7: Rendering (1) COMP Computer Graphics and Image Processing. Local illumination model. Global illumination model. Direct Direct.

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1 COMP27112 Computer Graphics and Image Processing 7: Rendering (1) Local and global illumination Direct Direct Direct Direct Indirect Local illumination model Global illumination model 2 1

2 Local and global models We can make models of light-matter interaction in two ways Locally: we treat each object in a scene separately from any other object Globally: we treat all objects together, and model the interactions between objects we ll develop a simple local illumination model in detail we ll look at global models in COMP37111 next year 3 Illumination models The interaction of light and matter is an extremely complex process In computer graphics we try to model this process. In other words, we approximate it Computer pictures are digital, with finite precision. We can only ever approximate. 4 2

3 Local illumination: elements We ll develop a model step-by-step, to include the following: Ambient illumination Diffuse reflection Positional light source Specular reflection Colour of lights and surfaces 5 Reflectivity There are three kinds of reflection: Perfect diffuse reflection Perfect specular reflection Imperfect specular reflection 6 3

4 Light/surface interaction Specularly reflected light Diffusely reflected light Pigment particles Transparent layer 7 Diffuse and specular reflection Diffuse reflection is absorption and uniform reradiation Some wavelengths are absorbed, some are reflected a green object looks green because it only reflects green Specular reflection is reflection at the air/ surface interface To a first approximation, the colour of the specular reflection is that of the light source 8 4

5 Perfect diffuse reflection Ken Brodlie Incident rays of light are reflected in all directions from the surface 9 Perfect diffuse reflection A perfect diffuse surface reflects an incoming ray across all angles (2D cross-section of previous slide) n The surface looks dull, or matte 10 5

6 Some diffuse reflectors Sponge Brick Carpet Felt 11 Perfect specular reflection A perfect specular surface reflects an incoming ray like a perfect mirror smooth 12 6

7 Imperfect specular reflection A imperfect specular surface reflects an incoming ray across a small range of angles irregular The surface looks shiny, with highlights 13 Some imperfect specular reflectors Lacquer-coated aluminium Glazed ceramic Stainless steel 14 7

8 Diffuse/specular surfaces Most surfaces exhibit a combination of diffuse and specular reflection n We can model these effects with varying degrees of realism 15 Illumination sources We begin our development of the local illumination model by considering diffuse reflection, and sources of illumination: Ambient illumination Point illumination source at infinity (directional illumination) Point illumination source in the scene 16 8

9 Ambient illumination Consider an environment with a light source Multiple reflections cause a general level of illumination in the scene 17 Ambient illumination If intensity of ambient light is I a Amount of light diffusely reflected from a surface is I ambient = k I a a Where k a is the ambient reflection coefficient of the surface 0 1 k a 18 9

10 Local illumination model v1 We now have the first term in the model we re developing I = ambient I = k a I a 19 Wireframe versus ambient Rendering with ambient illumination Wireframe rendering 20 10

11 Effect of ambient illumination Each object is uniformly illuminated Lose 3D information Ken Brodlie 21 Varying k a Ia is constant k = 0.1 k = 1.0 a a 22 11

12 True ambient lighting Note: the I = k a I a term is a gross simplification of true ambient illumination, which is not constant in a scene Advanced Interfaces Group 23 True ambient lighting Real scene (photograph) Scene modelled and rendered with accurate global illumination model Cornell University 24 12

13 Directional lighting Ken Brodlie We need to model the effects of different angles of incidence different distances from the light source 25 Directional lighting Let s consider light from a point source at infinity so we re only concerned with the direction ˆN 26 13

14 Describing surface orientation ˆL ˆN θ ˆN ˆL θ is surface normal is direction of light source is angle of incidence Note the vectors are normalised 27 Diffuse reflection: Lambert s Law I p ˆL ˆN θ I e Light source of intensity I p Effective intensity received is I e Lambert s Law: Ie = Ipcosθ Johann Heinrich Lambert ( ) 28 14

15 Lambert s Law derived I width x falling on a surface: Consider light of intensity and cross-sectional ˆN I x (The light is falling normal to the surface) n So width intensity x I on surface receives all of 29 Lambert s Law derived Now consider the light inclined at xʹ = x/ cosθ x ˆN, so θ x= xʹcosθ I cosθ I So width receives intensity θ xʹ x θ x 30 15

16 Diffuse reflectivity We express how good a diffuse reflector a surface is using k d k d is the diffuse reflection coefficient of the surface, 0 k d 1 Amount of diffusely reflected light is Idiffuse = Ipkd cosθ I = I k ( Nˆ Lˆ) diffuse p d 31 Local illumination model v2 I = ambient + diffuse I = k ˆ ˆ aia+ Ipkd( N L) 32 16

17 Ambient versus point source Rendering with a point light source and diffuse reflection Rendering with ambient illumination Ken Brodlie 33 Ambient versus point source Rendering with a point light source and diffuse reflection Rendering with ambient illumination 34 17

18 Effect of k d Varying k d from 0 to 1 35 Light source distance Physically, light intensity falls off with the square of distance travelled d After travelling, original intensity is now I e I p I e = I p 4π d

19 Light source distance While this is physically correct, it doesn t always work well for computer graphics We only have a limited number of pixel intensities, and often the 2 d term changes too rapidly, so instead we use: I e = kc l I p + k d + k q d 2 We can choose kc, kl, kqfor the best results 37 Local illumination model v3 I = ambient + distance (diffuse) I p I = k ( ˆ ˆ aia+ kdn L) dʹ Where dʹ = k + k d + k d c l q

20 Modelling specular reflection ˆL ˆN ˆR θ φ ˆV ˆR is a vector giving the direction of maximum specular reflection. ˆR θ ˆN makes an angle of with, as does (for a perfect mirror, angle of incidence == angle of reflection) ˆV is a vector pointing to the observer's position ˆL 39 Modelling specular reflection ˆL ˆN ˆR θ φ ˆV Experiment shows specular reflection varies with: φ ˆR θ Angle between and Incident angle and light wavelength So we seek a function ˆV λ Ispecular = S( φθ,, λ) 40 20

21 Modelling specular reflection S( φθ,, λ) What is this function? We ll look at the effects of in turn φθ,, λ First, φ ˆL ˆN ˆR φ ˆV 41 Modelling specular reflection ˆL ˆN ˆV ˆR Observed specular = 100% Specular reflection spread out, around ˆR Viewer sees maximum specular reflection when ˆV coincides with ˆR 42 21

22 Modelling specular reflection ˆL ˆN ˆV ˆR ˆV φ = 0 o Observed specular = 100% As diverges from by angle, viewer sees less specular reflection ˆR φ 43 Modelling specular reflection ˆL ˆN ˆR ˆV ˆV o φ = 20 Observed specular = 60% As diverges from by angle, viewer sees less specular reflection ˆR φ 44 22

23 Modelling specular reflection ˆL ˆN ˆR ˆV ˆV φ = 40 Observed specular = 5% As diverges from by angle, viewer sees less specular reflection ˆR φ o 45 Modelling specular reflection Variation of observed specular = F( φ) F But what is the function? Bui-Tuong Phong ( ) proposed using the function cos n φ 46 23

24 Phong s specular function This is a graph of against cos n φ 1.0 cos n φ φ n =1 n =10 n = 50 π /2 0 π /2 φ 47 Phong s specular function So we now have I = I cos n φ specular p Which we can rewrite using vectors as I = I ˆ ˆ p ( R V) n specular Normally we use 1 n 200 n =10 n =20 n =80 n =200 Richard Lobb 48 24

25 Incident angle and wavelength Recall Ispecular = S( φ, θλ, ) We ve accounted for φ Now we look at the effects of and θ λ 49 Modelling specular reflection ˆL ˆN ˆR θ φ ˆV Experiment shows specular reflection varies with: φ ˆR θ Angle between and Incident angle and light wavelength So we seek a function ˆV λ Ispecular = S( φθ,, λ) 50 25

26 Reflectivity of polished copper Reflectance Reflectance Red Green θ 90 o 0 90 o θ 0 λ Blue 51 Reflectance of aluminium Light polarization θ 52 26

27 Reflectance of a non-conductor Light polarization θ 53 Incident angle and wavelength This complex variation is expressed by the Fresnel equation (Augustin-Jean Fresnel, ) Ø A founder of the wave theory of light. Ø Developed theory of diffraction of light. Ø Obtained circularly polarised light Ø Developed the use of compound lenses instead of mirrors for lighthouses

28 Incident angle and wavelength This complex variation is expressed by the Fresnel equation (Augustin-Jean Fresnel, ) F = + F 2 2 sin ( φ θ) tan ( φ θ) sin ( φ+ θ) tan ( φ+ θ) is the fraction of light reflected sinθ = sin φ / µ µ is the refractive index of the material ( dependent) λ ˆL θ ˆN ˆR φ φ Air Material ˆT 55 Incident angle and wavelength In practice, we usually approximate with a single constant k s F k s is the specular reflection coefficient of the surface, 0 k s 1 Ispecular = I ( ) n pks R V But, we sacrifice accuracy for efficiency 56 28

29 Local illumination model v4 I = ambient + distance (diffuse + specular) I p I = k ( ˆ ˆ) ( ˆ ˆ aia+ kd ks ) d NL + RV ʹ n Where dʹ = k + k d + k d c l q 2 57 Diffuse and specular rendering Rendering with a point light source and diffuse and specular reflection Rendering with a point light source and diffuse reflection Ken Brodlie 58 29

30 Diffuse and specular rendering Rendering with a point light source and diffuse and specular reflection Rendering with a point light source and diffuse reflection 59 Varying k d and k s K d increasing K s increasing Alan Watt 60 30

31 Varying k s and exponent n K s increasing Exponent n increasing Alan Watt 61 Phong applet Richard Lobb PhongApplet/PhongDemoApplet.html 62 31

32 Phong demo 63 Inaccuracy of Phong model For a large angle of incidence, the Phong cos n term is incorrect Phong cos n approximation Accurate Fresnel-based reflection 64 32

33 Incorporating colour So far, we ve only considered light intensity, not colour It s easy to incorporate we express light colour as a triple of RGB intensities: And correspondingly we express surface colour using IpR, IpG, IpB kar, kag, kab kdr, kdg, kdb 65 Local illumination model v5 We now have a separate expression for each colour component. For example, for red: I = ambient Red + R distance (diffuse Red + specular) I pr ( ˆ ˆ) ( ˆ ˆ n IR = kariar + kdr ks ) d NL + RV ʹ 66 33

34 Multiple lights Finally, what if we have more than one light? Easy, compute illumination separately for each and sum. For lights: M I M = ambient + (diffuse + specular ) i= 1 i i 67 Multiple lights One light Two lights Ken Brodlie 68 34

35 Examples of the model in use AIG Lex Lennings nvidia Alan Watt James Sinnott 69 The standard model The local illumination model we ve developed is the standard model in use today Implemented in OpenGL Implemented in hardware on consumer 3D graphics cards 70 35