UTK CS 594  Advanced IsoSurfacing Algorithms (57 pages)
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Advanced IsoSurfacing Algorithms
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 Cs 594  Computer Systems Fundamentals
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Advanced Iso Surfacing Algorithms Jian Huang CS594 Spring 2002 This set of slides are developed and used by Prof Han Wei Shen at Ohio State University Iso contour surface Extractions 2D Iso contour 3D Iso surface Iso contour 0 Remember bi linear interpolation p2 p3 P p4 p0 p5 p1 To know the value of P we can first compute p4 and P5 and then linearly interpolate P Iso contour 1 Consider a simple case one cell data set The problem of extracting an iso contour is an inverse of value interpolation That is p2 p3 Given f p0 v0 f p1 v1 f p2 v2 f p3 v3 Find the point s P within the cell that have values F p C p0 p1 Iso contour 2 We can solve the problem based on linear interpolation p2 p3 1 Identify edges that contain points P that have value f P C 2 Calculate the positions of P p0 p1 3 Connect the points with lines Iso contouring Step 1 1 Identify edges that contain points P that have value f P C If v1 C v2 then the edge contains such a point v1 v2 Iso contouring Step 2 2 Calculate the position of P p1 P p2 v1 C v2 Use linear interpolation P P1 C v1 v2 v1 P2 P1 Iso contouring Step 3 p2 p0 p3 p1 Connect the points with line s Based on the principle of linear variation all the points on the line have values equal C Inside or Outside Just a naming convention 1 If a value is smaller than the iso value we call it Inside 2 If a value is greater than the iso value we call it Outside p2 p3 p0 p1 outside cell p2 p3 p0 p1 inside cell Iso surface Extraction Extend the same divide and conquer algorithm to three dimension 3D cells Look at one cell at a time Let s only focus on voxel Divide and Conquer 2 triangles How many cases Now we have 8 vertices So it is 2 8 256 How many unique topological cases Case Reduction 1 Value Symmetry Case Reduction 2 Rotation Symmetry By inspection we can reduce 256 14 Iso surface Cases Total number of cases 14 3 Marching Cubes Algorithm A Divide and Conquer Algorithm v8 v4 v6 Each cell has an index mapped to a value ranged 0 255 v3 v5 v1 v7 Vi is 1 or 0
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