1. CS552: Computer Graphics Lecture 33: Illumination and Shading

2. Recap Solid Modeling o Represent the solid object in a 3D space o B-Reps o Subdividing algorithms

3. Objective After completing this lecture, students will be able to o Explain the importance of VSDs o Solve the problem of backface culling

4. Surface Rendering Method Realistic displays of a scene are obtained by o Generating perspective projections of objects and o Applying natural lighting effects to the visible surfaces An illumination model is used to calculate the color of an illuminated position on the surface of an object. A surface-rendering method uses the color calculations from an illumination model to determine the pixel colors for all projected positions in a scene.

5. Global Illumination Direct illumination + Indirect illumination = Total illumination

6. Diffuse Inter-reflection Total illumination (normal image)

7. Diffuse Inter-reflection Direct illumination

8. Diffuse Interreflection Indirect illumination (diffuse interreflection)

9. Human face Total illumination (normal image)

10. Human face Direct illumination

11. Human face Indirect illumination

12. Illumination How do We Compute Radiance for a Sample Ray? o Must derive computer models for...  Emission at light sources  Scattering at surfaces  Reception at the camera WireframeWithout Illumination Direct Illumination

13. Overview Direct Illumination o Emission at light sources o Scattering at surfaces Global Illumination o Shadows o Refractions o Inter-object reflections Direct Illumination

14. Overview Direct Illumination o Emission at light sources o Scattering at surfaces Global Illumination o Shadows o Refractions o Inter-object reflections Direct Illumination

15. Modeling Light Source I L (x,y,z,  ) o Describes the intensity of energy, o Leaving a light source o Arriving at location(x,y,z) o From direction (  ) o With wavelength

16. Empirical Model Ideally Measure Irradiant Energy for “All” Situations o Too much storage o Difficult in practice

17. Light Source Model Simple Mathematical Models: o Point light o Directional light o Spot light

18. Point Light Source Models Omni-Directional Point Source (E.g., Bulb) o Intensity (I 0 ) o Position (px, py, pz) o Factors (k c, k l, k q ) for attenuation with distance (d)

19. Directional Light Source Models Point Light Source at Infinity (E.g., Sun) o Intensity (I 0 ) o Direction (dx,dy,dz) No attenuation with distance

20. Spot Light Source Models Point Light Source with Direction o Intensity (I 0 ), o Position (px, py, pz) o Direction (dx, dy, dz) o Attenuation

21. Directional Light Sources

22. Angular Intensity Attenuation Attenuate the light intensity o Angularly about the source o Radially out from the point-source position.

23. Overview Direct Illumination o Emission at light sources o Scattering at surfaces Global Illumination o Shadows o Refractions o Inter-object reflections Direct Illumination

24. Modeling Surface Reflection R s ( ,  ) o Describes the amount of incident energy o Arriving from direction (  ) o Leaving in direction ( ,  ) o With wavelength

25. Empirical Model Ideally Measure Radiant Energy for “All” Combinations of Incident Angles o Too much storage o Difficult in practice

26. Reflectance Model Simple Analytic Model: o Diffuse reflection + o Specular reflection + o Emission + o “Ambient” Based on model proposed by Phong Based on model proposed by Phong

27. Reflectance Model Simple Analytic Model: o Diffuse reflection + o Specular reflection + o Emission + o “Ambient” Based on model proposed by Phong Based on model proposed by Phong

28. Diffuse Reflection Assume Surface Reflects Equally in All Directions o Examples: chalk, clay

29. Diffuse Reflection How Much Light is Reflected? o Depends on angle of incident light o dL  dA  cos 

30. Diffuse Reflection Lambertian Model o Cosine law (dot product)

31. Reflectance Model Simple Analytic Model: o Diffuse reflection + o Specular reflection + o Emission + o “Ambient” Based on model proposed by Phong Based on model proposed by Phong

32. Specular Reflection Reflection is Strongest Near Mirror Angle o Examples: mirrors, metals

33. Specular Reflection How Much Light is Seen? o Depends on angle of incident light and angle to viewer

34. Specular Reflection Phong Model o {cos(  )} n

35. Reflectance Model Simple Analytic Model: o Diffuse reflection + o Specular reflection + o Emission + o “Ambient” Based on model proposed by Phong Based on model proposed by Phong

36. Emission Represents Light Emitting Directly From Polygon Emission ≠ 0

37. Reflectance Model Simple Analytic Model: o Diffuse reflection + o Specular reflection + o Emission + o “Ambient” Based on model proposed by Phong Based on model proposed by Phong

38. Ambient Term Represents Reflection of All Indirect Illumination

39. Reflectance Model Simple Analytic Model: o Diffuse reflection + o Specular reflection + o Emission + o “Ambient”

40. Reflectance Model Simple Analytic Model: o Diffuse reflection + o Specular reflection + o Emission + o “Ambient”

41. Reflectance Model Sum Diffuse, Specular, Emission, and Ambient

42. Surface Illumination Calculation Single Light Source:

43. Surface Illumination Calculation Multiple Light Sources:

44. Overview Direct Illumination o Emission at light sources o Scattering at surfaces Global Illumination o Shadows o Refractions o Inter-object reflections Global Illumination

46. Shadows Shadow Terms Tell Which Light Sources are Blocked o Cast ray towards each light source L i o S i = 0 if ray is blocked, S i = 1 otherwise Shadow Term

47. Ray Casting Trace Primary Rays from Camera o Direct illumination from unblocked lights only

48. Recursive Ray Tracing Also Trace Secondary Rays from Hit Surfaces o Global illumination from mirror reflection and transparency

49. Mirror Reflection Trace Secondary Ray in Direction of Mirror Reflection o Evaluate radiance along secondary ray and include it into illumination model Radiance for mirror reflection ray

50. Transparency Trace Secondary Ray in Direction of Refraction o Evaluate radiance along secondary ray and include it into illumination model Radiance for refraction ray

51. Transparency Transparency coefficient is fraction transmitted o K T = 1 if object is translucent, K T = 0 if object is opaque o 0 < K T < 1 if object is semi-translucent Transparency Coefficient

52. Refractive Transparency For Thin Surfaces, Can Ignore Change in Direction o Assume light travels straight through surface

53. Refractive Transparency For Solid Objects, Apply Snell’s Law: o  r sin  r  i  sin  i

54. Summary Direct Illumination o Ray casting o Usually use simple analytic approximations for light source emission and surface reflectance Global illumination o Recursive ray tracing o Incorporate shadows, mirror reflections, and pure refractions

55. Illumination Terminology Radiant power [flux] (Φ) o Rate at which light energy is transmitted (in Watts). Radiant Intensity (I) o Power radiated onto a unit solid angle in direction( in Watt/sr)  e.g.: energy distribution of a light source (inverse square law) Radiance (L) o Radiant intensity per unit projected surface area( in Watts/m 2 sr)  e.g.: light carried by a single ray (no inverse square law) Irradianc (E) o Incident flux density on a locally planar area (in Watts/m 2 ) Radiosity (B) o Exitant flux density from a locally planar area ( in Watts/m 2 )

56. Thank you Next Lecture: Rendering