Reflection Model

1. Reflection Model 고려대학교 컴퓨터 그래픽스 연구실 kucg.korea.ac.kr

2. Content • Shading • Light sources • Point, distant, and spot lights • Phong reflection model • Diffuse reflection • Specular reflection • Ambient reflection • Computation of vectors • Normal vectors, angle of reflection, and transmitted light kucg.korea.ac.kr

3. Shading • Determine a color for each filled pixel • How to choose a color • the color of the light source and of the surfaces determines the color of one or more pixels in the frame buffer kucg.korea.ac.kr

4. Light and Matter • Color is determined by multiple interactions among light sources and reflective surfaces • recursive reflection of light between surfaces accounts for subtle shading Rendering Equation kucg.korea.ac.kr

5. Light-Material Interactions • Specular surfaces – mirror • scatter reflected light in a narrow range of angle • Diffuse surfaces – chalk, clay • scatter reflected light all directions • Translucent surfaces – glass, water • refraction specular surface diffuse surface translucent surface kucg.korea.ac.kr

6. Light Sources • Illumination function I (x, y, z, θ, φ, λ) • each point (x, y, z) on the surface • direction of emission (θ, φ) • wavelength λ light source kucg.korea.ac.kr

7. Modeling Light Sources • Simple mathematical models: • ambient light • point light • distant light • spot light kucg.korea.ac.kr

8. Color Sources • Three-color theory • human perceive three primary colors – red, green, and blue • three-component intensity or luminance function • independent calculations kucg.korea.ac.kr

9. Ambient Light • Uniform lighting • identical at every point in the scene kucg.korea.ac.kr

10. Point Sources (1/2) • Emit light equally in all directions • p0: point source location • proportional to the inverse square distance point source illuminating a surface kucg.korea.ac.kr

11. Point Sources (2/2) • Large finite size of most light sources • umbra: full shadow • penumbra: partial shadow • Attenuation shadows created by finite-size light source kucg.korea.ac.kr

12. Spotlights • Characterized by a narrow range of angle through which light is emitted • ps: apex of a cone • ls: direction of pointing • θ: angle to determine width • Distribution of light • concentrate in the center • light intensity drop off spotlight attenuation exponent kucg.korea.ac.kr

13. Distant Light Sources • far from the surface  vector does not change • location  direction parallel light source kucg.korea.ac.kr

14. Phong Reflection Model (1/5) • Efficient and close enough approximation to physical reality to produce good renderings • Use 4 vectors • n: normal at p • v: direction from p to the viewer or COP • l: direction from light source • r: direction of reflectance • 3 types of material-light interactions • ambient, diffuse, and specular vectors used by the Phong model kucg.korea.ac.kr

15. Phong Reflection Model (2/5) • Simple analytic model: • Diffuse reflection + • Specular reflection + • Emission + • “Ambient” Based on model proposed by Phong kucg.korea.ac.kr

16. Phong Reflection Model (2/5) • Simple analytic model: • Diffuse reflection + • Specular reflection + • Emission + • “Ambient” Based on model proposed by Phong kucg.korea.ac.kr

17. Diffuse Reflection (1/3) • Assume surface reflects equally in all directions • Examples: chalk, clay kucg.korea.ac.kr

18. Diffuse Reflection (2/3) • How much light is reflected? • Depends on angle of incident light • dL = dAcos Q kucg.korea.ac.kr

19. Diffuse Reflection (3/3) • Lambertian model • Cosine law (dot product) kucg.korea.ac.kr

20. Phong Reflection Model (2/5) • Simple analytic model: • Diffuse reflection + • Specular reflection + • Emission + • “Ambient” Based on model proposed by Phong kucg.korea.ac.kr

21. Specular Reflection (1/3) • Reflection is strongest near mirror angle • Examples: mirrors, metals kucg.korea.ac.kr

22. Specular Reflection (2/3) • How much light is seen? • Depends on angle of incident light and angle to viewer kucg.korea.ac.kr

23. Specular Reflection (3/3) • Phong model • {cos(a)}n kucg.korea.ac.kr

24. Phong Reflection Model (2/5) • Simple analytic model: • Diffuse reflection + • Specular reflection + • Emission + • “Ambient” Based on model proposed by Phong kucg.korea.ac.kr

25. Emission • Represents light emitting directly from polygon Emission ≠ 0 kucg.korea.ac.kr

26. Phong Reflection Model (2/5) • Simple analytic model: • Diffuse reflection + • Specular reflection + • Emission + • “Ambient” Based on model proposed by Phong kucg.korea.ac.kr

27. Ambient Term • Represents reflection of all indirect illumination This is a total hack (avoids complexity of global illumination)! kucg.korea.ac.kr

28. Phong Reflection Model (3/5) • Simple analytic model: • Diffuse reflection + • Specular reflection + • Emission + • “Ambient” kucg.korea.ac.kr

29. Phong Reflection Model (4/5) • Simple analytic model: • Diffuse reflection + • Specular reflection + • Emission + • “Ambient” kucg.korea.ac.kr

30. Phong Reflection Model (5/5) • Sum diffuse, specular, emission, and ambient kucg.korea.ac.kr

31. Surface Illumination Calculation (1/2) • Single light source: kucg.korea.ac.kr

32. Surface Illumination Calculation (2/2) • Multiple light sources: kucg.korea.ac.kr

33. Computation of Reflection • Light source and reflection term • Ex. red intensity • Total Intensity kucg.korea.ac.kr

34. Ambient Reflection • Same at every point on the surface • Ambient reflection coefficient • amount reflected • some of light source is absorbed and some is reflected • three ambient coefficients – , , and • Ambient reflection term • can be any of the individual light sources • can be a global ambient term kucg.korea.ac.kr

35. Diffuse Reflection (1/2) • Characterized by rough surfaces • perfectly diffuse surface  so rough that there is no preferred angle of reflection • Lambert’s law • only the vertical component of light source rough surface at noon in the afternoon Lambert’s law kucg.korea.ac.kr

36. Diffuse Reflection (2/2) • Lambert’s law (cont’) • Diffuse reflection term • incorporate a distance term Lambert’s law kucg.korea.ac.kr

37. Specular Reflection • Specular surface is smooth • highlight in the direction of the viewer • Specular reflection term • shininess coefficient • α  infinite : mirror • 100 < α < 500 : metal • α < 100 : broad highlight specular surface specular highlights effect of shininess coefficient kucg.korea.ac.kr

38. Illumination Equation • Including the distance term kucg.korea.ac.kr

39. Utah Teapots with Different Material Properties kucg.korea.ac.kr

40. p1 p0 p2 Computation of Vectors (1/2) • Normal vectors • in OpenGL • Angle of reflection n glNormal3f(nx, ny, nz); glNormal3fv(pointer_to_normal); coplanar condition ① ② by ① and ② mirror kucg.korea.ac.kr

41. Computation of Vectors (2/2) • Halfway vector • half-angle: 2ψ=φ • Transmitted light • Snell’s law halfway vector perfect light transmission kucg.korea.ac.kr