); Shadow comparison should generate an INTENSITY result (or ALPHA result) glTexParameteri(GL_TEXTURE_2D, GL_DEPTH_TEXTURE_MODE_ARB, GL_INTENSITY) Set alpha test to discard false comparisons glAlphaFunc(GL_GEQUAL, 0.99f); glEnable(GL_ALPHA_TEST); This comparison produces a boolean texture value

32. From GL_ARB_SHADOW

33. Implementation Generate shadow map render the scene from light position Lighting, texturing, color buffer writes OFF Copy depth buffer content to a depth texture Note: shadow map is view independent (only need to be updated if scene or light moved) Ambient pass Render the scene from camera with only ambient lighting Diffuse Pass Set up necessary manipulations for coordinate transformation (eye coordinate to light coordinate) Set up shadow map parameters (compare_mode, compare_func, deptht texture_mode) Render the scene with lights on; the shadow map will generate a boolean texture result based on shadow test. The test will set the alpha values of the fragment. [in shadow  = 0, otherwise,  = 1] The alpha test will let the lit (unshadowed) fragment pass, covering the original ambient fragments. Final color is ambient pass + full color  [multitexture] Set shadowmap at the fourth texture unit Use the other three for original textures

34. FAQ Fov for light need to be the same as te fov of camera? No. The shadow comparison is solely based on depth texture and the converted clip coordinates in light coordinate system. The projection matrices (where fov plays a part) are of no importance. Aspect ratio of shadow map need to be the same as the aspect ratio of the window? No. (similar reason as in the left.) The projection matrices (where aspect ratio plays a part) are of no importance.

35. Trouble Shooting The artifact on the base is because the shadow map coverage contains only part of the base. It can be remedied by increasing the fov of the light frustum (but sacrificing the depth texture resolution) fov=45 fov=90

36. Using Shaders … Texgen is not performed The inverse of viewing matrix need to be computed directly (see projective texture) Only two passes are required First pass: generate shadow map Second pass: render the shadowed and lit part (one pass less than fixed functionality) Remove unwanted artifact (more precise control by rendering shadowed part only within light frustum)

37. Bias(1)

38. Bias(2)

40. Bias(3)

41. Alias(1)

42. Alias(2)

43. Issues Bias factor Depth in shadow map often slightly lower than that of the viewer Aliasing due to point-sampling Percentage closer filtering: instead of single point sample, take four closest. Bilinearly interpolate the results (in/out shadow) to calculate the lighting Provide pseudo-soft shadows

44. Shadow Map Advantage: Simple Shadow map is view independent Disadvantage: Shadow distance from light position may appear blocky Storage Light source in the view volume?

45. Shadow Volume Geometry-based technique first proposed by Frank Crow in 1977 Need stencil buffer!

46. Silhouette: the border of front/back facing polygons w.r.t. light source Point light [illustration here based on point light]

47. Z-pass Algorithm

49. Figure 6: When eye point is within the shadow volume, depth-pass stencil operation fails Pitfalls of Z-Pass

50. 1 Carmack’s reverse (Z-fail)

51. Shadow volume must be a closed volume (require front and back caps). Back cap can be at infinity !? Z-fail Requires Capping

52. Only need to close the back gap for point light (directional light is closed by definition: all rays intersect to a single point at infinity)

53. Reusing front cap Triangular-Fan We can build the front cap by using the front facing triangles with respect to the light source. The geometries used in the front cap can then be extruded, with their ordering reversed, to create the back cap.

54. Algorithm (Shadow Volume)

55. Bottlenecks

56. Silhouette Determination

57. View Frustum Clipping 1 Solution by Mark Kilgard

58. Solution by Eric Lengyel… Depth-clamping (Kilgard & Everitt): hardware solution View Frustum Clipping 2

59. Better, unless viewer enters shadow vol. Depends on type of games: z-pass sufficient for Diablo ( 暗黑 破壞神 )

60. Shadow Volume by Shaders Unless CPU is totally occupied, may not be beneficial (silhouette computation; too many vertices processed by shaders)

61. Advantages Support omnidirectional lights Exact shadow boundaries Disadvantages Fill-rate intensive Expensive to compute shadow volumes Hard shadow boundaries, not soft shadows Difficult to implement robustly

66. Area Light