Lighting and Reflectance COS 426

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Hope Fleming
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1 ighting and Reflectance COS 426

2 Ray Casting R2mage *RayCast(R3Scene *scene, int width, int height) { R2mage *image = new R2mage(width, height); for (int i = 0; i < width; i++) { for (int j = 0; j < height; j++) { R3Ray ray = ConstructRayThroughPixel(scene->camera, i, j); R3Rgb radiance = ComputeRadiance(scene, &ray); image->setpixel(i, j, radiance); } } return image; } Without llumination

3 Ray Casting R3Rgb ComputeRadiance(R3Scene *scene, R3Ray *ray) { R3ntersection intersection = Computentersection(scene, ray); return ComputeRadiance(scene, ray, intersection); } With llumination

4 llumination How do we compute radiance for a sample ray once we know what it hits? ComputeRadiance(scene, ray, intersection) Angel Figure 6.2

5 Goal Must derive computer models for... Emission at light sources Scattering at surfaces Reception at the camera Desirable features Concise Efficient to compute Accurate

6 Overview Direct llumination Emission at light sources Scattering at surfaces Global illumination Shadows Refractions nter-object reflections Direct llumination

7 Emission at ight Sources (x,y,z,θ,φ,λ)... describes the intensity of energy, leaving a light source, arriving at location(x,y,z),... from direction (θ,φ),... with wavelength λ (x,y,z) ight

8 Empirical Models deally measure irradiant energy for all situations Too much storage Difficult in practice λ

9 OpenG ight Source Models Simple mathematical models: Point light Spot light Directional light

10 Point ight Source Models omni-directional point source intensity ( 0 ), position (p x, p y, p z ), coefficients (c a, l a, q a ) for attenuation with distance (d) d ight (p x, p y, p z ) = c a + l a 0 d + q a d 2

11 Point ight Source = c a + l a 0 d + q a d 2 Physically-based: inverse square law c a = l a = 0 Use c a and l a 0 for (non-physical) artistic effects

12 Directional ight Source Models point light source at infinity intensity ( 0 ), direction (d x,d y,d z ) (d x, d y, d z ) No attenuation with distance = 0

13 Spot ight Source Models point light source with direction intensity ( 0 ), position (p x, p y, p z ), direction (d x, d y, d z ) attenuation with distance falloff (sd), and cutoff (sc) d (p x, p y, p z ) Θ = cos -1 ( D) D sc = c a sd 0(cosΘ) if Θ sc, 2 + lad + qad 0 otherwise

14 Cosine obes k (cos Θ) Common model for blob at origin

15 Overview Direct llumination Emission at light sources Scattering at surfaces Global illumination Shadows Refractions nter-object reflections Direct llumination

16 Scattering at Surfaces Bidirectional Reflectance Distribution Function f r (θ i,φ i,θ o,φ o,λ)... describes the aggregate fraction of incident energy, arriving from direction (θ i,φ i ),... leaving in direction (θ o,φ o ), with wavelength λ (θ o,φ o ) Surface λ (θ i,φ i )

17 Empirical Models deally measure BRDF for all combinations of angles: θ i,φ i,θ o,φ o Difficult in practice Too much storage

18 Parametric Models Approximate BRDF with simple parametric function that is fast to compute. Phong [75] Blinn-Phong [77] Cook-Torrance [81] He et al. [91] Ward [92] afortune et al. [97] Ashikhmin et al. [00] etc. afortune [97] Cook-Torrance [81]

19 OpenG Reflectance Model Simple analytic model: diffuse reflection + specular reflection + emission + ambient Based on model proposed by Phong Surface

20 OpenG Reflectance Model Simple analytic model: diffuse reflection + specular reflection + emission + ambient Based on Phong model proposed illumination by model Phong Surface

21 Diffuse Reflection Assume surface reflects equally in all directions Examples: chalk, clay Surface

22 Diffuse Reflection What is brightness of surface? Depends on angle of incident light θ Surface

23 Diffuse Reflection What is brightness of surface? Depends on angle of incident light d = dacosθ θ d da Surface

24 Diffuse Reflection ambertian model cosine law (dot product) N θ Surface = K ( N ) D D

25 OpenG Reflectance Model Simple analytic model: diffuse reflection + specular reflection + emission + ambient Surface

26 Specular Reflection Reflection is strongest near mirror angle Examples: mirrors, metals R θ N θ

27 Specular Reflection How much light is seen? Depends on: angle of incident light angle to viewer Viewer V R α θ N θ

28 Specular Reflection Phong Model (cos α) n This is a (vaguely physically-motivated) hack! Viewer V R α θ N θ = K ( V R) S S n

29 OpenG Reflectance Model Simple analytic model: diffuse reflection + specular reflection + emission + ambient Surface

30 Emission Represents light emanating directly from surface Note: does not automatically act as light source! Does not affect other surfaces in scene! Emission 0

31 OpenG Reflectance Model Simple analytic model: diffuse reflection + specular reflection + emission + ambient Surface

32 Ambient Term Represents reflection of all indirect illumination This is a hack (avoids complexity of global illumination)!

33 OpenG Reflectance Model Simple analytic model: diffuse reflection + specular reflection + emission + ambient Surface

34 OpenG Reflectance Model Simple analytic model: diffuse reflection + specular reflection + emission + ambient Surface

35 OpenG Reflectance Model Sum diffuse, specular, emission, and ambient eonard McMillan, MT

36 OpenG Reflectance Model Good model for plastic surfaces,

37 Direct llumination Calculation Single light source: Viewer R α θ N θ V = E + K A A + K D ( N ) + K ( V S R) n

38 Direct llumination Calculation Multiple light sources: N Viewer 1 Note: 2 all of the V K and are RGB colors E A A ( n K ( N ) + K ( V R ) ) = + K + D i S i

39 Overview Direct llumination Emission at light sources Scattering at surfaces Global illumination Shadows Transmissions nter-object reflections Global llumination

40 Global llumination Greg Ward

41 Ray Casting (last lecture) Trace primary rays from camera Direct illumination from unblocked lights only ( ) n i S i D A A E R V K N K K = ) ( ) (

42 Shadows Shadow term tells if light sources are blocked Cast ray towards each light source S = 0 if ray is blocked, S = 1 otherwise Shadow Term E A A ( n K ) D ( N i ) + K S ( V Ri ) S = + K +

43 Recursive Ray Tracing Also trace secondary rays from hit surfaces Mirror reflection and transparency ( ) T T R S n i S i D A A E K K S R V K N K K = ) ( ) (

44 Mirror reflections Trace secondary ray in mirror direction Evaluate radiance along secondary ray and include it into illumination model Radiance for mirror reflection ray E A A ( n K ( N ) + K ( V R ) S + K S R KT T = + K + ) + D i S i

45 Transparency Trace secondary ray in direction of refraction Evaluate radiance along secondary ray and include it into illumination model Radiance for refraction ray E A A ( n K ( N ) + K ( V R ) S + K S R KT T = + K + ) + D i S i

46 Transparency Transparency coefficient is fraction transmitted K T = 1 for translucent object, K T = 0 for opaque 0 < K T < 1 for object that is semi-translucent Transparency Coefficient E A A ( n K ( N ) + K ( V R ) S + K S R KT T = + K + ) + D i S i

47 Refractive Transparency For thin surfaces, can ignore change in direction Assume light travels straight through surface N η i η r Θ i T Θr T Θ i T

48 Refractive Tranparency For solid objects, apply Snell s law: η sin Θ = η sin Θ r r i i N η i η r Θ i T Θr T ηi = ( cosθi cosθr ) N η r ηi η r

49 Recursive Ray Tracing Ray tree represents illumination computation Ray traced through scene Ray tree ( ) T T R S n i S i D A A E K K S R V K N K K = ) ( ) (

50 Recursive Ray Tracing Ray tree represents illumination computation Ray traced through scene Ray tree ( ) T T R S n i S i D A A E K K S R V K N K K = ) ( ) (

$Recursive Ray Tracing ComputeRadiance is called recursively R3Rgb ComputeRadiance(R3Scene *scene, R3Ray *ray, R3ntersection& hit) { R3Ray specular_ray = SpecularRay(ray, hit); R3Ray$

51 Recursive Ray Tracing ComputeRadiance is called recursively R3Rgb ComputeRadiance(R3Scene *scene, R3Ray *ray, R3ntersection& hit) { R3Ray specular_ray = SpecularRay(ray, hit); R3Ray refractive_ray = RefractiveRay(ray, hit); R3Rgb radiance = Phong(scene, ray, hit) + Ks * ComputeRadiance(scene, specular_ray) + Kt * ComputeRadiance(scene, refractive_ray); return radiance; }

52 Example Turner Whitted, 1980

$illumination) ncorporate shadows, mirror reflections, and pure refractions All of this is an approximation so that it is practical to compute More on global illumination$

53 Summary Ray casting (direct llumination) Usually use simple analytic approximations for light source emission and surface reflectance Recursive ray tracing (global illumination) ncorporate shadows, mirror reflections, and pure refractions All of this is an approximation so that it is practical to compute More on global illumination next time!

54 llumination Terminology Radiant power [flux] (Φ) Rate at which light energy is transmitted (in Watts). Radiant ntensity () Power radiated onto a unit solid angle in direction (in Watts/sr)» e.g.: energy distribution of a light source (inverse square law) Radiance () Radiant intensity per unit projected surface area (in Watts/m 2 sr)» e.g.: light carried by a single ray (no inverse square law) rradiance (E) ncident flux density on a locally planar area (in Watts/m 2 )» e.g.: light hitting a surface at a point Radiosity (B) Exitant flux density from a locally planar area (in Watts/m 2 )

Illumination. Courtesy of Adam Finkelstein, Princeton University

Illumination. Courtesy of Adam Finkelstein, Princeton University llumination Courtesy of Adam Finkelstein, Princeton University Ray Casting mage RayCast(Camera camera, Scene scene, int width, int height) { mage image = new mage(width, height); for (int i = 0; i < width;