10_isosurfacing_4

10_isosurfacing_4 -...

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CS 53000 Introduction to Scientifc Visualization IsosurFacing September 29, 2009 CS 53000 - IsosurFacing - 09/29/2009 http://www.lib.berkeley.edu/EART/digital/topo.html Mount Kilimanjaro, Tanzania CS 53000 - IsosurFacing - 09/29/2009 Other examples CS 53000 - IsosurFacing - 09/29/2009 More examples
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CS 53000 - Isosurfacing - 09/29/2009 Colored Isosurfaces David Weinstein CS 53000 - Isosurfacing - 09/29/2009 Slices still have their place Colormapped slices CS 53000 - Isosurfacing - 09/29/2009 Properties of Isocontours Preimage of scalar value Concept generalizes to any dimension Manifolds of codimension 1 Closed (except at boundaries) Nested–different values don’t cross Can consider the zero-set case (generalizes) F(x, y) = k <–> F(x, y) - k = 0 Normals given by gradient vector of F CS 53000 - Isosurfacing - 09/29/2009 Where are the data values? Two solutions: Interpolate to get the “right” answer Subsampling or raycasting Dividing Cubes Approximate to get a “good” answer Geometric primitives Go cell by cell Data value f de±ned on grid points only f(x,y,z) S v But we want a continuous, closed surface
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CS 53000 - Isosurfacing - 09/29/2009 Contours in 2D Assign gometric primitives to “cells” consisting of 2x2 grid points CS 53000 - Isosurfacing - 09/29/2009 Contours in 2D Assign gometric primitives to “cells” consisting of 2x2 grid points Line segments CS 53000 - Isosurfacing - 09/29/2009 Contours in 2D Assign gometric primitives to “cells” consisting of 2x2 grid points Line segments How do we know how to organize the primitives? CS 53000 - Isosurfacing - 09/29/2009 Contours in 2D Assign gometric primitives to “cells” consisting of 2x2 grid points Line segments How do we know how to organize the primitives? Signs of the values of corners of cells
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Contours in 2D Assign gometric primitives to “cells” consisting of 2x2 grid points Line segments How do we know how to organize the primitives? Signs of the values of corners of cells How do we know the position of the primitives? CS 53000 - Isosurfacing - 09/29/2009 Contours in 2D Assign gometric primitives to “cells” consisting of 2x2 grid points Line segments How do we know how to organize the primitives? Signs of the values of corners of cells How do we know the position of the primitives? Interpolate along grid edges CS 53000 - Isosurfacing - 09/29/2009 Contours in 2D Idea: primitives must cross every grid line connecting two grid points of opposite sign + - x x Get cell Indentify grid lines w/cross Interpolate along grid lines Find crossings Primitives naturally chain together CS 53000 - Isosurfacing - 09/29/2009 Questions How many grid lines with crossings can there be? What are the different conFgurations
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