Mesh Simplification Plan Introduction Mesh Simplifications Current Techniques
![The Project (5) Ø Method 2: QEM ü p = [a b c d]](https://slidetodoc.com/presentation_image_h2/8b2a9e9ba719333aee017434d798509c/image-19.jpg "The Project (5) Ø Method 2: QEM ü p = [a b c d]")
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Mesh Simplification
Plan • • • Introduction Mesh Simplifications Current Techniques The Projet Results
Introduction Ø What’s a mesh? üVertices, edges, polygones üManifold (machine are able to make it) üNon-manifold Ø Meshes usage üScientific imaging, movies, games… Ø Common problems üStocking, rendering, data transferts…
Plan • • • Introduction Mesh Simplification Current Techniques The Project Results
Mesh Simplification Ø Idea üRemove « negligeable » elements Ø Caracteristics üFidelity to original morphology üTopology üRe-exploitation
Plan • • • Introduction Mesh Simplification Current Techniques The Project Results
Current Techniques Ø Decimation Ø Contraction Ø Clustering Ø Progressive Mesh Ø Statistics üWavelets, fractals, …
Decimation
Contraction
Clustering
Plan • • • Introduction Mesh Simplification Current Techniques The Project Results
The Project (1) Ø Studies on current techniques üSchroeder, Lorensen, Zarge üGarland, Heckbert Ø Implementation üC/C++ üOpen. GL üGLUT, GLUI
The Project (2) Ø Bounds üTriangulated meshes Ø Implemented triangulations methods üTriangle Fan üTriangle Strip Ø Optimal solution üDelaunay’s Triangulation
Triangulation : Triangle Fan
Triangulation : Triangle Strip
The Project (3) Ø Method 1: Edge Contraction üEdge Length • Distance criteria üPercentage • How many vertices to remove? üCardinality ordering • Stronger • Weaker • Goal : avoid « dumb » mesh browsing
Cardinalities, examples
The Project (4) Ø Method 2: QEM üQuadric Error Metric • One error value per vertex • Create valid vertices pairs • Compute the contraction cost üPercentage • How many vertices to remove?
The Project (5) Ø Method 2: QEM ü p = [a b c d] T , ax + by +cz +d = 0 ü Δ(v) = Σ p Є plans (v) (p. T v) ² ü 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) Ø Méthode 2: QEM (suite) ü Kp = pp. T = a² ab ac ad ab b² bc bd ac bc c² cd ad bd cd d² ü Q = Σ p Є plans (v) Kp
Plan • • • Introduction Mesh Simplification Current Techniques The Project Results
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Results « cow. obj » model (5804 faces) Method 1 « cow. obj » model (5804 faces) QEM Reduction Time(s) 10% 0. 390 10% 1. 081 50% 0. 810 50% 3. 044 80% 1. 051 80% 3. 825
Plan • • • Introduction Mesh Simplification The Current Techniques The Project Results
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