CSCE 641 Computer Graphics: Reflection Models

1. CSCE 641 Computer Graphics: Reflection Models Jinxiang Chai

2. Motivation • How to model surface properties of objects?

3. Reflection Models • Definition: Reflection is the process by which light incident on a surface interacts with the surface such that it leaves on the incident side without change in frequency.

4. Types of Reflection Functions • Ideal Specular • Reflection Law • Mirror

5. Types of Reflection Functions • Ideal Specular • Reflection Law • Mirror • Ideal Diffuse • Lambert’s Law • Matte

6. Types of Reflection Functions • Ideal Specular • Reflection Law • Mirror • Ideal Diffuse • Lambert’s Law • Matte • Specular • Glossy • Directional diffuse

7. Review: Local Illumination

8. Review: Local Illumination

9. Review: Local Illumination

10. Materials Plastic Metal Matte From Apodaca and Gritz, Advanced RenderMan

11. Mathematical Reflectance Models • How can we mathematically model reflectance property of an arbitrary surface? • - what’s the dimensionality? • - how to use it to compute outgoing radiance given incoming radiance?

12. Introduction • Radiometry and photometry - Radiant intensity - Irradiance - Radiance - Radiant exitance (radiosity)

13. Electromagnetic Spectrum • Visible light frequencies range between: • Red: 4.3x1014 hertz (700nm) • Violet: 7.5x1014 hertz (400nm)

14. Visible Light • The human eye can see “visible” light in the frequency between 400nm-700nm violet red

15. Spectral Energy Distribution • Three different types of lights

16. Spectral Energy Distribution • Three different types of lights • How can we measure the energy of light?

17. Photons • The basic quantity in lighting is the photon • The energy (in Joule) of a photon with wavelength λ is: qλ = hc/λ - c is the speed of light In vacuum, c = 299.792.458m/s - h ≈ 6.63*10-34Js is Planck’s constant

18. (Spectral) Radiant Energy • The spectral radiant energy, Qλ, in nλ photons with wavelength λ is • The radiant energy, Q, is the energy of a collection of photons, and is given as the integral of Qλ over all possible wavelengths:

19. Example: Fluorescent Bulb

20. Radiant Intensity • Definition: the radiant power radiated from a point on a light source into a unit solid angle in a particular direction. • - measured in watt per steradian

21. Radiance • Definition: the radiant power per unit projected surface area per solid angle

22. Radiance Per unit projected surface area - radiance varies with direction - incidence radiance and exitant radiance

23. Radiance • Ray of light arriving at or leaving a point on a surface in a given direction Radiance (arriving) Radiance (leaving)

24. Irradiance • Definition: the power per unit area incident on a surface.

25. Radiant Exitance • Definition: The radiant (luminous) exitance is the • energy per unit area leaving a surface. • In computer graphics, this quantity is often • referred to as the radiosity (B)

26. Directional Power Leaving a Surface

27. Uniform Diffuse Emitter

28. Projected Solid Angle

29. Uniform Diffuse Emitter

30. Reflection Models • Outline - Types of reflection models - The BRDF and reflectance - The reflection equation - Ideal reflection - Ideal diffuse - Cook-Torrance Model

31. Reflection Models • Definition: Reflection is the process by which light incident on a surface interacts with the surface such that it leaves on the incident side without change in frequency.

32. Reflection Models • Definition: Reflection is the process by which light incident on a surface interacts with the surface such that it leaves on the incident side without change in frequency.

33. Reflection Models • Definition: Reflection is the process by which light incident on a surface interacts with the surface such that it leaves on the incident side without change in frequency.

34. Reflection Models • Definition: Reflection is the process by which light incident on a surface interacts with the surface such that it leaves on the incident side without change in frequency.

35. Types of Reflection Functions • Ideal Specular • Reflection Law • Mirror

36. Types of Reflection Functions • Ideal Specular • Reflection Law • Mirror • Ideal Diffuse • Lambert’s Law • Matte

37. Types of Reflection Functions • Ideal Specular • Reflection Law • Mirror • Ideal Diffuse • Lambert’s Law • Matte • Specular • Glossy • Directional diffuse

38. Mathematical Reflectance Models • How can we mathematically model reflectance property of an arbitrary surface? • - what’s the dimensionality? • - how to use it to compute outgoing radiance given incoming radiance?

39. The Reflection Equation

40. The Reflection Equation How to model surface reflectance property?

41. The Reflection Equation How to model surface reflectance property?

42. The Reflection Equation How to model surface reflectance property? for a given incoming direction, the amount of light that is reflected in a certain outgoing direction

43. The Reflection Equation

44. The Reflection Equation Directional irradiance

45. The BRDF • Bidirectional Reflectance Distribution Function

46. Dimensionality of the BRDF • This is 6-D function • - x: 2D position • - (θi,φi): incoming direction • - (θr,φr): outgoing direction • Usually represented as 4-D • - ignoring x • - homogenous material property

47. Gonioreflectometer

48. Scattering Models

49. The BSSRDF • Bidirectional Surface Scattering Reflectance-Distribution Function Translucency

50. Properties of BRDF’s • 1. Linearity From Sillion, Arvo, Westin, Greenberg