Illumination. Michael Kazhdan ( /657) HB Ch. 14.1, 14.2 FvDFH 16.1, 16.2

Transcription

1 Illumination Michael Kazhdan ( /657) HB Ch. 14.1, 14.2 FvDFH 16.1, 16.2

2 Ray Casting Image RayCast(Camera camera, Scene scene, int width, int height) { Image image = new Image(width, height); for (int i = 0; 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; } Without Illumination

3 Ray Casting Image RayCast(Camera camera, Scene scene, int width, int height) { Image image = new Image(width, height); for (int i = 0; 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; } With Illumination

4 Illumination How do we compute radiance for a sample ray? image[i][j] = GetColor( scene, ray, hit ); Angel Figure 6.2

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

6 Overview Direct Illumination Emission at a light source Reflection off the surface Global illumination Shadows Inter-object reflections Transmissions Intersection Testing

7 Overview Direct Illumination Emission at light sources Reflection off the surface Global illumination Shadows Inter-object reflections Transmissions Lambertian Shading

8 Overview Direct Illumination Emission at light sources Reflection off the surface Global illumination Shadows Inter-object reflections Transmissions Phong Shading

9 Overview Direct Illumination Emission at light sources Reflection off the surface Global illumination Shadows Inter-object reflections Transmissions Shadow Computation

10 Overview Direct Illumination Emission at light sources Reflection off the surface Global illumination Shadows Inter-object reflections Transmissions Reflective Bouncing

11 Overview Direct Illumination Emission at light sources Reflection off the surface Global illumination Shadows Inter-object reflections Transmissions Refractive Bouncing

12 Overview Direct Illumination Emission at light sources Reflection off the surface Global illumination Shadows Inter-object reflections Transmissions

13 Modeling Light Sources I L (x, y, z, θ, φ, λ) describes the intensity of energy (I), leaving a light source (L), at a particular angle (θ, φ) arriving at a location (x, y, z), with a particular wavelength (λ) λ (θ, φ) (x, y, z) Light

14 Empirical Models Ideally measure irradiant energy for all situations Too much storage Difficult in practice λ (θ, φ) (x, y, z) Light

15 Simplified Light Source Models Simple mathematical models: Point light Directional light Spot light

16 Point Light Source Models omni-directional point source intensity I, (typically a three-channel value) position p = (p x, p y, p z ), factors (k c, k l, k q ) for attenuation with distance (δ) I δ (p x, p y, p z ) I L = I k c + k l δ + k q δ 2 Light The light hitting a surface point q comes in from direction q p.

17 Directional Light Source Models point light source at infinity intensity I, (typically a three-channel value) direction Ԧd = (d x, d y, d z ) I (d x, d y, d z ) No attenuation with distance k c = 1, k l = k q = 0 I L = I

18 Directional Light Source Models point light source at infinity intensity I, (typically a three-channel value) direction Ԧd = (d x, d y, d z ) I (d x, d y, d z ) No attenuation with distance k c = 1, k l = k q = 0 I L = I The light hitting a surface point q comes in from direction Ԧd.

19 Spot Light Source Models point light source with direction intensity I, (typically a three-channel value) position p = (p x, p y, p z ), attenuation (k c, k l, k q ) direction Ԧd = (d x, d y, d z ) cut-off and drop-off (γ, α) (p x, p y, p z ) Ԧd Ԧv γ δ How can we modify the intensity of a point light to decrease as g increases? Light I L = I k c + k l δ + k q δ 2

20 Spot Light Source Models point light source with direction intensity I, position p = (p x, p y, p z ), attenuation (k c, k l, k q ) direction Ԧd = (d x, d y, d z ) cut-off and drop-off (γ, α) (p x, p y, p z ) Ԧd Ԧv γ δ The light hitting a surface point q comes in from direction q p. Light I Ԧd, Ԧv α I L = k c + k l δ + k q δ 2 if Ԧd, Ԧv > cos γ 0 otherwise

21 Overview Direct Illumination Emission at light sources Direct light at surface points Global illumination Shadows Transmissions Inter-object reflections

22 Modeling Surface Reflectance R S (θ, φ, λ, γ, ψ) describes the fraction of incident energy (R), at the surface (S), arriving from direction (θ, φ), with wavelength (λ), leaving in direction γ, ψ, (γ, ψ) Surface λ (θ, φ)

23 Empirical Models Ideally measure radiant energy for all combinations of incident angles Too much storage Difficult in practice λ (θ, φ) (γ, ψ) Surface

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

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

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

27 Diffuse Reflection How much light is reflected? Depends on angle of incident light aka Lambertian θ Surface

28 Diffuse Reflection How much light is reflected? Depends on angle of incident light dl = da cos θ θ dl da Surface

29 Diffuse Reflection Lambertian model cosine law: cos θ = N, L K D is surface property I L is incoming light N θ L Surface I D = K D N, L I L

30 Diffuse Reflection Note that lights and surface properties have R,G, and B components! So amount of red light reflected is not necessarily equal to amount of green light, etc. You will need to run calculation below on EACH color channel This holds true for all lighting calculations I D Red = K D Red N, L I L Red

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

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

33 Specular Reflection Reflection is strongest near mirror angle Examples: metals, shiny apples Specular

34 Specular Reflection How much light is seen? Depends on how well the: reflected direction, and direction to the viewer line up. Viewer V R α θ N θ L

35 Specular Reflection Phong Model cos n α This is a physically-motivated hack! Viewer R α θ N θ L V I S = K S V, R n I L

36 Specular Reflection Reflection is strongest near mirror angle Examples: metals, shiny apples

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

38 Emission Represents light emanating directly from a surface that cannot be described by the three light sources Emission 0

39 Emission I E = I E Emission 0

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

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

42 Ambient Term Represents reflection of all indirect illumination I A = K A I L A

43 Simple Reflectance Model Simple analytic model: diffuse reflection + specular reflection + emission + ambient Light position dependent Light + viewer position dependent Surface

44 Simple Reflectance Model Simple analytic model: diffuse reflection + specular reflection + emission + ambient Light position dependent Light + viewer position dependent Surface

45 Surface Illumination Calculation Single light source: Viewer R α θ N θ L V I = I E + K A I L A + K D N, L I L + K S V, R n I L

46 Surface Illumination Calculation Multiple light source: L 2 Viewer N L 1 V I = I E + L K A I L A + K D N, L I L + K S V, R n I L