Class Assignment1 http://www.ticam.utexas.edu/~ckl/all/Comp_Geom/Proj1_Docs/klc/Assignment1.html
Extractions: A Unit cube is defined such that its centroid is located at the Origin of its local Co-Ordinate system and its faces align with the principal planes. An instance of the cube is to be scaled by 4 units in the X and Y directions. It is then translated 4 units in the Y direction and 3 units in the Z direction. Finally, the instance must be rotated 30 degrees about the Z-axis and 25 degrees about the Y-axis. Write a main program to determine the concatenated object transformation matrix that performs these transformations and prins the results. Perform the transformation and print out the original and transformed co-ordinates of each point.
Untitled F) INTERESTING LINKS TO MATHS SUBJECTS ( Sampling nodes ) General information about Maths Algebraic Curves in the Web Algebraic Surfaces in the Web Nice pictures from Bruce Hunt Some very cool pictures of surfaces! Fly through Barth's sextic !! http://www.ucy.ac.cy/~ddais/english/ms_en.htm
Extractions: Algebraic Curves in the Web Algebraic Curves (Geometry Center, Minnesota) Famous Curves Index (St. Andrews) The Cubic Surface Homepage (Mainz) Some pictures of algebraic curves (Minnesota) ... Projections of complex plane curves to real three-space Maple package for Algebraic Curves: examples and documentation Algebraic Surfaces in the Web Acme Klein Bottles Algebraic surfaces Nice pictures from Bruce Hunt Animated algebraic surfaces Some very cool pictures of surfaces! Barth's sextic Fly through Barth's sextic Benno Artmann's Topological Models Boy's Surface Build your own Boy's surface out of paper! Boy Surface Some interesting information and pictures. Duncan's Mathematical Models Some gifs of surfaces and whatnot. Cubic Surface Models of cubic surface made out of paper/wood by a fourth grade class in Italy Enriques surfaces Description, examples, and some amazing pictures.
Oracle's Query Model filter. Secondary Filter The secondary filter applies exact computaionalgeometry to the result set of the primary filter. These http://www.cast.uark.edu/local/uaclasses/advgis/oracle/spatial/query_model.html
Extractions: To query spatial data, each geometry must be represented in tiles. Tiles are fully tesselated regions defined in a total specified area. Each geometry is contained in one or more tiles, so the tiles can represent the approximate location of each geometry. Tiles are important for quick and accurate selection of geometries which are queried spatially or spatial joined because tiles contain a subset of all the geometries within the total area defined. Therefore, only a subset of the geometries have to be manipulated. Oracle uses a primary filter to find the tiles for all geometries used in a specific spatial query or join. These tiles are then used in a secondary filte r to find the exact result for the spatial query or spatial join. By using this two-tier query model Oracle can quickly extract relavant tiles (which contain the geometries) and then compute the complex spatial query or join only on the geometries contained in these tiles.
CFD (Computation Fluid Dynamics) This equation is generally unsteady and nonlinear. For a very simple geometryand boundary conditions, one can get a simple solution of this equation. http://www.seas.ucla.edu/~junwoo/ResearchDoc/cfd.html
Extractions: One of the fundamental equation in fluid mechanics is Navier-Stokes equation. This equation is generally unsteady and nonlinear. For a very simple geometry and boundary conditions, one can get a simple solution of this equation. However, its exact solution for the general situation is not solved yet (analytically). Moreover, some mathematicians and physicist claim that this equation has non-unique solutions. For the engineering purposes and as a supportive method, discretized Navier-Stokes equation has been solved with the help of modern computers. There are many advantages of using computers, of course. Since everything is done in the 'virtual' space, one can adjust parameters easily. Most of results are stored in digitized form, so that one can do post-processing according to the purpose. (statistics, animations, snapshots, slow-motions etc.) Moreover, one can easily simulate some virtual states to expand the knowledge of fluid motions, which could have been very hard to implement in the real experiments. Although, CFD cannot solve all the flow problems due to the limitation of computer resources. Nevertheless, CFD has provided priceless insights and practical information. Some people have shown some 'state-of-the-art' plots of fluid motions to expand our mind into the beauty of fluid-physics. Here are some examples :
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