7M836 Animation & Rendering

1. 7M836 Animation & Rendering Illumination models, light sources, reflection shading Arjan Kok a.j.f.kok@tue.nl

2. Graphics pipeline Geometric model Viewing Camera parameters Visible surface determination Light sources, materials Shading Rasterize Raster display

3. Illumination • Illumination model • Illumination (and therefore color) of point on surface is determined by simulation of light in scene • Illumination model is approximation of real light transport • Shading method • determines for which points illumination is computed • determines how illumination for other points is computed

4. Illumination models • Model(s) needed for • Emission of light • Distribution of light in scene • Desired model requirement • Accurate • Efficient to compute

5. Illumination models • Local illumination • Direct illumination • Emission of light sources • Scattering at surfaces • Global illumination • Shadows • Refraction • Interreflection • (Ray tracing + Radiosity)

6. Light source • IL (x, y, z, θ, φ, λ) • Intensity of energy • of light source L • arriving at point (x, y, z) • from direction (θ, φ) • with wavelength λ • Complex • Simpler model needed (x,y,z)

7. d Point light source • Emits light equally in all directions • Parameters • Intensity I0 • Position P (px,py,pz) • Attenuation factor(kc, kl, kq) for distance (d) to light source P

8. Point light source

9. Direction light source • Emits light in one direction • Can be regarded as point light source at infinity • E.g. sun • Parameters • Intenslity I0 • Direction D (dx,dy,dz) • IL = I0 D

10. Directional light source

11. d φ γ θ D P Spot light source • Point light source with direction • E.g. Spot light • Parameters • Intensity I0 • Position P (px,py,pz) • Direction D (dx,dy,dz) • “Hotspot” angle θ • Maximum angle φ • Exponent e

12. if γ ≤ θ if θ < γ ≤ φ if φ < γ Attenuation factor Spot light source φ θ

13. Spot light source

14. Spot light source

15. Other light sources • Linear light sources • Area sources • Spherical lights • …

16. λ (θ, φ) (γ, ψ) Reflection • Rs (θ, φ, γ, ψ, λ) • Amount of energy, • arriving from direction (θ, φ), • that is reflected in direction (γ, ψ) • with wavelength λ • Ideal • Describe this function for all combinations of θ, φ, γ, ψand λ • Impossible, simpler model(s) needed

17. Reflection model • Total intensity on point reflected in certain direction is determined by: • Diffusely reflected light • Specularly reflected light • Emission (for light sources) • Reflection of ambient light • Intensity not computed for all wavelengths λ, only for R, G and B

18. Diffuse reflection • Incoming light is reflected equally in all directions • Amount of reflected light depends only on angle of incident light viewer surface

19.  viewer surface Diffuse reflection • Lambert’ law: Reflected energy from a surface is proportional to the cosine of the angle of direction of incoming light and normal of surface • Id = kdILcos(θ) • kd is diffuse reflection coefficient

20.   Specular reflection • Models reflections of shiny surfaces

21. Specular reflection • Shininess depends on roughness surface • Incident light is reflected unequally in all directions • Reflection strongest near mirror angle very shiny less shiny

22. Specular reflection / Phong • Light intensity observed by viewer depends on angle of incident light and angle to viewer • Phong model: Is = ksILcosn(α) • ks is specular reflection coefficient • n is specular reflection exponent   α

23. Specular reflection / Phong increasing ks increasing n

24. Emission • Emission IE represents light that is emanated directly by surface • Used for light sources Emission ≠ 0

25. Ambient light • Even thought parts of scene are not directly lit by light sources, they can still be visible • Because of indirect illumination • “Ambient” light IA is an approach to this indirect illumination • Ambient light is independent of light sources and viewer position • Conbtribution of ambient light I = kAIA • kA is ambient reflection coefficient • IA is ambient intensitity (constant over scene) • Indirect illumination can be computed much better: e.g. radiosity

26. θ1 θ0 α1 α0 Total illumination Phong model • Total intensity Itotal at point P seen by viewer is

27. Total illumination Phong model • In previous formula kA, kD dependent on wavelength (different values for R, G and B) • Often division into color and reflection coefficient of surface where: • 0 ≤ kA, kD, kS≤ 1 • CA is ambient reflected color of surface • CD is diffuse reflected color of surface • Cs is specular reflected color of surface

28. Only emission and ambient

29. Including diffuse reflection

30. Including specular reflection

31. Illumination model • More advanced models: • Allows for angle between incident light and surface normal for specular reflection (Fresnel’s law) • Better models for surface roughness • Beter model for wavelength dependent reflection

32. Shading • Illumination model computes illumination for a point on surface • But how do we compute the illumination for all points on all (visible) surfaces? • Shading methods: • Flat shading • Gouraud shading • Phong shading

33. Flat shading • Determine illumination for one point on polygon • Use this illumination for all points on polygon • Disadvantages: • Does not account for changing direction to light source over polygon • Does not account for changing direction to eye over polygon • Discontinuity at polygon boundaries (when curved surface approximated by polygon mesh

34. Flat shading

35. Gouraud shading • Based on interpolation of illumination values • Compute illumination for vertices of polygon • Algorithm • for all vertices of polygon • get vertex normal • compute vertex illumination using this normal • for all pixels in projection of polygon • compute pixel illumination by interpolation of vertex illumination

36. IA IB ys IP Gouraud shading I1 I2 I3

37. Gouraud shading

38. Gouraud shading • Advantages • Interpolation is simple, hardware implementation • Continuous shading over curved surfaces possible • Disadvantages • Subtle illumination effects (e.g. highlights) require high subdivision of surface in very small polygons

39. Phong shading • Based on normal interpolation • Compute illumination for each point of polygon • Algorithm • for each vertex of polygon • get vertex normal • for each pixel in projection of polygon • compute point normal by interpolation of vertex normals • compute illumination using interpolated normal

40. Phong shading

41. Phong shading • Advantages • Nice highlights • Disadvantages • Computational expensive • Normal interpolation and application of illumination model for each pixel

42. Shading samengevat

43. Shading • Flat shading • 1x application of illumination model per polygon • 1 color per polygon • Gouraud shading • 1x application of illumination model per vertex • Interpolated colors • Phong shading • 1x application of illumination model per pixel • Nice highlights Increase computation time Increase quality

44. Grafische pijplijn Geometric model Viewing Camera parameters Visible surface determination Light sources, materials Shading Rasterize Raster display

45. trivial accept/reject modeling transformation viewing transformation z-buffer lighting display projection clipping Z-buffer & Gouraud shading

46. trivial accept/reject modeling transformation viewing transformation z-buffer lighting display projection clipping Z-buffer & Phong shading

47. What is still missing? • Shadows • Area light sources • “Real” mirroring • Transparency • Indirect diffuse reflection • Influence of atmosphere

48. Shadow • Illumination with shadows • Si = 0 if light of source i is blocked = 1 if light of source i is not blocked • Several methods to compute shadow • Shadow buffer • Ray casting • Shadow volumes • ..

49. Shadow buffer • Based on z-buffer algorithm • Rendering in 2 steps • Z-buffer from light source (= shadow buffer) to compute shadows • During “normal” rendering, when computing illumination of point read from shadow buffer if point is lit by light source

50. _ 3 3 5 5 _ Shadow buffer – step 1 • “Render” scene with light source position as viewpoint and store depth results in depth buffer • sbuffer(x,y) = minimum z-value after projection of all polygons on (x,y) 0 3 5 z