CS 445 / 645 Introduction to Computer Graphics Lecture 14 Lighting Lighting

Today we talk about lighting Typical three-step development process 1.Understand the real system – how does light work (Physics) 2.Determine what matters to us – what can we sense (Psyc) 3.Engineer a system that remains true to the portion of reality we can appreciate Typical three-step development process 1.Understand the real system – how does light work (Physics) 2.Determine what matters to us – what can we sense (Psyc) 3.Engineer a system that remains true to the portion of reality we can appreciate

What can we sense? Review of lecture notes about color What color do we see the best? Yellow-green at 550 nmYellow-green at 550 nm What color do we see the worst? Blue at 440 nmBlue at 440 nm How many fully saturated hues can be distinguished? 128 fully saturated hues128 fully saturated hues How many saturations can be distinguished for a given hue? 16 to 23 depending on hue16 to 23 depending on hue What color do we see the best? Yellow-green at 550 nmYellow-green at 550 nm What color do we see the worst? Blue at 440 nmBlue at 440 nm How many fully saturated hues can be distinguished? 128 fully saturated hues128 fully saturated hues How many saturations can be distinguished for a given hue? 16 to 23 depending on hue16 to 23 depending on hue

Engineer a Solution CIE Color Space International standard for describing a color (1931) Empirically determined parameterization (X, Y, Z) Any pure wavelength can be matched perceptually by positive combinations of X,Y,Z International standard for describing a color (1931) Empirically determined parameterization (X, Y, Z) Any pure wavelength can be matched perceptually by positive combinations of X,Y,Z

Engineer a Solution CIE Color Space The gamut of all colors perceivable is thus a three- dimensional shape in X,Y,Z

Engineer a Solution Devices Have Unique Color Gamuts Since X, Y, and Z are hypothetical light sources, no real device can produce the entire gamut of perceivable color

Engineer a Solution RGB Color Space (Color Cube) Define colors with (r, g, b) amounts of red, green, and blue

Engineer a Solution RGB Color Gamuts The RGB color cube sits within CIE color space something like this:

Engineer a Solution RGB Color Space RGB may be counter intuitive Must think about mixing colorsMust think about mixing colors Small changes in RGB value may have large or small perceived color changesSmall changes in RGB value may have large or small perceived color changes RGB may be counter intuitive Must think about mixing colorsMust think about mixing colors Small changes in RGB value may have large or small perceived color changesSmall changes in RGB value may have large or small perceived color changes

Engineer a Solution HSV Color Space A more intuitive color space HSV is an alternative: Hue - The color we see (red, green, purple)Hue - The color we see (red, green, purple) Saturation - How far is the color from gray (pink is less saturated than red, sky blue is less saturated than royal blue)Saturation - How far is the color from gray (pink is less saturated than red, sky blue is less saturated than royal blue) Brightness (Luminance) - How bright is the color (how bright are the lights illuminating the object?)Brightness (Luminance) - How bright is the color (how bright are the lights illuminating the object?) A more intuitive color space HSV is an alternative: Hue - The color we see (red, green, purple)Hue - The color we see (red, green, purple) Saturation - How far is the color from gray (pink is less saturated than red, sky blue is less saturated than royal blue)Saturation - How far is the color from gray (pink is less saturated than red, sky blue is less saturated than royal blue) Brightness (Luminance) - How bright is the color (how bright are the lights illuminating the object?)Brightness (Luminance) - How bright is the color (how bright are the lights illuminating the object?)

HSV Color Space H = HueH = Hue S = SaturationS = Saturation V = Value (or brightness)V = Value (or brightness) H = HueH = Hue S = SaturationS = Saturation V = Value (or brightness)V = Value (or brightness) Value Saturation Hue

Solving the Lighting Problem We somewhat understand the perception of light (color)We somewhat understand the perception of light (color) We engineered a solution to representing and generating color using computersWe engineered a solution to representing and generating color using computers We need to understand the interplay of light and objectsWe need to understand the interplay of light and objects We somewhat understand the perception of light (color)We somewhat understand the perception of light (color) We engineered a solution to representing and generating color using computersWe engineered a solution to representing and generating color using computers We need to understand the interplay of light and objectsWe need to understand the interplay of light and objects

Optical Illusion

Lighting Remember, we know how to rasterize Given a 3-D triangle and a 3-D viewpoint, we know which pixels represent the triangleGiven a 3-D triangle and a 3-D viewpoint, we know which pixels represent the triangle But what color should those pixels be? Remember, we know how to rasterize Given a 3-D triangle and a 3-D viewpoint, we know which pixels represent the triangleGiven a 3-D triangle and a 3-D viewpoint, we know which pixels represent the triangle But what color should those pixels be?

Lighting If we’re attempting to create a realistic image, we need to simulate the lighting of the surfaces in the scene Fundamentally simulation of physics and opticsFundamentally simulation of physics and optics As you’ll see, we use a lot of approximations (a.k.a perceptually based hacks) to do this simulation fast enoughAs you’ll see, we use a lot of approximations (a.k.a perceptually based hacks) to do this simulation fast enough If we’re attempting to create a realistic image, we need to simulate the lighting of the surfaces in the scene Fundamentally simulation of physics and opticsFundamentally simulation of physics and optics As you’ll see, we use a lot of approximations (a.k.a perceptually based hacks) to do this simulation fast enoughAs you’ll see, we use a lot of approximations (a.k.a perceptually based hacks) to do this simulation fast enough

Definitions Illumination: the transport of energy from light sources to surfaces & points Note: includes direct and indirect illuminationNote: includes direct and indirect illumination Illumination: the transport of energy from light sources to surfaces & points Note: includes direct and indirect illuminationNote: includes direct and indirect illumination Images by Henrik Wann Jensen

Definitions 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 (why the distinction?) 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 (why the distinction?)

Definitions Illumination models fall into two categories: Empirical: simple formulations that approximate observed phenomenonEmpirical: simple formulations that approximate observed phenomenon Physically based: models based on the actual physics of light interacting with matterPhysically based: models based on the actual physics of light interacting with matter We mostly use empirical models in interactive graphics for simplicity Increasingly, realistic graphics are using physically based models Illumination models fall into two categories: Empirical: simple formulations that approximate observed phenomenonEmpirical: simple formulations that approximate observed phenomenon Physically based: models based on the actual physics of light interacting with matterPhysically based: models based on the actual physics of light interacting with matter We mostly use empirical models in interactive graphics for simplicity Increasingly, realistic graphics are using physically based models

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

Components of Illumination Surface properties Reflectance spectrum (i.e., color of the surface)Reflectance spectrum (i.e., color of the surface) Subsurface reflectanceSubsurface reflectance Geometric attributesGeometric attributes –Position –Orientation –Micro-structure Surface properties Reflectance spectrum (i.e., color of the surface)Reflectance spectrum (i.e., color of the surface) Subsurface reflectanceSubsurface reflectance Geometric attributesGeometric attributes –Position –Orientation –Micro-structure

Simplifications for Interactive Graphics Only direct illumination from emitters to surfacesOnly direct illumination from emitters to surfaces Simplify geometry of emitters to trivial casesSimplify geometry of emitters to trivial cases Only direct illumination from emitters to surfacesOnly direct illumination from emitters to surfaces Simplify geometry of emitters to trivial casesSimplify geometry of emitters to trivial cases

Ambient Light Sources Objects not directly lit are typically still visible e.g., the ceiling in this room, undersides of deskse.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 equallyNo spatial or directional characteristics; illuminates all surfaces equally Amount reflected depends on surface propertiesAmount reflected depends on surface properties Objects not directly lit are typically still visible e.g., the ceiling in this room, undersides of deskse.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 equallyNo spatial or directional characteristics; illuminates all surfaces equally Amount reflected depends on surface propertiesAmount reflected depends on surface properties

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

Ambient Light Sources A scene lit only with an ambient light source: Light Position Not Important Viewer Position Not Important Surface Angle Not Important

Directional Light Sources For a directional light source we make simplifying assumptions Direction is constant for all surfaces in the sceneDirection is constant for all surfaces in the scene All rays of light from the source are parallelAll 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 For a directional light source we make simplifying assumptions Direction is constant for all surfaces in the sceneDirection is constant for all surfaces in the scene All rays of light from the source are parallelAll 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

Directional Light Sources The same scene lit with a directional and an ambient light source Light Position Not Important Viewer Position Not Important Surface Angle Important

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:So we need to calculate a normalized vector to the light source for every point we light: 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:So we need to calculate a normalized vector to the light source for every point we light: p l

Point Light Sources Using an ambient and a point light source: Light Position Important Viewer Position Important Surface Angle Important

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

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

Ideal diffuse reflection An ideal diffuse reflector, at the microscopic level, is a very rough surface (real-world example: chalk)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: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?What does the reflected intensity depend on? Ideal diffuse reflection An ideal diffuse reflector, at the microscopic level, is a very rough surface (real-world example: chalk)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: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?What does the reflected intensity depend on? The Physics of Reflection

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 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

Lambert’s Law

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

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

Specular Reflection Shiny surfaces exhibit specular reflection Polished metalPolished metal Glossy car finishGlossy 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 Shiny surfaces exhibit specular reflection Polished metalPolished metal Glossy car finishGlossy 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 Physics of Reflection At the microscopic level a specular reflecting surface is very smooth Thus rays of light are likely to bounce off the microgeometry in a mirror-like fashion The smoother the surface, the closer it becomes to a perfect mirror At the microscopic level a specular reflecting surface is very smooth Thus rays of light are likely to bounce off the microgeometry in a mirror-like fashion The smoother the surface, the closer it becomes to a perfect mirror

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

Non-Ideal Specular Reflectance Snell’s law applies to perfect mirror-like surfaces, but aside from mirrors (and chrome) few surfaces exhibit perfect specularity How can we capture the “softer” reflections of surface that are glossy rather than mirror-like? One option: model the microgeometry of the surface and explicitly bounce rays off of it Or… Snell’s law applies to perfect mirror-like surfaces, but aside from mirrors (and chrome) few surfaces exhibit perfect specularity How can we capture the “softer” reflections of surface that are glossy rather than mirror-like? One option: model the microgeometry of the surface and explicitly bounce rays off of it Or…

Non-Ideal Specular Reflectance: An Empirical Approximation 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 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

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

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? 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? Viewing angle – reflected angle

Calculating Phong Lighting The cos term of Phong lighting can be computed using vector arithmetic: V is the unit vector towards the viewerV is the unit vector towards the viewer R is the ideal reflectance directionR is the ideal reflectance direction An aside: we can efficiently calculate r? The cos term of Phong lighting can be computed using vector arithmetic: V is the unit vector towards the viewerV is the unit vector towards the viewer R is the ideal reflectance directionR is the ideal reflectance direction An aside: we can efficiently calculate r? v

Calculating The R Vector This is illustrated below:

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

The Phong Lighting Model Let’s combine ambient, diffuse, and specular components: Commonly called Phong lighting Note: once per lightNote: once per light Note: once per color componentNote: once per color component Do k a, k d, and k s vary with color component?Do k a, k d, and k s vary with color component? Let’s combine ambient, diffuse, and specular components: Commonly called Phong lighting Note: once per lightNote: once per light Note: once per color componentNote: once per color component Do k a, k d, and k s vary with color component?Do k a, k d, and k s vary with color component?

Phong Lighting: Intensity Plots

Lighting Review Lighting Models AmbientAmbient –Normals don’t matter Lambert/DiffuseLambert/Diffuse –Angle between surface normal and light Phong/SpecularPhong/Specular –Surface normal, light, and viewpoint Next Class, Shading Models… Lighting Models AmbientAmbient –Normals don’t matter Lambert/DiffuseLambert/Diffuse –Angle between surface normal and light Phong/SpecularPhong/Specular –Surface normal, light, and viewpoint Next Class, Shading Models…