CS 445 / 645 Introduction to Computer GraphicsEnvironment MappingMaterials from NVidiaSphere MappingBlinn/Newell Lattitude MappingCube MappingMultitexturingSlide 8AntialiasingWhat is a pixel?SamplesSlide 12Slide 13Line SegmentsSlide 15Area SamplingUnweighted Area SamplingWeighted Area SamplingSlide 19ImagesSampling and ImagePoint Sampling an ImagePoint SamplingSampling ErrorsFixing Sampling ErrorsSlide 26Slide 27Signal TheorySlide 29Fourier AnalysisFourier TransformNyquist Sampling TheoremNyquist RateBand-limited SignalsFlaws with Nyquist RateSlide 36Low-pass FilteringSlide 38Slide 39Slide 40Sinc FilterBilinear FilterSampling PipelineHow is this done today? Full Screen AntialiasingGeForce3GeForce3 - MultisamplingSlide 47Slide 48Slide 49ATI SmoothvisionATI NVidia comparison3dfxCS 445 / 645Introduction to Computer GraphicsLecture 20Lecture 20AntialiasingAntialiasingLecture 20Lecture 20AntialiasingAntialiasingEnvironment MappingUsed to model a object that reflects surrounding textures Used to model a object that reflects surrounding textures to the eyeto the eye•Polished sphere reflects walls and ceiling texturesPolished sphere reflects walls and ceiling textures•Cyborg in Terminator 2 reflects flaming destructionCyborg in Terminator 2 reflects flaming destructionTexture is distorted fish-Texture is distorted fish-eye view of environmenteye view of environmentSpherical texture mapping Spherical texture mapping creates texture coordinates creates texture coordinates that correctly index into that correctly index into this texture mapthis texture mapUsed to model a object that reflects surrounding textures Used to model a object that reflects surrounding textures to the eyeto the eye•Polished sphere reflects walls and ceiling texturesPolished sphere reflects walls and ceiling textures•Cyborg in Terminator 2 reflects flaming destructionCyborg in Terminator 2 reflects flaming destructionTexture is distorted fish-Texture is distorted fish-eye view of environmenteye view of environmentSpherical texture mapping Spherical texture mapping creates texture coordinates creates texture coordinates that correctly index into that correctly index into this texture mapthis texture mapMaterials from NVidiahttp://developer.nvidia.com/object/Cube_Mapping_Paper.htmlhttp://developer.nvidia.com/object/Cube_Mapping_Paper.htmlhttp://developer.nvidia.com/object/Cube_Mapping_Paper.htmlhttp://developer.nvidia.com/object/Cube_Mapping_Paper.htmlSphere MappingBlinn/Newell Lattitude MappingCube MappingMultitexturingPipelining of multiple texture applications to one Pipelining of multiple texture applications to one polygonpolygonThe results of each texture unit application is The results of each texture unit application is passed to the next texture unit, which adds its passed to the next texture unit, which adds its effectseffectsMore bookkeeping is required to pull this offMore bookkeeping is required to pull this offPipelining of multiple texture applications to one Pipelining of multiple texture applications to one polygonpolygonThe results of each texture unit application is The results of each texture unit application is passed to the next texture unit, which adds its passed to the next texture unit, which adds its effectseffectsMore bookkeeping is required to pull this offMore bookkeeping is required to pull this offAntialiasingWhat is a pixel?A pixel is not…A pixel is not…•A boxA box•A diskA disk•A teeny tiny little lightA teeny tiny little lightA pixel is a pointA pixel is a point•It has no dimensionIt has no dimension•It occupies no areaIt occupies no area•It cannot be seenIt cannot be seen•It can have a coordinateIt can have a coordinateA pixel is not…A pixel is not…•A boxA box•A diskA disk•A teeny tiny little lightA teeny tiny little lightA pixel is a pointA pixel is a point•It has no dimensionIt has no dimension•It occupies no areaIt occupies no area•It cannot be seenIt cannot be seen•It can have a coordinateIt can have a coordinateA pixel is more than a point, it is a sampleSamplesMost things in the real world are Most things in the real world are continuouscontinuousEverything in a computer is Everything in a computer is discretediscreteThe process of mapping a continuous function to a The process of mapping a continuous function to a discrete one is called discrete one is called samplingsamplingThe process of mapping a continuous variable to a The process of mapping a continuous variable to a discrete one is called discrete one is called quantizationquantizationRendering an image requires sampling and Rendering an image requires sampling and quantizationquantizationMost things in the real world are Most things in the real world are continuouscontinuousEverything in a computer is Everything in a computer is discretediscreteThe process of mapping a continuous function to a The process of mapping a continuous function to a discrete one is called discrete one is called samplingsamplingThe process of mapping a continuous variable to a The process of mapping a continuous variable to a discrete one is called discrete one is called quantizationquantizationRendering an image requires sampling and Rendering an image requires sampling and quantizationquantizationSamplesSamplesLine SegmentsWe tried to sample a line segment so it would map We tried to sample a line segment so it would map to a 2D raster displayto a 2D raster displayWe quantized the pixel values to 0 or 1We quantized the pixel values to 0 or 1We saw stair steps, or jaggiesWe saw stair steps, or jaggiesWe tried to sample a line segment so it would map We tried to sample a line segment so it would map to a 2D raster displayto a 2D raster displayWe quantized the pixel values to 0 or 1We quantized the pixel values to 0 or 1We saw stair steps, or jaggiesWe saw stair steps, or jaggiesLine SegmentsInstead, quantize to many shadesInstead, quantize to many shadesBut what sampling algorithm is used?But what sampling algorithm is used?Instead, quantize to many shadesInstead, quantize to many shadesBut what sampling algorithm is used?But what sampling algorithm is used?Area SamplingShade pixels according to the area covered by thickened Shade pixels according to the area covered by thickened linelineThis is This is unweightedunweighted area sampling area samplingA rough approximation formulated by dividing each pixel A rough approximation formulated by dividing each pixel into a finer grid of pixelsinto a finer
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