Ray Tracing: Special Topics CSCI 4239/5239 Advanced Computer Graphics Spring 2018

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1 Ray Tracing: Special Topics CSCI 4239/5239 Advanced Computer Graphics Spring 2018

2 Theoretical foundations Ray Tracing from the Ground Up Chapters Bidirectional Reflectance Distribution Function BRDF Describes how light is reflected on each bounce Chains to transfer colors

3 Radiometric Quantities Radiant Energy Q (J) Radiant Flux = dq/dt (W) 2 Radiant Flux Density d /da (W/m ) Irradiance E [Arriving flux density] Radiant exitance M [Leaving flux density] Radiant Intensity I d /d (W/m2/sr) Radiance L d2 /dad (W/m2/sr)

4 Ray Properties Radiance is constant along rays Radiance can be defined at the eye Radiance can be defined at a point

5 Angular Dependence on Irradiance Lambert's Law L = d2 /da d cos

6 Notation and Directions

7 BRDF Definition f(p, i, o) = dlo(p, ) / dli(p, ) cos i d i Properties Reciprocity Linearity f(p, i, o) = f(p, o, i) Sum all BDRFs at a point Conservation of energy Total re-radiated energy must be less than incident

8 Common BDRFs Diffuse f(p, i, o) = Md(p) Specular f(p, i, o) = Ms(p) (R o)s R = 2(N L)N-L

9 Bouncing Rays from Surfaces

10 Antialiasing

11 Super-sampling Pixels

12 Super-sampling Area Lights

13 Side-effects of Sampling Pattern

14 Depth of Field Important for realism Background is fuzzy Partly out of focus Imperfect optics Turbulence Graphic backgrounds are often too perfect

15 Thin Lens Theory

16 Out of Focus Images

17 Depth of Field Results

18 Ambient Occlusion Floor has a vague shadow outline Parts of object near floor is darker Ambient light is not anisotropic and uniform

19 Computing Ambient Occlusion

20 Ambient Occlusion Results

21 Mirror Reflection Mirror reflections are a signature of ray tracing Shiny objects Glass Metal Multiple reflections may occur Occurs naturally in ray tracing Requires tracing ray through multiple bounces Adds significant effort

22 Conservation of Energy Mirrors reflect almost all the energy Retains beam geometry

23 Number of Reflections 0 dull 1 simple mirror >1 hall of mirrors Effort grows with number of bounces

24 Hall of Mirrors (Showcases Ray Tracing)

25 Mirror vs Glossy Reflection Mirror reflections are perfect Glossy reflections are imperfect Reflected ray = 2(N V)N V + Super sample for many values of

26 Degrees of perfection

27 Simple Transparency Light passes through objects Light changes through object Rays are bent Colors are changed Rays multiply Reflected Transmitted

28 Refraction Index of refraction = c/v Vacuum 1 Air Water 1.33 Glass 1.5 Diamond 2.42 Snell's law sin i /sin t =

29 Media Transitions Direction of bend depends on whether the refrection index increases or decreases Air is very low Angles decrease into liquids Angles increase out of liquids

30 Internal reflections Critical angle Refraction bends ray back into medium Higher contrast causes larger critical angle That is why diamonds are so sparkly

31 Transparency require bifurcating rays

32 Objects Appearance Object inside other material Objects are magnified when not viewed parallel to the normal Object's apparent position is displaced Objects on other side Objects apparent position is displaced

33 Distortion by Glass Spheres Sphere as a lens Eye position is critical ``

34 Light movement through sphere Magnification Internal reflection

35 Realistic Transparency Three 's Air Glass Water Colored liquid Beveled edges Glass Meniscus Mixed transparency Foam is opaque

36 Reflectance and Attenuation

37 Multiple Internal Reflections

38 Colored Beaker

39 The Fish Bowl Making it real Complex shape Three media Colored media Beveled edges Challenges Multiple reflections Refraction

40

41 Adding Textures Per pixel modification of surface appearance Use texture coordinates to map textures to objects When ray tracing, you have to do this yourself Textures modify ray color on each bounce

42 Caustics

43 Tim Dunn's Gallery

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49 Production Ray Tracing Tim Dunn

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59 Reflections in Raster Methods Two possible approaches Textures (image space) Virtual objects (object space) Both approaches requires rendering the scene multiple times Mirrors can be planar or curved Mirrors are windows to the virtual scene

60 Virtual Objects Draw object where they seem to appear Clip to reflector

61 Planar Reflection Equation Point on mirror P Normal vector V

62 Rendering Order Reflections are difficult when the mirror is an object inside the scene Mirror on wall is easier

63 Limiting the Reflector User defined clipping volume Front and back clipping planes Frustrum Stencil buffer Special cases Scissors test Alpha blending

64 Reflections using Textures Quads Simple mirrors Environment maps Cube map Sphere map

65 Reflections from Curved Surfaces Cannot be done using virtual objects Readily done by distorting textures

66 Inter-reflections Hall of mirrors requires multiple passes Similar to max-levels

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