1. Graphics Graphics Lab @ Korea University cgvr.korea.ac.kr Illumination Model 고려대학교 컴퓨터 그래픽스 연구실

2. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Illumination How do We Compute Radiance for a Sample Ray? Must derive computer models for...  Emission at light sources  Scattering at surfaces  Reception at the camera WireframeWithout Illumination Direct Illumination

3. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Overview Direct Illumination Emission at light sources Scattering at surfaces Global Illumination Shadows Refractions Inter-object reflections Direct Illumination

4. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Overview Direct Illumination Emission at light sources Scattering at surfaces Global Illumination Shadows Refractions Inter-object reflections Direct Illumination

5. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Modeling Light Source I L (x,y,z,  ) Describes the intensity of energy, Leaving a light source Arriving at location(x,y,z) From direction (  ) With wavelength

6. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Empirical Model Ideally Measure Irradiant Energy for “All” Situations Too much storage Difficult in practice

7. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Light Source Model Simple Mathematical Models: Point light Directional light Spot light

8. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Point Light Source Models Omni-Directional Point Source (E.g., Bulb) Intensity (I 0 ) Position (px, py, pz) Factors (k c, k l, k q ) for attenuation with distance (d)

9. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Directional Light Source Models Point Light Source at Infinity (E.g., Sun) Intensity (I 0 ) Direction (dx,dy,dz) No attenuation with distance

10. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Spot Light Source Models Point Light Source with Direction (E.g., Luxo) Intensity (I 0 ), Position (px, py, pz) Direction (dx, dy, dz) Attenuation

11. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Overview Direct Illumination Emission at light sources Scattering at surfaces Global Illumination Shadows Refractions Inter-object reflections Direct Illumination

12. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Modeling Surface Reflection R s ( ,  ) Describes the amount of incident energy Arriving from direction (  ) Leaving in direction ( ,  ) With wavelength

13. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Empirical Model Ideally Measure Radiant Energy for “All” Combinations of Incident Angles Too much storage Difficult in practice

14. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Reflectance Model Simple Analytic Model: Diffuse reflection + Specular reflection + Emission + “Ambient” Based on model proposed by Phong Based on model proposed by Phong

15. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Reflectance Model Simple Analytic Model: Diffuse reflection + Specular reflection + Emission + “Ambient” Based on model proposed by Phong Based on model proposed by Phong

16. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Diffuse Reflection Assume Surface Reflects Equally in All Directions Examples: chalk, clay

17. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Diffuse Reflection How Much Light is Reflected? Depends on angle of incident light dL  dA  cos 

18. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Diffuse Reflection Lambertian Model Cosine law (dot product)

19. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Reflectance Model Simple Analytic Model: Diffuse reflection + Specular reflection + Emission + “Ambient” Based on model proposed by Phong Based on model proposed by Phong

20. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Specular Reflection Reflection is Strongest Near Mirror Angle Examples: mirrors, metals

21. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Specular Reflection How Much Light is Seen? Depends on angle of incident light and angle to viewer

22. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Specular Reflection Phong Model {cos(  )} n

23. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Reflectance Model Simple Analytic Model: Diffuse reflection + Specular reflection + Emission + “Ambient” Based on model proposed by Phong Based on model proposed by Phong

24. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Emission Represents Light Emitting Directly From Polygon Emission ≠ 0

25. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Reflectance Model Simple Analytic Model: Diffuse reflection + Specular reflection + Emission + “Ambient” Based on model proposed by Phong Based on model proposed by Phong

26. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Ambient Term Represents Reflection of All Indirect Illumination This is a total hack (avoids complexity of global illumination)!

27. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Reflectance Model Simple Analytic Model: Diffuse reflection + Specular reflection + Emission + “Ambient”

28. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Reflectance Model Simple Analytic Model: Diffuse reflection + Specular reflection + Emission + “Ambient”

29. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Reflectance Model Sum Diffuse, Specular, Emission, and Ambient

30. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Surface Illumination Calculation Single Light Source:

31. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Surface Illumination Calculation Multiple Light Sources:

32. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Overview Direct Illumination Emission at light sources Scattering at surfaces Global Illumination Shadows Refractions Inter-object reflections Global Illumination

33. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Global Illumination

34. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Shadows Shadow Terms Tell Which Light Sources are Blocked Cast ray towards each light source L i S i = 0 if ray is blocked, S i = 1 otherwise Shadow Term

35. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Ray Casting Trace Primary Rays from Camera Direct illumination from unblocked lights only

36. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Recursive Ray Tracing Also Trace Secondary Rays from Hit Surfaces Global illumination from mirror reflection and transparency

37. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Mirror Reflection Trace Secondary Ray in Direction of Mirror Reflection Evaluate radiance along secondary ray and include it into illumination model Radiance for mirror reflection ray

38. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Transparency Trace Secondary Ray in Direction of Refraction Evaluate radiance along secondary ray and include it into illumination model Radiance for refraction ray

39. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Transparency Transparency coefficient is fraction transmitted K T = 1 if object is translucent, K T = 0 if object is opaque 0 < K T < 1 if object is semi-translucent Transparency Coefficient

40. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Refractive Transparency For Thin Surfaces, Can Ignore Change in Direction Assume light travels straight through surface

41. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Refractive Transparency For Solid Objects, Apply Snell’s Law:  r sin  r  i  sin  i

42. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Summary Direct Illumination Ray casting Usually use simple analytic approximations for light source emission and surface reflectance Global illumination Recursive ray tracing Incorporate shadows, mirror reflections, and pure refractions

43. CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr Illumination Terminology Radiant power [flux] (Φ) Rate at which light energy is transmitted (in Watts). Radiant Intensity (I) 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) 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) Incident flux density on a locally planar area (in Watts/m 2 ) Radiosity (B) Exitant flux density from a locally planar area ( in Watts/m 2 )