Review 2 Illumination Shading Texturing and Anti aliasing Jian Huang CS594 Spring 2002 Illumination Vs Shading Illumination lighting model determine the color of a surface point by simulating some light attributes Shading model applies the illumination models at a set of points and colors the whole image Local illumination Only consider the light the observer position and the object material properties Basic Illumination Model Simple and fast method for calculating surface intensity at a given point Lighting calculating are based on The background lighting conditions The light source specification color position Optical properties of surfaces Glossy OR matte Opaque OR transparent control refection and absorption Ambient light background light The light that is the result from the light reflecting off other surfaces in the environment A general level of brightness for a scene that is independent of the light positions or surface directions ambient light Has no direction Each light source has an ambient light contribution Ia For a given surface we can specify how much ambient light the surface can reflect using an ambient reflection coefficient Ka 0 Ka 1 Ambient Light So the amount of light that the surface reflect is therefore Iamb Ka Ia Diffuse Light The illumination that a surface receives from a light source and reflects equally in all directions This type of reflection is called Lambertian Reflection thus Lambertian surfaces The brightness of the surface is indepenent of the observer position since the light is reflected in all direction equally Lambert s Law How much light the surface receives from a light source depends on the angle between its angle and the vector from the surface point to the light light vector Lambert s law the radiant energy Id from a small surface da for a given light source is Id IL cos IL the intensity of the light source is the angle between the surface normal N and light vector L The Diffuse Component Surface s material property assuming that the surface can reflect Kd 0 Kd 1 diffuse reflection coefficient amount of diffuse light Idiff Kd IL cos If N and L are normalized cos N L Idiff Kd IL N L The total diffuse reflection ambient diffuse Idiff Ka Ia Kd IL N L Examples Sphere diffusely lighted from various angles Specular Light These are the bright spots on objects such as polished metal apple Light reflected from the surface unequally to all directions The result of near total reflection of the incident light in a concentrated region around the specular reflection angle Phong s Model for Specular How much reflection light you can see depends on where you are Phong Illumination Curves Specular exponents are much larger than 1 Values of 100 are not uncommon n glossiness rate of falloff Specular Highlights Shiny surfaces change appearance when viewpoint is changed Specularities are caused by microscopically smooth surfaces A mirror is a perfect specular reflector Phong Illumination Moving Light Change n Putting It All Together Single Light white light source Flat Shading Smooth Shading Need to have per vertex normals Gouraud Shading Interpolate color across triangles Fast supported by most of the graphics accelerator cards Phong Shading Interpolate normals across triangles More accurate but slow Not widely supported by hardware Gouraud Shading Normals are computed at the polygon vertices If we only have per face normals the normal at each vertex is the average of the normals of its adjacent faces Intensity interpolation linearly interpolate the pixel intensity color across a polygon surface Gouraud Shading Phong Shading Model Gouraud shading does not properly handle specular highlights specially when the n parameter is large small highlight Reason colors are interpolated Solution Phong Shading Model 1 Compute averaged normal at vertices 2 Interpolate normals along edges and scan lines component by component 3 Compute per pixel illumination Phong Shading What Dreams May Come How to efficiently add graphics detail Solution its really a cheat MAP surface detail from a predefined easy to model table texture to a simple polygon How Texture Mapping Problem 1 Fitting a square peg in a round hole We deal with non linear transformations Which parts map where Texture Mapping Problem 2 Mapping from a pixel to a texel Aliasing is a huge problem What is a Texture Given the texture image index u v want F u v a continuous reconstruction R u v G u v B u v I u v index u v alpha u v normals u v surface height u v RGB Textures Places an image on the object Typical texture mapping Opacity Textures A binary mask really redefines the geometry Bump Mapping This modifies the surface normals More on this later Displacement Mapping Modifies the surface position in the direction of the surface normal Texture and Texel Each pixel in a texture map is called a Texel Each Texel is associated with a u v 2D texture coordinate The range of u v is 0 0 1 0 u v tuple For any u v in the range of 0 1 0 1 we can find the corresponding value in the texture using some interpolation Two Stage Mapping 1 Model the mapping x y z u v 2 Do the mapping Image space scan For each y For each x compute u x y and v x y copy texture u v to image x y Samples the warped texture at the appropriate image pixels inverse mapping Image space scan Problems Finding the inverse mapping Use one of the analytical mappings Bi linear or triangle inverse mapping May miss parts of the texture map Image Texture Inverse Mapping Need to transform back to world space to do the interpolation Orientation in 3D image space 5 1 1 6 5 7 Foreshortening 8 1 6 2 Texture space scan For each v For each u compute x u v and y u v copy texture u v to image x y Places each texture sample to the mapped image pixel Forward mapping Texture space scan Problems May not fill image Forward mapping needed Texture Image Texture Mapping Mapping to a 3D Plane Simple Affine transformation rotate scale translate v y z u x Texture Mapping Mapping to a Cylinder Rotate translate and scale in the uv plane u v z x r cos y r sin v u Texture Mapping Mapping to Sphere Impossible Severe distortion at the poles u v x r sin cos y r sin sin z r cos Sampling What we have in computer graphics is a point sampling of our scene or I x f x ST x What we would like is more of an integration across the pixel or larger area I x f x h x What should h x be Sampling Theorem The Shannon Sampling Theorem A band limited signal f x with a cutoff frequency of that is sampled
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