mesh simplification
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
Mesh Simplification
Plan
• Introduction
• Mesh Simplifications
• Current Techniques
• The Projet
• Results
Introduction
What’s a mesh?Vertices, edges, polygonesManifold (machine are able to make it)Non-manifold
Meshes usageScientific imaging, movies, games…
Common problemsStocking, rendering, data transferts…
Plan
• Introduction
• Mesh Simplification
• Current Techniques
• The Project
• Results
Mesh Simplification
IdeaRemove « negligeable » elements
CaracteristicsFidelity to original morphologyTopologyRe-exploitation
Plan
• Introduction
• Mesh Simplification
• Current Techniques
• The Project
• Results
Current Techniques
DecimationContractionClusteringProgressive MeshStatistics
Wavelets, fractals,…
Decimation
Contraction
Clustering
Plan
• Introduction
• Mesh Simplification
• Current Techniques
• The Project
• Results
The Project (1)
Studies on current techniquesSchroeder, Lorensen, ZargeGarland, Heckbert
ImplementationC/C++OpenGLGLUT, GLUI
The Project (2)
BoundsTriangulated meshes
Implemented triangulations methodsTriangle FanTriangle Strip
Optimal solutionDelaunay’s Triangulation
Triangulation : Triangle Fan
Triangulation : Triangle Strip
The Project (3)
Method 1: Edge ContractionEdge 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: QEMQuadric 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) (pT v) ² Δ(v) = Σ p Є plans (v) (vT p) (pT v)
= Σ p Є plans (v) vT (ppT) v
= vT [ Σ p Є plans (v) Kp] v
The Project (6)
Méthode 2: QEM (suite)
a² ab ac ad Kp = ppT = 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
Results
Results
Results
Results
Results
Results
Results
Results
Results
Results
Results
Results
Results
Results
Results
Results
Reduction Time(s)
10% 0.390
50% 0.810
80% 1.051
« cow.obj » model(5804 faces) Method 1
Reduction Time(s)
10% 1.081
50% 3.044
80% 3.825
« cow.obj » model(5804 faces) QEM
Plan
• Introduction
• Mesh Simplification
• Current Techniques
• The Project
• Results
The
EOF ;)