Progressive Meshes A Talk by Wallner and Wurzer

Progressive Meshes A Talk by Wallner and Wurzer for the overfull Math. Meth auditorium

What it‘s all about. . . Wallner and Wurzer 2 Vienna University of Technology

Overview n n n Wallner and Wurzer Advantages PM‘s Definition and Basics Geo. Morphs Mesh Compression Selective Refinement Construction 3 Vienna University of Technology

Let‘s start off. . . Wallner and Wurzer 4 Vienna University of Technology

Advantages of PM‘s n n n Mesh Simplification LOD Approximation Progressive Transmission Mesh Compression Selective Refinement Wallner and Wurzer 5 Vienna University of Technology

Definition and Basics (1) n A corner is a (vertex, face) tuple n We are speaking of a sharp edge if u it is a boundary adge u the adjacent faces have different discrete values or u adjacent corners have different scalar values Wallner and Wurzer 6 Vienna University of Technology

Definition and Basics (2) n Traditional Mesh K V n Progressive Mesh M 0 Wallner and Wurzer (M 0, {Vsplit 0… Vsplitn-1}) 7 Vienna University of Technology

Definition and Basics (3) vsplit vt vr vl vl v’s vr vs ecol lossless ! Wallner and Wurzer 8 Vienna University of Technology

Definitions and Basics (4) ^ M. . . Full-Detailed Mesh (all vertices) M 0. . . Minimal Detailed Version 13, 546 500 ^ Mn M= ecoln-1 Wallner and Wurzer 152 M 175 ecoli 9 150 M 1 ecol 0 M 0 Vienna University of Technology

Geomorph n Smooth visual transition between two meshes Mf, Mc Mf v 1 v 2 v 3 v 4 v 5 v 6 v 7 v 8 Wallner and Wurzer Mc v 1 v 2 v 3 Mf « c V V F PM with geomorph 10 Vienna University of Technology

Geomorph (2) Wallner and Wurzer 11 Vienna University of Technology

Mesh Compression vspl(vs , vl , vr , vs’ , vt’ , …) vl vs vr Wallner and Wurzer vt’ vl vr vs’ 12 Record deltas: l v’ - v t s l v’ - v s s l … Vienna University of Technology

Selective Refinement M 0 Wallner and Wurzer vspl 0 13 vspl 1 vspli-1 vspln-1 Vienna University of Technology

Selective Refinement (2) n Rules for the vertex splits: u All involved vertices are present u do. Refine(v) == TRUE neighbours should be further refined u vertex is absent a previous vertex split was not executed, based on the two upper rules Wallner and Wurzer 14 Vienna University of Technology

Selective Refinement (3) View Frustum Split not performed. . . because this split was not performed. . . which makes this vertex „not present“ Wallner and Wurzer 15 Vienna University of Technology

Selective Refinement (4) View Frustum if this would be present Wallner and Wurzer 16 Vienna University of Technology

Construction Task: Construct Mn-1, Mn-2, . . . M 0 Naive Algorithm: { select random edge to collapse until resolution M 0 faces } Wallner and Wurzer 17 Vienna University of Technology

Construction (2) n Problems of naive algorithm: 1. 2. 3. Geometry is not preserved Color, Normals etc. are not preserved Discontinuities are not preserved Wallner and Wurzer 18 Vienna University of Technology

Construction (3) n Better algorithm: n n (Re-)Sample object Simplify Object Use energy function to measure accuracy Extend to preserve. . . n n n Wallner and Wurzer surface geometry color and normals discontinuities 19 Vienna University of Technology

Energy Function E(V)= Edist(V) + Espring(V) + Escalar(V)+Edisc(V) E negative perform split (= less energy used for simplified mesh) Wallner and Wurzer 20 further explanations Vienna University of Technology

With better algorithm. . . Wallner and Wurzer 21 Vienna University of Technology

Summary n PM have many advantages: u lossless u captures discrete attributes u captures discontinuities n n continuous-resolution smooth LOD space-efficient progressive Wallner and Wurzer 22 Vienna University of Technology

Links (1) n Progressive Meshes [ Hoppe ] http: //research. microsoft. com/~hoppe/ (all images in this talk except those explicitly labeled courtesy of H. Hoppe) Wallner and Wurzer 23 Vienna University of Technology

Links (2) n quadric error metric scheme [ Garland Heckbert ] http: //graphics. uiuc. edu/~garland/papers. html n memoryless scheme [ Lindstrom and Turk ] http: //www. cs. gatech. edu/gvu/people/Phd/Peter. Lindstrom. html Wallner and Wurzer 24 Vienna University of Technology

Thank you for your attention ! Progressive Meshes Wallner and Wurzer

Discussion Note n Problem of this approach: pictures courtesy of Markus Gross Wallner and Wurzer 26 Vienna University of Technology

Discussion Note picture courtesy of Markus Gross n Better Approach: Wallner and Wurzer 27 Vienna University of Technology