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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 20031 Progressive Meshes (SIGGRAPH ’96) By Hugues Hoppe Presented by Yong Kil and Christopher Co
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 20032 Previous Work [Schroeder-etal92] (decimation) [Turk92] (re-tiling) [Hoppe-etal93] (mesh optimization) [Rossignac-Borrel93] (vertex clustering) [Cohen-etal96] (simplification envelopes)... MRA (later) 13,000 1,000200 ?
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 20033 Introduction What is Progressive Mesh? Arbitrary mesh M stored as coarser mesh M 0 together with a sequence of n detail records that indicate how to incrementally refine M 0 exactly back into the original mesh M = M n.150 M0M0M0M0 M1M1M1M1 vspl 0 152 M 175 500 … vspl i … 13,546 vspl n-1 MnMnMnMn progressive mesh (PM) representation vspl 0 … vspl i … vspl n-1 M0M0M0M0 MnMnMnMn
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 20034 Edge Collapse and Vertex Split ecol(v s,v t, v s ) vlvlvlvl vrvrvrvr vt vt vt vt vs vs vs vs vsvsvsvs vlvlvlvl vrvrvrvr ’ ’ vspl(s,l,r,t, A) A = ( {v s,v t }, {discrete values}, {scalar values} ) Discrete values: associated with faces. Discrete values: associated with faces. I.e. material identifier such as texture map. I.e. material identifier such as texture map. Scalar values: associated with corners (vertex, face). Scalar values: associated with corners (vertex, face). E.g color, normal, texture coordinate. E.g color, normal, texture coordinate.
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 20035 PM Construction 13,546500152 150 faces M0M0M0M0 M1M1M1M1 M 175 ecol 0 ecol i ecol n-1 MnMnMnMn ecol(v s,v t, v s ) vlvlvlvl vrvrvrvr vtvtvtvt vsvsvsvs vsvsvsvs vlvlvlvl vrvrvrvr ’ ’ vspl(v s,v l,v r, A)
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 20036 Mesh Simplification Which edge to collapse? Minimize the Energy Function: –E(M) = E dist (M) + E spring (M) + E scalar (M) + E disc (M) For each potential edge collapse, calculate ∆E and add to priority queue. Pop edge from queue (with lowest ∆E) and collapse. Update affected edges and every pop next edge. (b) Sampled points X = {x 1, x 2, …, x n } (a) Object to be sampled Sample Points X
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 20037 Distance Energy Surface of M
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 20038 Spring Energy
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 20039 Distance and Spring Where to collapse to have local minimum energy? Mesh Optimization (Hoppe ’93) creates non-linear equations and solves using iterative method. PM chooses 3 locations out of the infinite set: {0, 0.5, 1} vtvtvtvt vsvsvsvs vsvsvsvs ’ vsvsvsvs ? ’
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200310 Scalar Energy
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200311 Discontinuity Energy Sharp Edge (in yellow) 1.Boundary edge 2.Two adjacent faces have different discrete attributes 3.Adjacent corners have different scalar attributes. xixi
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200312 Using PM – LOD13,546500152 150 faces M0M0M0M0 M1M1M1M1 M 175 MnMnMnMn Each intermediate representation of the mesh can be considered a LOD
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200313 Using PM – Transmission and Compression Transmission –Transmit M 0, then transmit sequence of vsplit records Compression –Use connectivity coding and efficient use of bits –Use delta-encoding to reduce storage of scalar attributes –Coherence in mesh attributes can be exploited
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200314 Geomorph Alpha blend between different resolutions to avoid “snapping” Blending occurs between each pair of vertices related by edge collapses performed (ancestor map)
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200315 Selective Refinement M0M0M0M0 vspl 0 vspl 1 vspl i-1 vspl n-1
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200316 Selective Refinement Perform vspl( s i, l i, r i, A i ) if: (1) vertices {s i,l i,r i } exist (2) REFINE(s i ) is true REFINE(s i ) is defined per application Relax constraint (1’) vertex s i and A’(l i ) and A’(r i ) exist Perform vspl( s i, A’(l i ), A’(r i ), A i ) A’() is an ancestor map similar to that used by geomorphin
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200317 Previous Work - MRA Multiresolution Analysis (MRA) Analysis produces base mesh with wavelet coefficients (B) using filter A Synthesis produces mesh of desired resolution using a refining filter and a perturbing filter Figure courtesy of Lounsbery, et al. (`94)
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200318 PM vs. MRA Advantages of MRA –encodes geometry & color independently –supports multiresolution editing –guarantees maximum error bound Advantages of PM –lossless –can be more accurate –captures discrete attributes –captures discontinuities (creases)
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200319 Results – PM vs. MRA
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200320 Results – E scalar
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200321 Results – Radiosity Solution
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200322 Conclusion Contribution: PM data structure Advantages –Solves a variety of problems (LOD, Progressive Transmission, Selective Refinement, etc.) –Deals with various mesh attributes aside from geometry Disadvantages –Mesh parameterization can be non-intuitive –Energy function is complex
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200323 Sharing Mesh Attributes wedge vertex face corner
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200324 Vertex Correspondence MnMnMnMn M0M0M0M0 McMcMcMc MfMfMfMf v1v1v1v1 v2v2v2v2 v3v3v3v3 v4v4v4v4 v5v5v5v5 v6v6v6v6 v7v7v7v7 v8v8v8v8 v1v1v1v1 v2v2v2v2 v3v3v3v3 M f-1 v1v1v1v1 v2v2v2v2 v3v3v3v3 v4v4v4v4 v5v5v5v5 v6v6v6v6 v7v7v7v7 ecol M f-2 v1v1v1v1 v2v2v2v2 v3v3v3v3 v4v4v4v4 v5v5v5v5 v6v6v6v6 ecol ecol
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200325 Select refine b a a b
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200326 Misc MRA vs PM? Review of PM –Selective refinement as primary contribution. –What improvements have been made from this paper. i.e. who refers to this paper?
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200327 Figures
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200328 vertex corner face
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200329 {f 1 } : { v 1, v 2, v 3 } {f 2 } : { v 3, v 2, v 4 } … connectivity geometry {v 1 } : (x,y,z) {v 2 } : (x,y,z) … face attributes {f 1 } : “skin material” {f 2 } : “brown hair” …
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200330 {v 2,f 1 } : (n x,n y,n z ) (u,v) {v 2,f 2 } : (n x,n y,n z ) (u,v) … corner attrib. {f 1 } : { v 1, v 2, v 3 } {f 2 } : { v 3, v 2, v 4 } … connectivity geometry {v 1 } : (x,y,z) {v 2 } : (x,y,z) … face attributes {f 1 } : “skin material” {f 2 } : “brown hair” …
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200331 PM benefit PM VnVnVnVn MnMnMnMn M0M0M0M0 n progressive transmission n continuous-resolution n smooth LOD n geometry compression lossless n single resolution vspl FnFnFnFn attributes
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200332 ecol(v s,v t, v s ) vlvlvlvl vrvrvrvr vtvtvtvt vsvsvsvs vsvsvsvs vlvlvlvl vrvrvrvr ’ ’
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200333 Vertex Split vsvsvsvs vlvlvlvl vrvrvrvr vspl(v s,v l,v r, v s,v t,…) vlvlvlvl vrvrvrvr vtvtvtvt vsvsvsvs ’’ ’ ’ attributes
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visualization and graphics research group CIPIC Feb 18, 2003Multiresolution (ECS 289L) - Winter 200334 Reconstruction150 M0M0M0M0 M1M1M1M1 vspl 0 152 M 175 500 … vspl i … 13,546 vspl n-1 MnMnMnMn progressive mesh (PM) representation vspl 0 … vspl i … vspl n-1 M0M0M0M0 MnMnMnMn
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