CS361

1. Week 15 - Wednesday CS361

2. Last time • What did we talk about last time? • Review up to Exam 1

3. Questions?

4. Project 4

5. Review up to Exam 2

6. Shading

7. Lambertian shading • Diffuse exitanceMdiff = cdiff ELcosθ • Lambertian (diffuse) shading assumes that outgoing radiance is (linearly) proportional to irradiance • Because diffuse radiance is assumed to be the same in all directions, we divide by π • Final Lambertian radiance Ldiff =

8. Specular shading • Specular shading is dependent on the angles between the surface normal to the light vector and to the view vector • For the calculation, we compute h, the half vector half between v and l

9. Specular shading equation • The total specularexitance is almost exactly the same as the total diffuse exitance: • Mspec = cspec ELcosθ • What is seen by the viewer is a fraction of Mspec dependent on the half vector h • Final specular radiance • Lspec = • Where does m come from? • It's the smoothness parameter

10. Implementing the shading equation • Final lighting is:

11. Aliasing

12. Screen based antialiasing • Jaggies are caused by insufficient sampling • A simple method to increase sampling is full-scene antialiasing, which essentially renders to a higher resolution and then averages neighboring pixels together • The accumulation buffer method is similar, except that the rendering is done with tiny offsets and the pixel values summed together

13. FSAA schemes A variety of FSAA schemes exist with different tradeoffs between quality and computational cost

14. Multisampleantialiasing • Supersampling techniques (like FSAA) are very expensive because the full shader has to run multiple times • Multisampleantialiasing (MSAA) attempts to sample the same pixel multiple times but only run the shader once • Expensive angle calculations can be done once while different texture colors can be averaged • Color samples are not averaged if they are off the edge of a pixel

15. Transparency

16. Sorting • Drawing transparent things correctly is order dependent • One approach is to do the following: • Render all the opaque objects • Sort the centroids of the transparent objects in distance from the viewer • Render the transparent objects in back to front order • To make sure that you don't draw on top of an opaque object, you test against the Z-buffer but don't update it

17. Problems with sorting • It is not always possible to sort polygons • They can interpenetrate • Hacks: • At the very least, use a Z-buffer test but not replacement • Turning off culling can help • Or render transparent polygons twice: once for each face

18. Depth peeling • It is possible to use two depth buffers to render transparency correctly • First render all the opaque objects updating the depth buffer • On the second (and future) rendering passes, render those fragments that are closer than the z values in the first depth buffer but further than the value in the second depth buffer • Repeat the process until no pixels are updated

19. Texturing

20. Texturing • We've got polygons, but they are all one color • At most, we could have different colors at each vertex • We want to "paint" a picture on the polygon • Because the surface is supposed to be colorful • To appear as if there is greater complexity than there is (a texture of bricks rather than a complex geometry of bricks) • To apply other effects to the surface such as changes in material or normal • Textures are usually images, but they could be procedurally generated too

21. Texture pipeline • Transformed value • We never get tired of pipelines • Go from object space to parameter space • Go from parameter space to texture space • Get the texture value • Transform the texture value • The u, v values are usually in the range [0,1]

22. Magnification • Magnification is often done by filtering the source texture in one of several ways: • Nearest neighbor (the worst) takes the closest texel to the one needed • Bilinear interpolation linearly interpolates between the four neighbors • Bicubic interpolation probably gives the best visual quality at greater computational expense (and is generally not directly supported) • Detail textures is another approach

23. Minification • Minification is just as big of a problem (if not bigger) • Bilinear interpolation can work • But an onscreen pixel might be influenced by many more than just its four neighbors • We want to, if possible, have only a single texel per pixel • Main techniques: • Mipmapping • Summed-area tables • Anisotropic filtering

24. Mipmapping in action • Typically a chain of mipmaps is created, each half the size of the previous • That's why cards like square power of 2 textures • Often the filtered version is made with a box filter, but better filters exist • The trick is figuring out which mipmap level to use • The level d can be computed based on the change in u relative to a change in x

25. Trilinear filtering • One way to improve quality is to interpolate between u and vtexels from the nearest two d levels • Picking d can be affected by a level of detail bias term which may vary for the kind of texture being used

26. Summed-area table • Sometimes we are magnifying in one axis of the texture and minifying in the other • Summed area tables are another method to reduce the resulting overblurring • It sums up the relevant pixels values in the texture • It works by precomputing all possible rectangles

27. Anisotropic filtering • Summed area tables work poorly for non-rectangular projections into texture space • Modern hardware uses unconstrained anisotropic filtering • The shorter side of the projected area determines d, the mipmap index • The longer side of the projected area is a line of anisotropy • Multiple samples are taken along this line • Memory requirements are no greater than regular mipmapping

28. Alpha Mapping • Alpha values allow for interesting effects • Decaling is when you apply a texture that is mostly transparent to a (usually already textured) surface • Cutouts can be used to give the impression of a much more complex underlying polygon • 1-bit alpha doesn't require sorting • Cutouts are not always convincing from every angle

29. Bump Mapping

30. Bump mapping • Bump mapping refers to a wide range of techniques designed to increase small scale detail • Most bump mapping is implemented per-pixel in the pixel shader • 3D effects of bump mapping are greater than textures alone, but less than full geometry

31. Normal maps • The results are the same, but these kinds of deformations are usually stored in normal maps • Normal maps give the full 3-component normal change • Normal maps can be in world space (uncommon) • Only usable if the object never moves • Or object space • Requires the object only to undergo rigid body transforms • Or tangent space • Relative to the surface, can assume positive z • Lighting and the surface have to be in the same space to do shading • Filtering normal maps is tricky

32. Parallax mapping • Bump mapping doesn't change what can be seen, just the normal • High enough bumps should block each other • Parallax mapping approximates the part of the image you should see by moving from the height back to the view vector and taking the value at that point • The final point used is:

33. Relief mapping • The weakness of parallax mapping is that it can't tell where it first intersects the heightfield • Samples are made along the view vector into the heightfield • Three different research groups proposed the idea at the same time, all with slightly different techniques for doing the sampling • There is much active research here • Polygon boundaries are still flat in most models

34. Heightfield texturing • Yet another possibility is to change vertex position based on texture values • Called displacement mapping • With the geometry shader, new vertices can be created on the fly • Occlusion, self-shadowing, and realistic outlines are possible and fast • Unfortunately, collision detection becomes more difficult

35. Types of lights • Real light behaves consistently (but in a complex way) • For rendering purposes, we often divide light into categories that are easy to model • Directional lights (like the sun) • Omni lights (located at a point, but evenly illuminate in all directions) • Spotlights (located at a point and have intensity that varies with direction) • Textured lights (give light projections variety in shape or color)

36. BRDFs

37. BRDF theory • The bidirectional reflectance distribution function is a function that describes the difference between outgoing radiance and incoming irradiance • This function changes based on: • Wavelength • Angle of light to surface • Angle of viewer from surface • For point or directional lights, we do not need differentials and can write the BRDF:

38. Revenge of the BRDF • The BRDF is supposed to account for all the light interactions we discussed in Chapter 5 (reflection and refraction) • We can see the similarity to the lighting equation from Chapter 5, now with a BRDF:

39. Fresnel reflectance • Fresnel reflectance is an ideal mathematical description of how perfectly smooth materials reflect light • The angle of reflection is the same as the angle of incidence and can be computed: • The transmitted (visible) radiance Lt is based on the Fresnel reflectance and the angle of refraction of light into the material:

40. External reflection • Reflectance is obviously dependent on angle • Perpendicular (0°) gives essentially the specular color of the material • Higher angles will become more reflective • The function RF(θi) is also dependent on material (and the light color)

41. Snell's Law • The angle of refraction into the material is related to the angle of incidence and the refractive indexes of the materials below the interface and above the interface: • We can combine this identity with the previous equation:

42. Area Lighting

43. Area light sources • Area lights are complex • The book describes the 3D integration over a hemisphere of angles needed to properly quantify radiance • No lights in reality are point lights • All lights have an area that has some effect

44. Ambient light • The simplest model of indirect light is ambient light • This is light that has a constant value • It doesn't change with direction • It doesn't change with distance • Without modeling occlusion (which usually ends up looking like shadows) ambient lighting can look very bad • We can add ambient lighting to our existing BRDF formulation with a constant term:

45. Environment Mapping

46. Environment mapping • A more complicated tool for area lighting is environment mapping (EM) • The key assumption of EM is that only direction matters • Light sources must be far away • The object does not reflect itself • In EM, we make a 2D table of the incoming radiance based on direction • Because the table is 2D, we can store it in an image

47. EM algorithm • Steps: • Generate or load a 2D image representing the environment • For each pixel that contains a reflective object, compute the normal at the corresponding location on the surface • Compute the reflected view vector from the view vector and the normal • Use the reflected view vector to compute an index into the environment map • Use the texel for incoming radiance

48. Sphere mapping • Imagine the environment is viewed through a perfectly reflective sphere • The resulting sphere map (also called a light probe) is what you'd see if you photographed such a sphere (like a Christmas ornament) • There sphere map has a basis giving its own coordinate system (h,u,f) • The image was generated by looking along the f axis, with h to the right and u up (all normalized)

49. Cubic environmental mapping • Cubic environmental mapping is the most popular current method • Fast • Flexible • Take a camera, render a scene facing in all six directions • Generate six textures • For each point on the surface of the object you're rendering, map to the appropriate texel in the cube

50. Pros and cons of cubic mapping • Pros • Fast, supported by hardware • View independent • Shader Model 4.0 can generate a cube map in a single pass with the geometry shader • Cons • It has better sampling uniformity than sphere maps, but not perfect (isocubes improve this) • Still requires high dynamic range textures (lots of memory) • Still only works for distant objects