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UCSD CSE 167 - Antialiasing

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AntialiasingCSE167: Computer GraphicsInstructor: Steve RotenbergUCSD, Fall 2005Texture MinificationConsider a texture mapped triangleAssume that we point sample our texture so that we use the nearest texel to the center of the pixel to get our colorIf we are far enough away from the triangle so that individual texels in the texture end up being smaller than a single pixel in the framebuffer, we run into a potential problemIf the object (or camera) moves a tiny amount, we may see drastic changes in the pixel color, as different texels will rapidly pass in front of the pixel centerThis causes a flickering problem known as shimmering or buzzingTexture buzzing is an example of aliasingSmall TrianglesA similar problem happens with very small trianglesScan conversion is usually designed to point sample triangles by coloring the pixel according to the triangle that hits the center of the pixelThis has the potential to miss small trianglesIf we have small, moving triangles, they may cause pixels to flicker on and off as they cross the pixel centersA related problem can be seen when very thin triangles cause pixel gapsThese are more examples of aliasing problemsStairsteppingWhat about the jagged right angle patterns we see at the edges of triangles?This is known as the stairstepping problem, also affectionately known as “the jaggies”These can be visually distracting, especially for high contrast edges near horizontal or verticalStairstepping is another form of aliasingMoiré PatternsWhen we try to render high detail patterns with a lot of regularity (like a grid), we occasionally see strange concentric curve patterns formingThese are known as Moiré patterns and are another form of aliasingYou can actually seethese in real life if youhold two windowscreens in front ofeach otherThe Propeller ProblemConsider an animation of a spinning propeller, that is rendering at 30 frames per secondIf the propeller is spinning at 1 rotation per second, then each image shows the propeller rotated an additional 12 degrees, resulting in the appearance of correct motionIf the propeller is now spinning at 30 rotations per second, each image shows the propeller rotated an additional 360 degrees from the previous image, resulting in the appearance of the propeller sitting still!If it is spinning at 29 rotations per second, it will actually look like it is slowly turning backwardsThese are known as strobing problems and are another form of aliasingAliasingThese examples cover a wide range of problems, but they all result from essentially the same thingIn each situation, we are starting with a continuous signalWe then sample the signal at discreet pointsThose samples are then used to reconstruct a new signal, that is intended to represent the original signalHowever, the reconstructed signals are a false representation of the original signalsIn the English language, when a person uses a false name, that is known as an alias, and so it was adapted in signal analysis to apply to falsely represented signalsAliasing in computer graphics usually results in visually distracting artifacts, and a lot of effort goes into trying to stop it. This is known as antialiasingSignalsThe term signal is pretty abstract, and has been borrowed from the science of signal analysisSignal analysis is very important to several areas of engineering, especially electrical, audio, and communicationsSignal analysis includes a variety of mathematical methods for examining signals such as Fourier analysis, filters, sampling theory, digital signal processing (DSP), and moreIn electronics, a one dimensional signal can refer to a voltage changing over time. In audio, it can refer to the sound pressure changing over timeIn computer graphics, a one dimensional signal could refer to a horizontal or vertical line in our image. Notice that in this case, the signal doesn’t have to change over time, instead it varies over space (the x or y coordinate)Often signals are treated as functions of one variable and examples are given in the 1D case, however the concepts of signal analysis extend to multidimensional signals as well, and so we can think of our entire 2D image as a signalSamplingIf we think of our image as a bunch of perfect triangles in continuous (floating point) device space, then we are thinking of our image as a continuous signalThis continuous signal is can have essentially infinite resolution if necessary, as the edges of triangles are perfect straight linesTo render this image onto a regular grid of pixels, we must employ some sort of discreet sampling techniqueIn essence, we take our original continuous image and sample it onto a finite resolution grid of pixelsIf our signal represents the red intensity of our virtual scene along some horizontal line, then the sampled version consists of a row of discreet 8 bit red valuesThis is similar to what happens when a continuous analog sound signal is digitally sampled onto a CDReconstructionOnce we have our sampled signal, we then reconstruct itIn the case of computer graphics, this reconstruction takes place as a bunch of colored pixels on a monitorIn the case of CD audio, the reconstruction happens in a DAC (digital to analog converter) and then finally in the physical movements of the speaker itselfReconstruction FiltersNormally, there is some sort of additional filtration that happens at the reconstruction phaseIn other words, the actual pixels on the monitor are not perfect squares of uniform color. Instead they will have some sort of color distributionAdditional filtration happens in the human eye so that the grid of pixels appears to be a continuous imageIn audio, the perfect digital signal is filtered first by the analog electronic circuitry and then by the physical limitations of the speaker movementLow Frequency SignalsOriginal signalPoint sampled at relatively high frequencyReconstructed signalHigh Frequency SignalsOriginal signalPoint sampled at relatively low frequencyReconstructed signalRegular SignalsOriginal repeating signalPoint sampled at relatively low frequencyReconstructed signal repeating at incorrect frequencyNyquist FrequencyTheoretically, in order to adequately reconstruct a signal of frequency x, the original signal must be sampled with a frequency of greater than 2xThis is known as


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UCSD CSE 167 - Antialiasing

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