Rendering Light Reflection Models

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1 Rendering Light Reflection Models Visual Imaging in the Electronic Age Donald P. Greenberg October 3, 2017 Lecture #13

2 Program of Computer Graphics, Cornell University General Electric - 167

3 Cornell in Perspective Film Program of Computer Graphics, Cornell University

4

5 Direct Model Illumination Camera Perspective Raster Operations Image Storage Display

6 Perspective Model Transformation Perspective transformation Clipping Culling Matrix multiplication Camera Perspective Raster Operations Image Storage Display

7 Goal of Realistic Imaging The resulting images should be physically accurate and perceptually indistinguishable from real world scenes

8 Goal of Realistic Imaging From Strobel, Photographic Materials and Processes Focal Press, 186.

9 Direct Lighting and Indirect Lighting Direct Indirect Direct

10 Direct Lighting and Indirect Lighting

11 Assumptions In Direct Lighting Light travels directly from light source to all object surfaces (no occlusion) no shadows All light sources are point light sources (no geometric area) No interreflections from any surfaces Lights maybe directional, spot or omni lights

12 Cornell Box with Cameras

13 Photograph

14 Rendering Framework 17

15 Raster Model Operations Conversion from polygons to pixels Hidden surface removal (z-buffer) Incremental shading Camera Perspective Raster Operations Image Storage Display

16 Diffuse Reflections Roy S. Berns. Billmeyer and Saltzman s Principles of Color Technology, 3 rd Ed. 2000, John Wiley & Sons, Inc. p. 12.

17 Specular Reflections Roy S. Berns. Billmeyer and Saltzman s Principles of Color Technology, 3 rd Ed. 2000, John Wiley & Sons, Inc. p. 12.

18 Glossy Reflections Roy S. Berns. Billmeyer and Saltzman s Principles of Color Technology, 3 rd Ed. 2000, John Wiley & Sons, Inc. p. 12.

19 Reflectance - Three Forms Ideal diffuse (Lambertian) Ideal specular Directional diffuse

20 Diffuse Reflections Observer I N θ Light Source L I = k d cosθ

21 How do you find the angle ββ? If you know the surface definition (it s planar equation), you can find it s normal direction NN. A unit normal in this direction is NN NN If you know the location of the light source LL, you can find the illumination direction LL. A unit normal in this direction is LL LL

22 Cosine Calculations Dot Product Definition N L = N L cosθ cosθ = N L N L = N N L L Usually, the normal and light source vector directions are given as unit normals.

23 Gouraud Flat Polygon Shading Each polygon is shaded based on a single normal. Gouraud Thesis

24 Gouraud Smooth Shading Four polygons approximating a surface in the vicinity of point A. The shading at point R is computed as two types of successive linear interpolations: across polygon edges: P between A and B, Q between A and D; across the scan line: R between P and Q. B 2 A P R Q 1 C 3 D 4 scan line Gouraud Thesis

25 Gouraud Smooth Shading Each pixel is shaded by interpolating intensities computed at each of the polygon s vertices. Gouraud Thesis

26 Steps in Gouraud Shading For each polygon Compute vertex intensities (using any illumination model) Compute slopes (linear interpolation) in spatial (image) domain (picture plane) and intensity domain (real environment) Increment by scan line For each scan line Compute slope in intensity domain (real environment) Render each pixel Note the intensity computations are based on object space data, but all interpolation is done in image space.

27 Diffuse Shading Jeremy Birn. Digital Lighting & Rendering, p. 74.

28 Phong Model Assumptions The reflection function can be represented by three components: a constant ambient term, and diffuse and specular components Isotropic (rotationally symmetric) Point or parallel light source (one vector direction) Computationally simple

29 Phong Model Specular Reflection Observer V I R β θ r N θ i Light Source L I = k s cos n β

30 How do you find the angle ββ? If you know the illumination direction LL, you can find the reflection direction RR (angle of reflection = angle of incidence) If you know the location of the observer, you can find the view direction VV The specular reflection component is a function of the angle ββ, the angle between the view direction and the reflection vector

31 Variation of cos n β

32 Phong Reflection Model I j Diffuse Specular Mirror Reflection Vector R V Diffuse = Specular = k d s ( N L) k ( R V ) n

33 Phong Goblet Bui Toung Phong Thesis

34 Phong Equation II = II aa + II dd + II ss = [kk aa +kk dd (NN LL)](oooooooooooo cccccccccc) + kk ss (RR VV) 2 (lllllllll cccccccccc) Where kk aa = constant ambient term and kk aa +kk dd + kk ss = 1

35 Phong Model with Constant Ambient Term and Variations of Specular Exponent Roy Hall

36 Phong Model with Constant Specular Exponent and Variation of Ambient Term Roy Hall

37 Reflection Geometry (BRDF) dω i θ i θ r dω r ϕ i ϕ r Bidirectional Reflection Distribution Function

38 Gonioreflectometer Spectroradiometer Mirror Light Source Mirror Sample

39 Reflection Processes First surface reflections Multiple surface reflections Subsurface reflections

40 Gaussian Distribution m = 0.2 m = 0.6 Where m=root mean square slope of the microfacets

41 Experiment Data Aluminum, σ 0 =0.28µ

42 Comparison of experiment and theory Aluminum σ 0 = 0.28µ, τ =1.77µ

43 Bidirectional Reflectance (BRDF) λ directional diffuse specular θ uniform diffuse τ σ

44 Retro-Reflection

45 Retroreflection

46 Reflectance of Copper Mirror

47 Light Reflected from Copper

48 Cook s Copper Spheres

49 Cook-Torrance Renderings

50 Copper Vase Copper-colored plastic Copper

51 Reflection from Plastic Incident Light Specular Reflection (white) Diffuse Reflection (colored) Vinyl Substrate (white) Pigment Particles (colored)

52 The geometry of scattering from a layered surface ACM Computer Graphics, SIGGRAPH 13 p. 166

53 Phong Goblet Bui Toung Phong Thesis

54 Brushed Stainless Steel

55 Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, Pat Hanrahan. A Practical Model for Subsurface Light Transport, ACM Siggraph 2001, August 2001, Los Angeles, CA, pp

56 3D Studio Max: Material Editor

57 3D Studio Max: Material Editor

58 End...

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