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CGT511-08-3D Objects

CGT511-08-3D Objects - 3D object representation 3D object...

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CGT 511 3D objects d ř i h š h Bed ich Beneš, Ph.D. Purdue University Department of Computer Graphics Technology 3D object representation 3D bj t t ti Volume representation Boundary representation Procedural 3D object representation Voxels Oct tree Wire frame Surfaces Fractals Particle systems CSG Polygonal Free form Grammars Bézier surfaces NURBS © Bedrich Benes Implicit surfaces 3D object rendering points lines surfaces volume images © http://http.developer.nvidia.co m/GPUGems/elementLinks/fig 39 05 jpg 39-05.jpg © Bedrich Benes Representation and Rendering Can we display object represented as l i i t t ti ? voxels using point representation? points using volumetric techniques? B-rep as lines? B rep as lines? etc? © Bedrich Benes
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Volume representation Two main categories: voxels i f h 3D i di enumeration of the 3D space using coordinates CSG tree representation tree representation © Bedrich Benes Volume representation Advantages: An easy collision test Disadvantages: Displaying Memory requirement © Bedrich Benes Voxels Voxel is an acronym for volume element an object has its resolution given by an ordered triple e g 50x20x20 voxels an ordered triple e.g., 50x20x20 voxels typical data structure is a 3D array data[n][m][l] The voxel value depends on the application: density temperature pollution intensity density, temperature, pollution intensity Application areas medicine, meteorology, astronomy , geology, etc. © Bedrich Benes medicine, meteorology, astronomy , geology, etc. Voxels Example: How much memory is needed for object in the l i 200 200 200 l ? resolution 200x200x200 voxels? unsigned char is represented in 1 byte spa e 1 200 200 200 7 6 MB space = 1 x 200 x 200 x 200 = 7.6 MB © Bedrich Benes
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Voxels There are three problems with voxels: 1) data storage - data is too huge 2) data acquisition - we must measure data inside an object 3) data visualization - how can we display the data i id ? inside © Bedrich Benes Voxels Example: Wooden log scanned in 512x512x1024 loaded into the GPU and used to texture polygonal © Bedrich Benes quads Voxels Example: Weather data in Weather data in resolution 512x512x512 displayed using texture slicing © Bedrich Benes Voxels - Displaying Direct Volume Rendering (DVR) An object is displayed without a conversion Can focus on the surface, or h the inner structure Common way of displaying is using raycasting © Bedrich Benes
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Voxels - Displaying Raycasting A ray is sent from the viewpoint (camera) It t t th l d t th h it It penetrates the volume and traverses through it What value is used for displaying? © Bedrich Benes Voxels - Displaying Raycasting © Bedrich Benes (C) Petr Felkel Voxels - Displaying First hit (corresponds to the surface) © Bedrich Benes (C) Petr Felkel Voxels - Displaying Distance to the first hit © Bedrich Benes (C) Petr Felkel
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Voxels - Displaying Integrated value of the volume on the ray (sum) © Bedrich Benes (C) Petr Felkel Voxels - Displaying Maximum along the ray © Bedrich Benes (C) Petr Felkel Voxels - Displaying
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