illumination 2013, Fall

Ray Casting Image RayCast(Camera camera, Scene scene, int width, int height) { Image image = new Image(width, height); for (int i; i< width; i++) for (int j=0; j<height; j++) { Ray ray=ConstructRayThroughPixel(camera, i, j); Intersection hit = FIndIntersection(ray, scene); Image[i][j]=GetColor(scene, ray, hit); } return image; }

Illumination How do we compute radiance for a sample ray? image[i][j]=GetColor(scene, ray, hit);

Goal Must derive computer models for …  Emission at light source  Scattering at surface  Reception at the camera Desirable feature …  Concise  Efficient to compute  “Accurate”

Overview Direct Illumination (=Local illumination)  Emission at light sources  Scattering at surfaces Global illumination  Shadows  Refractions  Inter-object reflections

Modeling Light Sources …  Describes the intensity of energy,  Leaving a light source,  Arriving at location (x, y, z),  From direction (   With wavelength

Empirical Models Ideally measure Irradiant energy for “all” situations  Too much storage  Difficult in practice

OpenGL Light Source Models Simple mathematical models:  Point light  Directional light  Spot light

Point Light Source Models omni-directional point source  Intensity (I 0 ),  Position (px, py, pz),  Factors (K c, K l, K q ) for attenuation with distance (d)

Directional Light Source Models point light source at infinity  Intensity (I 0 ),  Direction (dx, dy, dz)

Spot Light Source (1/2) Models point light source with direction  Intensity (I 0 ),  Position (px, py, pz),  Direction (dx, dy, dz)  Attenuation

Spot Light Source (2/2) Models point light source with direction  intensity (I 0 ),  position (px, py, pz),  direction (dx, dy, dz)  attenuation with distance  falloff (sd), and cutoff (sc)

Light Falling on a Surface Move surface away from light  Inverse square law:  Tilt surface away from light Cosine law:

Overview Direct Illumination (=Local illumination)  Emission at light sources  Scattering at surfaces Global illumination  Shadows  Refractions  Inter-object reflections

Modeling Surface Reflectance BRDF (θ i, φ i, θ o, φ o, λ)…  Bidirectional Reflectance Distribution Function  describes the amount of incident energy,  arriving from direction (θ i, φ i   쎄타  파이   leaving in direction (θ o, φ o )   with wavelength   람다 

Empirical Models Ideally measure BRDF for “all” combinations of angles : θ i, φ i, θ o, φ o  Difficult in practice  Too much storage

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]  Lafortune et al. [97]  Ashikhmin et al. [00]  etc.

OpenGL Reflectance Model Simple analytic model:  Diffuse reflection +  Specular reflection +  Emission +  “Ambient”

Diffuse Reflection Assume surface reflects equally in all directions  Example: chalk, clay

Diffuse Reflection How much light is reflected?  Depends on angle of incident light

Diffuse Reflection Lambertian model  Cosine law (dot product)

Specular Reflection Reflection is strongest near mirror angle  Examples: mirrors, metals

Specular Reflection How much light is seen? Depend on:  Angle of incident light  Angle to viewer

Specular Reflection Phong Model  cos (  n : This is a physically-motivated hack!

Emission Represent light eminating directly from polygon

Ambient Term Represents reflection of all indirect illumination  This is a total hack Avoid complexity of global illumination

OpenGL Reflectance Model Simple analytic model:  Diffuse reflection +  Specular reflection +  Emission +  “Ambient”

OpenGL Reflectance Model Sum diffuse, specular, emission, and ambient

Surface Illumination Calculation Single light source:

Surface Illumination Calculation Multiple light sources:

Example

Overview Direct Illumination (=Local illumination)  Emission at light sources  Scattering at surfaces Global illumination  Shadows  Refractions  Inter-object reflections Global Illumination

Shadows Shadow term tells if light sources are blocked  Cast ray towards each light source L i  S i = 0 if ray is blocked, S i = 1 otherwise

Ray Casting Trace primary rays from camera  Direct illumination from unblocked light only

Recursive Ray Tracing Also trace secondary rays from hit surfaces  Global illumination from mirror reflection and transparency

Mirror reflections Trace secondary rays in mirror direction  Evaluate radiance along secondary ray and include it into illumination model

Transparency Trace secondary rays in direction of refraction  Evaluate radiance along secondary ray and include it into illumination model

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

Refractive Transparency For thin surfaces, can ignore change in direction  Assume light travels straight through surface 에타

Refractive Transparency For solid objects, apply Snell’s law:

Refractive Index ( 굴절률 ) in Maya ⊙ Vacuum: 1.00 ⊙ Air: ⊙ Acetone: 1.36 ⊙ Alcohol: ⊙ Amorphous Selenium: 2.92 ⊙ Calspar 1: 1.16 ⊙ Calspar 2: ⊙ Carbon Disulfide( 탄소 황화물 ): 1.63 ⊙ Chromium Oxide( 크롬 산화물 ): ⊙ Copper Oxide( 구리 산화물 ): ⊙ Crown Glass( 크라운 창 유리 ): 1.52 ⊙ Crystal: 2.00 ⊙ Diamond: ⊙ Emerald: 1.57 ⊙ Ethyl Alcohol( 에틸 알콜 ): 1.36 ⊙ Flourite: ⊙ Fused Quartz( 석영, 수정 ): 1.46 ⊙ Heaviest Flint Glass( 렌즈, 프리즘 등 광학용 고급유리 ): 1.89 ⊙ Heavy Flint Glass: 1.65 ⊙ Glass: 1.5 ⊙ Ice: ⊙ lodine Crystal: 3.34 ⊙ Lapis Lazuli( 청금석 ): 1.61 ⊙ Light Flint Glass: ⊙ Liquid Carbon Dioxide: 1.2 ⊙ Polystyrene( 폴리스티렌 ): 1.55 ⊙ Quartz 1( 석영 ): ⊙ Quartz 2: ⊙ Ruby: 1.77 ⊙ Sapphire: 1.77 ⊙ Sodium Chloride1( 소금 ): ⊙ Sodium Chloride2( 소금 ): ⊙ Sugar Solution 30%(30% 설탕물 ): 1.38 ⊙ Sugar Solution 80%(80% 설탕물 ): 1.49 ⊙ Topaz( 황옥 ): 1.61 ⊙ Water_ 섭씨 20 도에서의 물 : ⊙ Zinc Crown Glass: 1.517

Recursive Ray Tracing Ray Tree represents illumination computation

Recursive Ray Tracing GetColor call RayTrace recursively Image RayTrace(Camera camera, Scene scene, int width, int height) { Image image = new Image(width, height); for (int i; i< width; i++) for (int j=0; j<height; j++) { Ray ray=ConstructRayThroughPixel(camera, i, j); Intersection hit = FIndIntersection(ray, scene); Image[i][j]=GetColor(scene, ray, hit); } return image; }

Recursive Ray Tracing GetColor is called recursively Color GetColor(Scene scene, Ray ray) { Intersection hit = FindIntersection(ray, scene); Ray specular_ray = SpecularRay(ray, hit); Ray refractive_ray = RefractiveRay(ray, hit); Color color = Phong(scene, ray, hit) + Ks * GetColor(scene, specular_ray, hit) + Kt * GetColor(scene, refractive_ray, hit); return color; }

Summary Ray casting (direct illumination)  Usually use simple analytic approximations for light source emission and surface reflectance Recursive ray tracing (global illumination)  Incorporate shadows, mirror reflections, and pure refractions All of this is an approximation So that it is practical to compute

Illumination Terminology Radiant power [flux] (  )  Rate at which light energy is transmitted (in Watts) Radiant Intensity (I)  Power radiated onto a unit solid angle in direction (in Watts/sr) Ex) energy distribution of a light source (inverse square law) Radiance (L)  Radiant intensity per unit projected area (in Watts/m 2 /sr) Ex) light carried by a single ray (no inverse square law) Irradiance (E)  Incident flux density on a locally planar area (in Watts/m 2 ) Ex) light hitting a surface at a point Radiosity (B)  Exitant flux density on a locally planar area (in Watts/m 2 )