Computer Graphics. Illumination Models and Surface-Rendering Methods. Somsak Walairacht, Computer Engineering, KMITL

Transcription

1 Computer Graphics Chapter 10 llumination Models and Surface-Rendering Methods Somsak Walairacht, Computer Engineering, KMTL

2 Outline Light Sources Surface Lighting Effects Basic llumination Models Polygon Rendering Methods Texture Mapping Ray-Tracing Radiosity / Computer Graphics 2

3 llumination Model Lighting model or Shading model Calculate the color of an illuminated positions on the surface of an object Ray-tracing Topics Light sources Basic models Lighting-surface effects / Computer Graphics 3

4 Surface-Rendering Method Shading Method Determine the pixel color using color calculations from an illumination model Scan-line, mage-space algorithms Topics Polygon rendering methods Ray-tracing Radiosity Texture Mapping / Computer Graphics 4

5 Why Lighting? f we don t have lighting effects nothing looks three dimensional / Computer Graphics 5

6 Photorealism in Computer Graphics Accurate representation of surface properties Good physical descriptions of light effects in the scene Reflections Transparency Surface texture Shadows / Computer Graphics 6

7 / Computer Graphics 7

8 Light Sources Point light Simplest, position and color nfinite distant light Large source, the sun Constant distance to any ypositions Directional vector and color Radial intensity attenuation Directional light Spotlight, cone beam Directional vector, angular limit, position, and color Extended light Large source closed to object Light emitting surface / Computer Graphics 8

9 Point Light Sources A point source is the simplest model we can use for a light source Simply define The position of the light The RGB values for the colour of the light Light is emitted in all directions Useful for small light sources / Computer Graphics 9

10 Radial ntensity Attenuation As light moves from a light source its intensity i diminished i i d At any distance d l away from the light source the intensity diminishes by a 1 factor of 2 d l However, using this factor does not produce very good results so we use something different / Computer Graphics 10

11 Radial ntensity Attenuation An inverse quadratic function is used instead 1 fradatten(d dl ) 2 a a d a d 0 where the coefficients a 0, a 1, and a 2 can be varied to produce optimal results 1 l 2 l / Computer Graphics 11

12 nfinite Distant Light Sources A large light source, like the sun, can be modelled as a point light source However, it will have very little directional effect Radial intensity attenuation is not used / Computer Graphics 12

13 Directional Light Sources To turn a point light source into a spotlight, simply add a vector direction and an angular limit θ l / Computer Graphics 13

14 Directional Light Sources & Spotlight Effects Denote V light as the unit vector in the direction of the light V obj as the unit vector from the light source to an object The dot-product of these two vectors gives us the angle between them V obj V light cos f this angle is inside the light s angular limit then the object is within the spotlight / Computer Graphics 14

15 Angular ntensity Attenuation As well as light intensity decreasing as we move away from a light source, it also decreases angularly A commonly used function for calculating angular attenuation is: f angatten al ( ) cos 0 where the attenuation exponent a l is assigned some positive value and angle is measured from the cone axis / Computer Graphics 15

16 Extended Light Sources Approximate it as a light-emitting surface We can set the direction for the point sources Behind the lightemitting surface are not illuminated / Computer Graphics 16

17 Reflected Light The colors that we perceived are determined by the nature of the light reflected from an object For example, if white light is shone onto a green object most wavelengths are absorbed, while green light is reflected from the object Colors Absorbed / Computer Graphics 17

18 Surface Lighting Effects The amount of incident light reflected by a surface depends on the type of material Shiny materials reflect more of the incident light Dull surfaces absorb more of the incident light For transparent surfaces, some of the light is also transmitted through the material / Computer Graphics 18

19 Diffuse Reflection Surfaces that are rough or grainy tend to reflect light in all directions This scattered light is called Diffuse Reflection / Computer Graphics 19

20 Specular Reflection Additionally to diffuse reflection some of the reflected light is concentrated into a highlight or bright spot This is called Specular Reflection / Computer Graphics 20

21 Basic llumination Model We will consider a basic illumination model which h gives reasonably good results and is used in most graphics systems The important components are: Ambient light Diffuse reflection Specular reflection / Computer Graphics 21

22 Basic llumination Model Ambient Diffuse Specular Final mage / Computer Graphics 22

23 Ambient Light To incorporate background light we simply set a general brightness level for ascene ndependent of viewing direction and the spatial orientation ti of a surface Assuming only monochromatic light effects, we designate ambient light with the value a / Computer Graphics 23

24 Diffuse Reflection Assume that surfaces reflect incident light with equal intensity in all directions Such surfaces are referred to as deal Diffuse Reflectors or Lambertian Reflectors / Computer Graphics 24

25 Diffuse Reflection A parameter k d is set for each surface that determines the fraction of incident light that is to be scattered as diffuse reflections from that surface This parameter is known as the Diffuse- Reflection Coefficient or the Diffuse Reflectivity it k d is assigned a value between 0.0 and : dull surface that absorbs almost all light 1.0: shiny surface that reflects almost all light / Computer Graphics 25

26 Diffuse Reflection Ambient Light For background lighting effects we can assume that every surface is fully illuminated by the ambient light a Therefore the ambient contribution ti to the diffuse reflection is given as: k ambdiff d a Ambient light alone is very uninteresting so we need some other lights in a scene as well / Computer Graphics 26

27 Diffuse Reflection Brightness depends on the orientation of a surface The amount of incident light on a surface is given as: cos l, incident l So we can model the diffuse reflections as: k l, diff d l, incident k d l cos / Computer Graphics 27

28 Diffuse Reflection Assuming we denote the normal for a surface as N and the unit direction vector to the light source as L then: So, N L cos l, diff k d l ( N 0 L) if if N N L L / Computer Graphics 28

29 Combining Ambient And ncident Diffuse Reflections Most graphics packages use two separate diffuse-reflection f coefficients: k a for ambient light a k d for incident light The total diffuse reflection equation for a single point source can then be given as: diff k a a k k d a l a ( N L) if if N L N L / Computer Graphics 29

30 Combining Ambient And ncident Diffuse Reflections / Computer Graphics 30

31 Ambient Light k a a / Computer Graphics 31

32 Ambient and Diffuse Reflection k a a k d l ( N L) / Computer Graphics 32

33 Specular Reflection The bright spot on a shiny surface is the result of near total of the incident light in a concentrated region around the specular reflection angle The specular reflection angle equals the angle of the incident light / Computer Graphics 33

34 Specular Reflection A perfect mirror reflects light only in the specular-reflection reflection direction Other objects exhibit specular reflections over a finite range of viewing positions around vector R / Computer Graphics 34

35 Effect of n shiny The effect of n s on the angular range in which we can expect to see specular reflections / Computer Graphics 35

36 The Phong Specular Reflection Model An empirical model for calculating specular reflection range Developed in 1973 by Phong Bui Tuong The intensity of specular reflection is set proportional to the angle between the viewing vector and the specular reflection vector / Computer Graphics 36

37 Phong Model The specular reflection intensity is proportional to cos n s The angle can be varied between 0 and 90 so that cos varies from 1.0 to 0.0 The Specular-Reflection Exponent, n s is determined by the type of surface we want to display Shiny surfaces have a very large value (>100) Rough surfaces would have a value near / Computer Graphics 37

38 Phong Model The specular reflection intensity is given as: n k cos s l, spec s l Since, V R cos l, spec n k V R s if V R 0 and N L ( ) s l 0.0 if V R 0 or N L / Computer Graphics 38

39 Phong Model Calculate of vector R R+L = (2NL)N R=(2NL)N L More efficient, use Halfway vector H / Computer Graphics 39

40 The Halfway Vector Blinn proposed an alternative to Phong's model that uses the halfway vector The halfway vector is the direction of maximum highlights f the surface is oriented so that the normal is aligned along, the viewer sees the brightest specular highlights l, spec H k ( N H ) s L V L V l n s / Computer Graphics 40

41 Blinn Phong Reflection Model Using halfway angle Set specular reflection exponent, n s close to the formal expression / Computer Graphics 41

42 Diffuse and Specular Constants The diffuse constant determines the intensity of the diffuse component Notice that the diffuse component gets bi brighter across the rows The specular constant determines the intensity of the specular component Notice that the specular component gets brighter up the columns / Computer Graphics 42

43 Combining Diffuse & Specular Reflections Effects of diffuse and specular reflections can be combined as diff spec k k ( N L) k ( N H ) a a d l For any number of light sources in a scene ambdiff l, diff l, k a a n l1 n l1 l k d s l spec n s N L k N H / Computer Graphics 43 s n s

44 RGB Color Considerations For an RGB color description each intensity specification is a three element vector So, for each light source: l,, lr lg Similarly il l all parameters are given as vectors: k k, k, k k k, k, k a ar ag ab lb k, k d s k sr, k sg, sb dr dg db / Computer Graphics 44

45 Total llumination k a l a k d k d ( L N) / Computer Graphics 45

46 Total llumination k a a l k d ( L N) k ( H s N) n s n / Computer Graphics s 46

47 Total llumination k a a l k d ( L N) k ( H s N) n s n / Computer Graphics s 47

48 Total llumination k a a l k d ( L N) k ( H s N) n s n / Computer Graphics s 48

49 Single Light Source k a a l k d ( L N) k ( H s N) n s / Computer Graphics 49

50 Multiple Light Sources k a a i i k d ( L i N) k s ( H i N) n s / Computer Graphics 50

51 Attenuation Decrease intensity with distance from light d = distance to light r = radius of attenuation for light att( d, r) max(0,1 d r) att( d, r) att ( d, r ) att ( d, r ) max(0,1 d max(0,(1 e d 2 r 2 2 d r 2 2 r ) 2 ) 2 ) / Computer Graphics 51

52 Attenuation k a a i i n s k L N ) k ( H N ) att( d, r ) d ( i s i i / Computer Graphics 52

53 Attenuation ), ( ) ( ) ( i n i s i d i a a r d att N H k N L k k s ), ( ) ( ) ( i i i s i d i a a / Computer Graphics 53

54 Spot Lights Eliminate light contribution outside of a cone A spotcoeff L A cos( ), L A cos( ), L A 0 L / Computer Graphics Surface 54

55 Spot Lights k a a i i k ( L N) k ( H N) ns spotcoeff d i s i i / Computer Graphics 55

56 Spot Lights k a a i i k ( L N) k ( H N) ns spotcoeff d i s i i / Computer Graphics 56

57 Spot Lights k a a i i k ( L N) k ( H N) ns spotcoeff d i s i i / Computer Graphics 57

58 No Surface Rendering VS Flat Surface Rendering No Surface Rendering Flat Surface Rendering / Computer Graphics 64

59 Flat Surface Rendering VS Gouraud Surface Rendering Flat Surface Rendering Gouraud Surface Rendering / Computer Graphics 66

60 Gouraud Surface Rendering VS Phong Surface Rendering Gouraud Surface Rendering Phong Surface Rendering / Computer Graphics 68

61 Flat Surface Rendering The simplest method for rendering a polygon surface The same colour is assigned to all surface positions The illumination at a single point on the surface is calculated and used for the entire surface Flat surface rendering is extremely fast, but can be unrealistic / Computer Graphics 69

62 Gouraud Surface Rendering Gouraud surface shading was developed in the 1970s by Henri Gouraud Worked at the University of Utah along with van Sutherland and David Evans Often also called intensity- interpolation surface rendering ntensity levels are calculated at each vertex and interpolated across the surface / Computer Graphics 70

63 Gouraud Surface Rendering (cont ) To render a polygon, Gouraud surface rendering proceeds as follows: 1. Determine the average unit normal vector at each vertex of the polygon 2. Apply an illumination model at each polygon vertex to obtain the light intensity at that position 3. Linearly interpolate the vertex intensities over the projected area of the polygon / Computer Graphics 71

64 N 4 Gouraud Surface Rendering (cont ) N v N 1 v N 2 The average unit normal vector at v is given as: N v N N 1 1 N N 2 2 N N or more generally: n 3 3 N N i N 3 i1 Nv n N i / Computer Graphics i1 72 N 4 4

65 Gouraud Surface Rendering Gouraud Surface Rendering (cont ) llumination values are linearly y y y y 3 y interpolated across each scan-line y y y y y y y y 1 3 y Scan-line p y y y y y y y y x x x x x x x x p p p / Computer Graphics 73 2 x

66 Advantages of Gouraud Surface Rendering / Computer Graphics 74

67 Gouraud Surface Rendering mplementation Gouraud surfacing rendering can be implemented relatively efficiently using an iterative approach Typically Grouaud shading is implemented as part of a visible ibl surface detection technique / Computer Graphics 76

68 Problems with Gouraud Shading Gouraud shading tends to miss certain highlighting n particular Gouraud shading has a problem with specular reflections Also, Gouraud shading can introduce anomalies known as Machbands / Computer Graphics 77

69 Problems with Gouraud Shading (cont ) Gouraud shading Phong shading The major problem with Gouraud shading is in handling specular reflections / Computer Graphics 78

70 The Machband Effect A psychological phenomenon whereby we see bright bands where two blocks of solid color meet High light can get lost or grow Corners on silhouette remain Machband effect is visible at some edges A good demo is available to experiment with this at: s490-96to97/anson/machbandingapplet/ 96t 97/ /M t/ / Computer Graphics 79

71 Phong Shading ncremental normal vector update along and between scan lines Comparison to Gouraud shading Better highlights Less Machbanding More costly / Computer Graphics 80

72 Phong Surface Rendering A more accurate interpolation based approach for rendering a polygon was developed by Phong Bui Tuong Basically the Phong surface rendering model (or normal-vector interpolation ti rendering) interpolates normal vectors instead of intensity values / Computer Graphics 81

73 Phong Surface Rendering (cont ) To render a polygon, Phong surface rendering proceeds as follows: 1. Determine the average unit normal vector at each vertex of the polygon 2. Linearly interpolate the vertex normals over the projected area of the polygon 3. Apply an illumination model at positions along scan lines to calculate pixel intensities using the interpolated normal vectors / Computer Graphics 82

74 Phong Surface Rendering g g (cont ) N 3 N N y y y y N y y y y N N N y y y y N y y y y N N 4 Scan line N y y y y N p p 4 5 N y y N y y N p p N 2 N 5 p N y y N y y N p p p / Computer Graphics 83 2

75 Phong Surface Rendering mplementation Phong shading is much slower than Gouraud shading as the lighting model is revaluated so many times Typically, Phong shading is implemented as part of a visible surface detection technique / Computer Graphics 84

76 Texture Mapping Three steps to applying a texture 1. Specify the texture Read or generate image Assign to texture Enable texturing 2. Assign texture t coordinates to vertices Proper mapping function is left to application 3. Specify texture t parameters Wrapping, Filtering / Computer Graphics 85

77 Texture Coordinates Specify a texture coordinate at each vertex Mapping between (s, t) and (u, v) t 0, 1 Texture Space Object Space a 1, 1 (s, t) = (0.2, 0.8) A c (0.4, 0.2) b B C 0, 0 1, 0 (0.8, 0.4) s / Computer Graphics 87

78 Transformations Rectangular Pattern Array Surface Pixel Area Texture Space (s, t) Object Space mage Space (u, v) (x, y) Texture - Surface Transformation u = f u (s,t) = a u s + b u t + c u v = f v (s,t) = a v s + b v t + c v Viewing and projection Transformation Texture scanning (s,t) (x,y) nverse scanning (x,y) (s,t) / Computer Graphics 88

79 Mapping Functions Basic problem is how to find the maps Consider mapping from texture coordinates to a point a surface Appear to need three functions x = x(s,t) y = y(s,t) z = z(s,t) But we really want to go the other way t s (x,y,z) / Computer Graphics 89

80 Backward Mapping We really want to go backwards A Given a pixel, we want to know to which point on an object it corresponds Given a point on an object, we want to know to B which point in the texture it corresponds Need a map of the form s = s(x,y,z) t = t(x,y,z) Such functions are difficult to find in general / Computer Graphics 90

81 Texture Mapping Projecting pixel areas to texture space = inverse scanning (x,y)(s,t) A B / Computer Graphics 91

82 Example: Surface Texture Mapping

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84 Planar Map Shape Determine which component was projected by looking for color changes in coordinate directions When moving parallel to the x-axis, an object s color changes. When moving up and down along the y-axis, the object s color also changes. However, movement along the z-axis does not produce a change in color / Computer Graphics 94

85 Cylinder Map Shape An (x,y,z) value is converted to cylindrical coordinates of ( r, theta, height ) theta is converted into x-coordinate height is converted into y-coordinate / Computer Graphics 95

86 Sphere Map Shape The (x,y,z) value of a point is converted into spherical coordinates The latitude is converted into an x-coordinate The longitude is converted into a y-coordinate / Computer Graphics 96

87 Box Map Shape Enclosing box is usually axis-parallel bounding box of object Six rectangles onto which the texture is mapped Similar to planar mapping / Computer Graphics 97

88 Bump Mapping Bump mapping affects object surfaces, making them appear rough, wrinkled, or dented Bump mapping alters the surface normals before the shading calculation takes place / Computer Graphics 99

89 Environment Mapping A two-dimensional texture mapping technique that uses a map shape of a box and a map parameter of a reflection ray it s easy to create reflections with a ray tracer, ray tracing is still too expensive for long animations / Computer Graphics 100

90 Ray Tracing Provides rendering method with Refraction/Transparent surfaces Reflective surfaces Shadows / Computer Graphics 101 mage taken from

91 Ray-Tracing Principle A global illumination based rendering method t traces rays of light from the eye back through the image plane into the scene Handles shadows, multiple specular reflections, and texture mapping / Computer Graphics 102

92 Rays & Ray Tree Corresponding binary ray-tracing tree Primary-, Secondary-, Reflected-, Transmitted- Rays / Computer Graphics 103

93 Radiosity Light can be reflected between two objects that have diffuse surfaces This is commonly called color bleeding Radiosity it treats t light as energy llumination of the scene is the transfer of energy mage created by Erik Svanholm 2002 Zumtobel Staff / Computer Graphics 106

94 Radiosity Method Describe the physical process of light distribution in a diffuse reflecting environment Areas that are not illuminated directly are also not completely dark Every objects act as a secondary light source / Computer Graphics 107

95 Ray-Tracing VS Radiosity Ray-Tracing Radiosity mage-space Object-Space From Eye to Light From Light to Surface Specular Reflection Diffuse Reflection / Computer Graphics 108

96 OpenGL llumination and Surface Rendering Functions / Computer Graphics 109

97 OpenGL Texture Functions / Computer Graphics 110

98 End of Chapter / Computer Graphics 111