Definitions. CSC 706 Computer Graphics. Components of Illumination. Components of Illumination. Lighting. Lighting. Two types of lights in scenes
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1 Definitions CSC 706 Computer Graphics Light llumination: 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- Dpoint, usually on a surface Shading: the process of assigning colors to pixels Components of llumination 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 Components of llumination 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 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 Lighting Two types of lights in scenes point light sources ambient light Light is absorbed, reflected, transmitted Reflected light diffuse specular
2 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 Ambient Light Uniform background glow the amount of ambient light reflected depends on the material of the surface = a where is the a, a ambient reflection coefficient a = 0, 0.1, 0.3, 0.5, 0.7 Ambient Light Sources 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 ) reflected = k ambient ambient A scene lit only with an ambient light source: Directional Light Sources 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 The same scene lit with a directional and an ambient light source
3 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 l normalized vector to the light source for every point we light: Point Light Sources Using an ambient and a point light source: p Other Light Sources Spotlights are point sources whose intensity falls off directionally. Requires color, point direction, falloff parameters Supported by OpenGL Other Light Sources Area light sources define a 2- Demissive surface (usually a disc or polygon) Good example: fluorescent light panels Capable of generating soft shadows (why? ) The Physics of Reflection deal 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? Diffuse reflection Reflected intensity does not depend on the direction of the viewer no contribution from the surface point to viewer vector ncoming 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
4 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 Lambert s Cosine Law deal 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 Lambert s Law Computing Diffuse Reflection The angle between the surface normal and the incoming light is the angle of incidence: l n θ diffuse = k d light cos θ n practice we use vector arithmetic: diffuse = k d light (n l) Diffuse Lighting Examples We need only consider angles from 0 to 90 (Why?) A Lambertian sphere seen at several different lighting angles: Diffuse reflection Lambert s model diffuse reflection s m d s d MAX =, 0 s m where is thediffuse reflective constant d 0.8,1 0.6, 0.4, 0.2, = 0, d
5 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 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 Non-deal Specular Reflectance Snell s law applies to perfect mirror- like surfaces, but aside from mirrors (and chrome) few surfaces exhibit perfect specularity n 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 Non-deal Specular Reflectance: An Empirical Approximation An illustration of this angular falloff: How might we model this falloff? Phong Lighting The most common lighting model in computer graphics was suggested by Phong: specular = k s 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 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
6 Specular reflection r depends on s and m ( s m) r = - s m m 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 sp s smax =, 0 r v where is thespecular reflective constant s 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? Calculating Phong Lighting The cos term of Phong lighting can be computed using vector arithmetic: specular = k s light nshiny ( Vˆ Rˆ ) V is the unit vector towards the viewer R is the ideal reflectance direction Calculating The R Vector Rˆ = This is illustrated below: Rˆ + Lˆ = ( 2( Nˆ Lˆ ) Nˆ Lˆ ( 2( Nˆ Lˆ ))N ˆ ( 2( Nˆ Lˆ ) Nˆ Lˆ An aside: we can efficiently calculate R Rˆ = Phong Examples These spheres illustrate the Phong model as L and n shiny are varied: Specular reflection d = 0.25, 0.5, 0.75 f = 3, 6, 9, 25, 200
7 Total Light Add diffuse, specular, and ambient terms to compute the total amount of light that reaches the eye from a point P s m = + a a d d max 0, + s m sp h m s max 0, h m Colors OpenGL deals with colors individually computes red, green, and blue components separately r = ar ar + dr dr ( lambert) + spr spr (phong) g = ag ag + dg dg ( lambert) + spg spg (phong) b = ab ab + db db ( lambert) + spb spb (phong) s m lambert = max 0, s m h m phong= max 0, h m 40 OpenGL Lighting OpenGL Lighting Making a light source maximum of 8 light sources GL_LGHT0, GL_LGHT1, GL_LGHT7 properties position ambient, diffuse, and specular components distance attenuation local or remote viewpoint front and back face lighting global ambient light Position directional or positional maintained in my Lightnfo struct // Lighting static int numactivelights; typedef struct _Lightnfo { GLfloat xyz[4]; GLfloat *rgb; int enable; } Lightnfo; initialized with a single white light // Light information Lightnfo linfo[] = { {{ 0.0f, 0.0f, 2.0f, 0.0f}, white}, }; const int MAX_LGHTS = (sizeof(linfo) / sizeof(linfo[0])); 41 42
8 43 OpenGL Lighting OpenGL Lighting nitialize OpenGL with Lightnfo gllightfv(gl_lght0 + num, GL_SPECULAR, dim); gllightfv(gl_lght0 + num, GL_POSTON, linfo[num].xyz); gllightfv(gl_lght0 + num, GL_DFFUSE, linfo[num].rgb); Tell OpenGL to perform lighting calculations glenable(gl_lghtng); for light num glenable(gl_lght0 + num); Bind material properties Front and back face rendering, default front face rendering only glcullface(gl_back); glenable(gl_cull_face); glmaterialfv(gl_front, GL_AMBENT, matamb); glmaterialfv(gl_front, GL_DFFUSE, matdiff); glmaterialfv(gl_front, GL_SPECULAR, matspec); glmaterialfv(gl_front, GL_EMSSON, matemission); glmaterialf(gl_front, GL_SHNNESS, 100.0); 44 OpenGL Lighting 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_lght0, GL_POSTON, linfo[0].xyz); } global ambient light // Global ambient light GLfloat modelamb[4] = {0.7, 0.1, 0.1, 1.0}; gllightmodelfv(gl_lght_model_ambent, modelamb); Backface lighting 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_AMBENT, matambback); glmaterialfv(gl_back, GL_DFFUSE, matdiffback); glmaterialfv(gl_back, GL_SPECULAR, matspecback); glmaterialfv(gl_back, GL_EMSSON, matemissionback); glmaterialf(gl_back, GL_SHNNESS, ); enable two sided lighting gllightmodelf(gl_lght_model_two_sde, GL_TRUE); Flat Shading The simplest approach, flat shading, calculates illumination at a single point for each polygon: f an object really is faceted, is this accurate? 47
9 s 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 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 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 Flat Shading 52 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 c 1 + t 1 (c 2 -c 1 ) Does this eliminate the facets? 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 3 c 1 + t 2 (c 3 -c 1 ) Gouraud shading attempts to smooth out the shading across the polygon facets Begin by calculating the normal at each vertex N 54
10 55 A feasible way to do this is by averaging the normals from surrounding facets Then apply the reflection model to calculate intensities at each vertex N We use linear interpolation to calculate intensity at edge intersection P RED P = (1-α) RED P1 + α RED P2 where P divides P1P2 in the ratio α : 1 α Similarly for Q P1 P P2 P3 Q P4 56 Then we do further linear interpolation to calculate colour of pixels on scanline PQ P1 P P2 P3 Q 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 Artifacts Often appears dull, chalky Lacks accurate specular component f included, will be averaged over entire polygon C 2 C 1 C 3 Can t shade that effect! 59
11 61 Phong shading has a similar first step, in that vertex normals are calculated - typically as average of normals of surrounding faces N However rather than calculate intensity at vertices and then interpolate intensities as we do in Gouraud shading... n Phong shading we interpolate normals at each pixel... P2 N2 N P N1 P1 P3 Q P and apply the reflection model at each pixel to calculate the intensity - RED, GREEN, BLUE P2 N2 N P N1 P1 P3 Q P4 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 63 Linearly interpolate the vertex normals Compute lighting equations at each pixel Can use specular component N 1 total = k a ambient + # lights i= 1 i kd n ( Nˆ Lˆ ) + ks ( Vˆ Rˆ ) shiny N 4 N 2 N 3 Remember: Normals used in diffuse and specular terms Discontinuity in normal s rate of change is harder to detect 66
12 67 Phong versus 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 Shortcomings of Shading Polygonal silhouettes remain Gouraud Phong Gouraud versus Phong Wall Lights Wall Lights with Fewer Polygons Simple Shading - Without Taking Account of Normals 71 72
13 73 Constant or Flat Shading - Each Polygon has Constant Shade 74 with Curved Surfaces Better llumination Model 77
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