1Lighting and ShadingCS148: Intro to CGInstructor: Dan MorrisTA: Sean WalkerJuly 14, 2005Pre-lecture business{ meshes.cpp example from last class{ pp2 is due today{ pp3 goes out today{ start thinking about pp4{ Remote students: email fax #’sOutline for today{ Lighting{ Shading{ Lighting and shading in OpenGLWhat have we done so far?{ We can model objects or load objects that someone else modeled{ We can create a scene with objects and a camera{ We know how our objects get transformed and rasterizedOpenGL magicpixelsobject coordinatesWhat color is an object?{ So far, we’ve used glColor3f() to say “my object is blue”{ But what color should a blue sphere’s pixels really be?What color is an object? [light.cpp]{ Pixel color – and color in the real world – depend on:z Light color and positionz Material propertiesz Camera positionz Object geometry, medium2We can’t capture all of these things…{ …so we make approximations depending on our compute power, our need for realism, etc.Illumination Models{ Part of our approximation is our mathematical representation of how light interacts with objects{ For example, one illumination model might be:pixel color == object colorWhat would a sphere look like under this illumination model?A blue sphere with this illumination modelIllumination Models{ Today we’ll look at the individual illumination models that make up the OpenGL lighting system:z Diffuse lightingz Ambient lightingz Specular lighting{ All of our examples will be in grayscale for right nowLighting framework{ We want to decide what color some point p on an object should be from a viewer’s perspective{ What data do we have to work with?pnslighteyev{ Lightz Positionz Brightness{ Objectz Materialz Surface normalDiffuse Lighting Model{ A fraction of incoming light is reradiated “diffusely” in all directions{ Some of this light will reach the eye{ Since light is radiated equally in all directions, the orientation of the surface relative to the eye doesn’t matterDiffuse Light: Surface orientation{ The orientation of the surface relative to the light does matter{ The “brightness” of a surface depends on how many photons hit a unit area{ If the light “sees” more of the object, it will hit it with more photonsWhen the object faces away from the light, a smaller portion of the light’s energy hits a unit area on the object3Diffuse Light: Lambert’s Law{ If s (vector to light) and n (normal) are “more aligned”, the object should be brighter{ What operation tells us “how aligned” two vectors are?{ Lambert’s law:Id= Ld(us•un)z Id: output (pixel) brightnessz Ld: light intensityz usand un: unit versions of s and nWhat’s the most important missing piece here?Diffuse Light: Diffuse Coefficient{ rd: diffuse reflection coefficient{ Captures many complex properties of an object in one number: how much light does it reflect?{ OpenGL convention: 0.0 --> 1.0Specular Lighting Model{ Light scatters most strongly in one direction{ Specifically, light scatters most strongly in the same direction a mirror would reflectSpecular (Mirror-Like) Reflection{ Angle of incidence ==angle of reflection{ Clearly r will be useful in deciding how bright the object appears…nθθrs’What is r in terms of s and n?{ Decompose s’:z m = (s’•un)un(parallel to n)z e = s’–m (perpendicular to n){ What is r in terms of e and m?z r = e + (-m)z r = e + (-m) = (s’–m) – m = s’–2mz r = s’–2 ( s’•un) unnrs’mee-mSpecular Illumination{ More light goes out along the direction r{ The more the view axis v lines up with r, the brighter the object should appear{ Is= Lsrs(ur•uv)What does each term mean?{ Doesn’t capture the fact that some materials are “more specular” than others{ rstells us what color the material reflects, but now how that color falls off with angle4Specular Illumination: Phong Model{ Add a parameter f that tells us “how specular” a material is:Is= Lsrs(ur•uv)f{ Higher f = more specular; light falls off faster as v moves away from r{ In OpenGL terminology, f is “shininess”Specular Illumination: ExamplesWhich sphere isshinier?Same shininessas above spheres,both have reducedrsAmbient Lighting Model{ Stuff pointing away from lights isn’t really pitch black{ But we can’t model all the reflections in a real scene...{ So we just add “ambient lighting” that doesn’t depend on orientation:Ia= LaraAmbient Lighting: Examples{ Too much ambient light: everything gets washed out{ Too little ambient light: very deep shadowsPutting it All Together{ In our illumination model, the light at a point is equal to:I = Lara+ Ldrd(us• un) + Lsrs(ur• uv)f{ We can do this computation for all lights in a scene and add the results togetherWhat happens if the surface normal points away from the light?Outline for today{ Lighting{ Shading{ Lighting and shading in OpenGL5An aside: Normals in OpenGL{ Normals in OpenGL are associated with vertices, not faces{ Why? Objects in 3D graphics are usually discrete approximations of continuous real-world objects{ Surface normal actually changes over the surface of the “real” object{ Vertex normals are ”samples” of the real normalAn aside: Normals in OpenGL{ Before I call glVertex(), I usually call:{ glNormal3f(x,y,z);To tell GL what the current surface normal is.{ Normals are transformed through the whole pipeline, so they’re specified in object coordinates{ Mesh files usually specify normalsLimitations of our lighting model{ Now we know how to compute the pixel color for a given point{ This took a few multiplications, so it would be expensive to do this for every single pixel{ Plus, we don’t usually have exact surface normals everywhere, since we often approximate curved objects with flat polygonsShading{ Shading is the process of filling polygons with color based on the illumination at some points on the polygon{ Usually we evaluate I (illumination) at vertices, and use that data to shade the polygonFlat Shading{ Simplest, fastest shading algorithm:z Pick a point on the polygonz Compute illumination at that pointz Fill the whole polygon with that colorGouraud Shading{ Most realistic shading algorithm supported by OpenGLz Compute illumination at all verticesz Interpolate illumination values when rasterizing the polygon453216Flat Shading vs. Gouraud ShadingWhen might I want flat shading?Phong Shading{ Instead of interpolating color, interpolate normals and re-compute color at each pixel{ Also