Overview. Goals. MipMapping. P5 MipMap Texturing. What are MipMaps. MipMapping in OpenGL. Generating MipMaps Filtering.

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1 Overview What are MipMaps MipMapping in OpenGL P5 MipMap Texturing Generating MipMaps Filtering Alexandra Junghans Advanced Filters You can explain why it is a good idea to use MipMaps Goals You know how to generate MipMaps in OpenGL automatically You know the different filters for MipMap generation given by the OpenGL and you know the properties of these filters You can implement more sophisticated filters by yourself MipMapping Textured objects can be viewed at different distances from the viewpoint Problem: Which level of detail (LOD) should one use for the texture image, meaning which resolution should be choosen? Too high resolution --> Aliasing effects Too small resolution --> Too few details visible Solution: use different levels of detail according to distance between object and viewpoint

2 MipMapping II History: 1983 Lance Williams uses the word MipMap in his paper Pyramidal Parametrics Mip = multum in parvo means in latin many things in small place Solves LOD problem by generating a pyramide of textures, starting from level 0 with highest resolution down to a texture consisting of just one pixel, where each level has half of the size of the prior level. Texture Pyramide MipMapping III Given a set of MipMaps OpenGl automatically determines which texture map to use based on the projected size of the object With this approach always the appropriate level of detail is choosen MipMapping in OpenGL I First load textures for every MipMap level using void glteximage2d( GL_TEXTURE2D, GLint level, GLint components, GLsizei width, GLsizei height, GLint border, GLenum format, GLenum type, const GLvoid *pixels ) Be careful: if you forget one of the levels, MipMapping is disabled by OpenGL without any warning Level 0 has the highest resolution MipMap Generation The problem

3 MipMap Generation Generating smaller texture versions potentially produces aliasing Hence, every resolution has to be filtered GLU offers automatic MipMap Generation with filtering: glubuild*dmipmaps()constructs the pyramid and calls for each level glteximage*d() to load the image MipMap Generation - Filtering Recall Minification/Magnification setting Calculation of MipMap depends on scale factor λ between texture image and the size (in pixels) of the polygon to be textured ; define λ = log(texture_size/polygon_size) λ > 0 --> use minification filter λ < 0 --> use magnification filter Mini- and Magnification Filters available in OpenGL Magnification filters: always level 0 is used to compute texel values! GL_NEAREST (point sampling) GL_LINEAR (bilinear sampling) Minification filters: one or two most appropriate mipmaps are used to compute texel values GL_NEAREST, GL_LINEAR GL_NEAREST_MIPMAP_NEAREST, GL_NEAREST_MIPMAP_LINEAR GL_LINEAR_MIPMAP_NEAREST, GL_LINEAR_MIPMAP_LINEAR ( trilinear) Setting Mini- and Magnification Filters Use void gltexparameteri( GLenum target, GLenum param_name, GLint param )to load the appropriate filters. param_name can be GL_TEXTURE_MIN_FILTER GL_TEXTURE_MAG_FILTER For detailed information about the filters see OpenGl man pages

4 Nearest Neighbor Nearest Neighbor-Exercise P5 Plot the texel to nearest point Leads to pixelization Jagged texel edges Given Pixel *p and *p1 Now at current level the value of mipmap is *p = getmipmappixel (x, y, level) At the higher level *p1 = getmipmappixel (x*2, y*2, level) Now assign the intensities from p1 to p and copy it into the texturearray Bi-Linear boxfilter in Exercise P5 Compute average of 2x2 array of texels nearest calculated Pixel Smooth transition between texels Get pixel values at higher level for the current pixel Pixel Values are at (x*2, y*2), (x*2 +1, y*2), (x*2,y*2+1) and (x*2+1, y*2+1) Now Average and assign the values

5 Tri-Linear Advanced Filtering To solve Mip-Banding Smoothly blend the transition from one mip level to the next Combination: bilinear interpolation between texels linear between mipmap levels From information processing theory we know that a low pass filter (like a gaussian or a sinc filter) is optimal when we want to avoid aliasing effects Unfortunately this is computational expensive Therefore we discretize the filter into a matrix and perform a discrete convolution with our texture image Filter matrix : /256 { } >= 8x8 Samples Optimal to represent Angled-Objects Unevenly sample the image according to the perspective and Situation Advanced Filtering II- Anisotropic Filtering Exercise P5-MipMapping Implement coloredmipmap(level): with this you can observe where the MipMap levels start Implement boxfilter & bilinearfilter If you like: Feel free to implement trilinearfilter using the bilinearfilter and boxfilter implementations