CSC 470 Computer Graphics. Light

Transcription

1 CSC 470 Computer Graphics Light

2 Definitions Illumination: the transport of energy from light sources to surfaces & points Note: includes direct and indirect illumination Lighting: the process of computing the luminous intensity (i.e., outgoing light) at a particular 3-D point, usually on a surface Shading: the process of assigning colors to pixels

3 Components of Illumination Two components of illumination: light sources and surface properties Light sources (or emitters) Spectrum of emittance (i.e., color of the light) Geometric attributes Position Direction Shape Directional attenuation

4 Components of Illumination Surface properties Reflectance spectrum (i.e., color of the surface) Geometric attributes Position Orientation Micro-structure Common simplifications in interactive graphics Only direct illumination from emitters to surfaces Simplify geometry of emitters to trivial cases

5 Lighting Three vectors are needed to compute the intensity of reflected light m: normal vector at a surface point v: vector from a surface point to the viewer s: vector from a surface point to the light

6 Lighting Two types of lights in scenes point light sources ambient light Light is absorbed, reflected, transmitted Reflected light diffuse specular

7 Ambient Light Sources Objects not directly lit are typically still visible E.g., the ceiling in this room, undersides of desks This is the result of indirect illumination from emitters, bouncing off intermediate surfaces Too expensive to calculate (in real time), so we use a hack called an ambient light source No spatial or directional characteristics; illuminates all surfaces equally Amount reflected depends on surface properties

8 Ambient Light Uniform background glow the amount of ambient light reflected depends on the material of the surface I = I a ρ where ρ a, a is the ambient reflection coefficient ρ a = 0, 0.1, 0.3, 0.5, 0.7

9 Ambient Light Sources For each sampled wavelength, the ambient light reflected from a surface depends on The surface properties, k ambient The intensity of the ambient light source (constant for all points on all surfaces ) I reflected = k ambient I ambient

10 Ambient Light Sources A scene lit only with an ambient light source:

11 Directional Light Sources For a directional light source we make the simplifying assumption that all rays of light from the source are parallel As if the source were infinitely far away from the surfaces in the scene A good approximation to sunlight The direction from a surface to the light source is important in lighting the surface With a directional light source, this direction is constant for all surfaces in the scene

12 Directional Light Sources The same scene lit with a directional and an ambient light source

13 Point Light Sources A point light source emits light equally in all directions from a single point The direction to the light from a point on a surface thus differs for different points: So we need to calculate a normalized vector to the light source for every point we light: l p

14 Point Light Sources Using an ambient and a point light source:

15 Other Light Sources Spotlights are point sources whose intensity falls off directionally. Requires color, point direction, falloff parameters Supported by OpenGL

16 Other Light Sources Area light sources define a 2-D emissive surface (usually a disc or polygon) Good example: fluorescent light panels Capable of generating soft shadows (why? )

17 The Physics of Reflection Ideal diffuse reflection An ideal diffuse reflector, at the microscopic level, is a very rough surface (real-world example: chalk) Because of these microscopic variations, an incoming ray of light is equally likely to be reflected in any direction over the hemisphere: What does the reflected intensity depend on?

18 Diffuse reflection Reflected intensity does not depend on the direction of the viewer no contribution from the surface point to viewer vector Incoming light does depend on the direction of the light proportional to the area subtended by the facet Lamberts Law: intensity relationship between light source and surface orientation

19 Diffuse reflection Light to surface point vector parallel or nearly parallel to surface normal little variation in reflected intensity As light to surface point vector vector is perpendicular or nearly perpendicular to the surface normal small amount of reflection Model with the cosine dot product between s and m

20 Lambert s Cosine Law Ideal diffuse surfaces reflect according to Lambert s cosine law: The energy reflected by a small portion of a surface from a light source in a given direction is proportional to the cosine of the angle between that direction and the surface normal These are often called Lambertian surfaces Note that the reflected intensity is independent of the viewing direction, but does depend on the surface orientation with regard to the light source

21 Lambert s Law

22 Computing Diffuse Reflection The angle between the surface normal and the incoming light is the angle of incidence: l n θ I diffuse = k d I light cos θ In practice we use vector arithmetic: I diffuse = k d I light (n l)

23 Diffuse Lighting Examples We need only consider angles from 0 to 90 (Why?) A Lambertian sphere seen at several different lighting angles:

24 Diffuse reflection Lambert s model diffuse reflection s m I d I s ρ d MAX =, 0 s m where ρ is thediffuse reflective d constant ρ d = 0, 0.2, 0.4, 0.6, 0.8,1

25 Specular Reflection Shiny surfaces exhibit specular reflection Polished metal Glossy car finish A light shining on a specular surface causes a bright spot known as a specular highlight Where these highlights appear is a function of the viewer s position, so specular reflectance is view-dependent

26 The Optics of Reflection Reflection follows Snell s Laws: The incoming ray and reflected ray lie in a plane with the surface normal The angle that the reflected ray forms with the surface normal equals the angle formed by the incoming ray and the surface normal: θ (l)ight = θ (r)eflection

27 Non-Ideal Specular Reflectance Snell s law applies to perfect mirror-like surfaces, but aside from mirrors (and chrome) few surfaces exhibit perfect specularity In general, we expect most reflected light to travel in direction predicted by Snell s Law But because of microscopic surface variations, some light may be reflected in a direction slightly off the ideal reflected ray As the angle from the ideal reflected ray increases, we expect less light to be reflected

28 Non-Ideal Specular Reflectance: An Empirical Approximation An illustration of this angular falloff: How might we model this falloff?

29 Phong Lighting The most common lighting model in computer graphics was suggested by Phong: I specular = k s I light ( ) n cosφ shiny The n shiny term is a purely empirical constant that varies the rate of falloff Though this model has no physical basis, it works (sort of) in practice v

30 Specular reflection Lighting highlights for shiny surfaces Phong model simple, reasonable results, OpenGL support Amount of reflected light is greatest when the reflection angle equals the incident angle reflected light falls off and reflection differes

31 Specular reflection r depends on s and m r = - s + 2 ( s m) m m 2 specular light falls off as the angle between r and v increases Phong models this drop-off as a cosine of the angle raised to a power (1-200) r v I sp I s ρ smax =, 0 r v where ρ is thespecular reflective s constant

32 Phong Lighting: The n shiny Term This diagram shows how the Phong reflectance term drops off with divergence of the viewing angle from the ideal reflected ray: What does this term control, visually?

33 Calculating Phong Lighting The cos term of Phong lighting can be computed using vector arithmetic: I specular = ksilight V is the unit vector towards the viewer R is the ideal reflectance direction ( Vˆ Rˆ ) nshiny An aside: we can efficiently calculate R Rˆ = ( ( ) 2 Nˆ Lˆ Nˆ Lˆ

34 Calculating The R Vector Rˆ = ( ( ) 2 Nˆ Lˆ Nˆ Lˆ This is illustrated below: Rˆ + Lˆ = ( ( ) 2 Nˆ Lˆ )Nˆ

35 Phong Examples These spheres illustrate the Phong model as L and n shiny are varied:

36 Specular reflection ρ d = 0.25, 0.5, 0.75 f = 3, 6, 9, 25, 200

37 Total Light Add diffuse, specular, and ambient terms to compute the total amount of light that reaches the eye from a point P I = I ρ + I a a d s m ρ d max 0, + I s m sp h m ρ s max 0, h m

38 Colors OpenGL deals with colors individually computes red, green, and blue components separately I I I r g b = = = I I I ar ag ab ρ ar + I dr ρ dr ( lambert) + I spr ρ spr (phong) ρ ag + I dg ρ dg ( lambert) + I spg ρ spg (phong) ρ ab + I db ρ db ( lambert) + I spb ρ spb (phong) lambert = max 0, s m s m phong= max 0, h m h m

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41 OpenGL Lighting Making a light source maximum of 8 light sources GL_LIGHT0, GL_LIGHT1, GL_LIGHT7 properties position ambient, diffuse, and specular components distance attenuation local or remote viewpoint front and back face lighting global ambient light 41

42 OpenGL Lighting Position directional or positional maintained in my LightInfo struct // Lighting static int numactivelights; typedef struct _LightInfo { GLfloat xyz[4]; GLfloat *rgb; int enable; } LightInfo; initialized with a single white light // Light information LightInfo linfo[] = { {{ 0.0f, 0.0f, 2.0f, 0.0f}, white}, }; const int MAX_LIGHTS = (sizeof(linfo) / sizeof(linfo[0])); 42

43 OpenGL Lighting Initialize OpenGL with LightInfo gllightfv(gl_light0 + num, GL_SPECULAR, dim); gllightfv(gl_light0 + num, GL_POSITION, linfo[num].xyz); gllightfv(gl_light0 + num, GL_DIFFUSE, linfo[num].rgb); Tell OpenGL to perform lighting calculations glenable(gl_lighting); for light num glenable(gl_light0 + num); Bind material properties glmaterialfv(gl_front, GL_AMBIENT, matamb); glmaterialfv(gl_front, GL_DIFFUSE, matdiff); glmaterialfv(gl_front, GL_SPECULAR, matspec); glmaterialfv(gl_front, GL_EMISSION, matemission); glmaterialf(gl_front, GL_SHININESS, 100.0); 43

44 OpenGL Lighting Front and back face rendering, default front face rendering only glcullface(gl_back); glenable(gl_cull_face); 44

45 OpenGL Lighting movable, directional, light change position after setting viewpoint // Change light angle, reset light position if (spinning_light) { light_angle = (light_angle + 1) % 360; linfo[0].xyz[1] = light_dist * sin(deg2rad(light_angle)); linfo[0].xyz[2] = light_dist * cos(deg2rad(light_angle)); gllightfv(gl_light0, GL_POSITION, linfo[0].xyz); } global ambient light // Global ambient light GLfloat modelamb[4] = {0.7, 0.1, 0.1, 1.0}; gllightmodelfv(gl_light_model_ambient, modelamb); 45

46 OpenGL Lighting Backfacelighting assign material properties to backfaces // Backface material properties for all shapes GLfloat matambback[4] = {0.0, 0.0, 0.2, 1.0}; GLfloat matdiffback[4] = {0.0, 0.0, 0.8, 1.0}; GLfloat matspecback[4] = {0.0, 0.0, 0.4, 1.0}; GLfloat matemissionback[4] = {0.0, 0.0, 0.2, 1.0}; bind material properties // bind backface material properties glmaterialfv(gl_back, GL_AMBIENT, matambback); glmaterialfv(gl_back, GL_DIFFUSE, matdiffback); glmaterialfv(gl_back, GL_SPECULAR, matspecback); glmaterialfv(gl_back, GL_EMISSION, matemissionback); glmaterialf(gl_back, GL_SHININESS, ); enable two sided lighting gllightmodelf(gl_light_model_two_side, GL_TRUE); 46

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48 Flat Shading The simplest approach, flat shading, calculates illumination at a single point for each polygon: If an object really is faceted, is this accurate?

49 Is flat shading realistic for faceted object? No: For point sources, the direction to light varies across the facet For specular reflectance, direction to eye varies across the facet

50 Flat Shading We can refine it a bit by evaluating the Phong lighting model at each pixel of each polygon, but the result is still clearly faceted: To get smoother-looking surfaces we introduce vertex normals at each vertex Usually different from facet normal Used only for shading Think of as a better approximation of the real surface that the polygons approximate

51 Vertex Normals Vertex normals may be Provided with the model Computed from first principles Approximated by averaging the normals of the facets that share the vertex

52 Flat Shading 52

53 Gouraud Shading This is the most common approach Perform Phong lighting at the vertices Linearly interpolate the resulting colors over faces Along edges Along scanlines C 1 This is what OpenGL does Does this eliminate the facets? c 1 + t 1 (c 2 -c 1 ) C 3 c 1 + t 1 (c 2 -c 1 ) + t 3 (c 1 + t 2 (c 3 -c 1 )- c 1 + t 1 (c 2 -c 1 )) C 2 c 1 + t 2 (c 3 -c 1 )

54 Gouraud Shading Gouraud Shading Gouraud shading attempts to smooth out the shading across the polygon facets Begin by calculating the normal at each vertex N 54

55 Gouraud Shading Gouraud Shading A feasible way to do this is by averaging the normals from surrounding facets N Then apply the reflection model to calculate intensities at each vertex 55

56 Gouraud Shading Gouraud Shading We use linear interpolation to calculate intensity at edge intersection P I RED P = (1-α)I RED P1 + αi RED P2 where P divides P1P2 in the ratio α : 1 α Similarly for Q P1 P P2 P3 Q P4 56

57 Gouraud Shading Gouraud Shading Then we do further linear interpolation to calculate colour of pixels on scanline PQ P P2 P3 Q P1 57

58 Gouraud Shading 58

59 Gouraud Shading Limitations - Specular Highlights Gouraud shading gives intensities within a polygon which are a weighted average of the intensities at vertices a specular highlight at a vertex tends to be smoothed out over a larger area than it should cover a specular highlight in the middle of a polygon will never be shown 59

60 Gouraud Shading Artifacts Often appears dull, chalky Lacks accurate specular component If included, will be averaged over entire polygon C 1 C 3 C 2 Can t shade that effect!

61 Phong Shading Phong Shading Phong shading has a similar first step, in that vertex normals are calculated - typically as average of normals of surrounding faces N 61

62 Phong Shading Phong Shading However rather than calculate intensity at vertices and then interpolate intensities as we do in Gouraud shading... In Phong shading we interpolate normals at each pixel... N1 N2 P1 N P2 P P3 Q P4 62

63 Phong Shading Phong Shading... and apply the reflection model at each pixel to calculate the intensity -I RED, I GREEN, I BLUE N2 N N1 P2 P P3 Q P1 P4 63

64 Phong Shading Phong shading is not the same as Phong lighting, though they are sometimes mixed up Phong lighting: the empirical model we ve been discussing to calculate illumination at a point on a surface Phong shading: linearly interpolating the surface normal across the facet, applying the Phong lighting model at every pixel Same input as Gouraud shading Usually very smooth-looking results: But, considerably more expensive

65 Phong Shading Linearly interpolate the vertex normals Compute lighting equations at each pixel Can use specular component N 1 I total = k a I ambient + # lights i= 1 I i k d ( Nˆ Lˆ ) + k ( Vˆ Rˆ ) s n shiny N 4 N 3 Remember: Normals used in diffuse and specular terms N 2 Discontinuity in normal s rate of change is harder to detect

66 Phong Shading 66

67 Phong versus Gouraud Shading Phong versus Gouraud Shading A major advantage of Phong shading over Gouraud is that specular highlights tend to be much more accurate vertex highlight is much sharper a highlight can occur within a polygon Also Mach banding greatly reduced The cost is a substantial increase in processing time because reflection model applied per pixel But there are limitations to both Gouraud and Phong 67

68 Shortcomings of Shading Polygonal silhouettes remain Gouraud Phong

69 Gouraud versus Phong 69

70 Wall Lights 70

71 Wall Lights with Fewer Polygons 71

72 Simple Shading - Without Taking Account of Normals 72

73 Constant or Flat Shading - Each Polygon has Constant Shade 73

74 Gouraud Shading 74

75 Phong Shading 75

76 Phong Shading with Curved Surfaces 76

77 Better Illumination Model 77