Mesh Simplification

Plan Introduction Mesh Simplifications Current Techniques The Projet Results

Introduction  What’s a mesh? Vertices, edges, polygones Manifold (machine are able to make it) Non-manifold  Meshes usage Scientific imaging, movies, games…  Common problems Stocking, rendering, data transferts…

Plan Introduction Mesh Simplification Current Techniques The Project Results

Mesh Simplification  Idea Remove « negligeable » elements  Caracteristics Fidelity to original morphology Topology Re-exploitation

Plan Introduction Mesh Simplification Current Techniques The Project Results

Current Techniques  Decimation  Contraction  Clustering  Progressive Mesh  Statistics Wavelets, fractals,…

Decimation

Contraction

Clustering

Plan Introduction Mesh Simplification Current Techniques The Project Results

The Project (1)  Studies on current techniques Schroeder, Lorensen, Zarge Garland, Heckbert  Implementation C/C++ OpenGL GLUT, GLUI

The Project (2)  Bounds Triangulated meshes  Implemented triangulations methods Triangle Fan Triangle Strip  Optimal solution Delaunay’s Triangulation

Triangulation : Triangle Fan

Triangulation : Triangle Strip

The Project (3)  Method 1: Edge Contraction Edge Length Distance criteria Percentage How many vertices to remove? Cardinality ordering Stronger Weaker Goal : avoid « dumb » mesh browsing

Cardinalities, examples

The Project (4)  Method 2: QEM Quadric Error Metric One error value per vertex Create valid vertices pairs Compute the contraction cost Percentage How many vertices to remove?

The Project (5)  Method 2: QEM p = [a b c d] T, ax + by +cz +d = 0 Δ(v) = Σ p Є plans (v) (p T v) ² Δ(v) = Σ p Є plans (v) (v T p) (p T v) = Σ p Є plans (v) v T (pp T ) v = v T [ Σ p Є plans (v) Kp] v

The Project (6)  Méthode 2: QEM (suite) a² ab ac ad Kp = pp T = ab b² bc bd ac bc c² cd ad bd cd d² Q = Σ p Є plans (v) Kp

Plan Introduction Mesh Simplification Current Techniques The Project Results

ReductionTime(s) 10% % %1.051 « cow.obj » model (5804 faces) Method 1 ReductionTime(s) 10% % %3.825 « cow.obj » model (5804 faces) QEM

Plan Introduction Mesh Simplification Current Techniques The Project Results The

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