preserving sharp edges in geometry images
DESCRIPTION
Preserving Sharp Edges in Geometry Images. Mathieu Gauthier Pierre Poulin LIGUM, Dept . I.R.O. Université De Montréal Graphics INTERFACE 2009. Geometry Images. What are they ?. Simple mesh representation data structure - PowerPoint PPT PresentationTRANSCRIPT
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MATHIEU GAUTHIERPIERRE POULIN
LIGUM, DEPT. I .R .O.UNIVERSITÉ DE MONTRÉAL
GRAPHICS INTERFACE 2009
Preserving Sharp Edges in Geometry Images
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Geometry Images
Simple mesh representation data structure Encodes mesh geometry and connectivity in
an image-like array
What are they?
257 × 257 Geometry Image
Reconstruction
Vertices Positions4 Neighbours = 1 Quad
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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Geometry ImagesHow to create them?
Original Model Cut Sampling Geometry Image
ReconstructionSampling GridParameterization
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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Motivation
…And there in lies the problem: The regular grid used to sample the parameterization cannot capture sharp features
The problem
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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Motivation
Add constraints such that sharp features align with the sampling grid in the parameterization domain
It makes the process very difficult to converge
Non-linear, energy function is not smooth, infinity or no good solution
One solution
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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MotivationSimple example
Slightly perturbating the grid, such as done in dual contouring [JLSW02], might simply and more easily resolve some alignment problems
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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Grid Alignment to the Sharp FeaturesIdentifying sharp features
Input 3D Model Parameterization
Sharp Edge Sharp Corner
Chain of Sharp Edges = Sharp Segment
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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Grid Alignment to the Sharp FeaturesCorner & Edge Snapping - Part 1
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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Grid Alignment to the Sharp FeaturesCorner & Edge Snapping - Part 2
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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Grid Alignment to the Sharp FeaturesCorner & Edge Snapping - Part 3
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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Sampling
UVs coordinates are no longer implicitWe can no longer use 1 normal per vertex, we
need more, especially for lighting.
What about UVs and normals?
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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SamplingNormals
Because of the regular structure of the geometry image and the way we remesh, we will never need more than 8 normals around a vertex (one per octant)
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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SamplingNormals of Corners
To sample the normals around a sharp corner, we simply iterate in CCW order between sharp edges, compute the angle-weighted normal and assign it to all the associated octants
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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Sampling
For a sample snapped to a sharp edge, the procedure is very similar, only two normals will be computed and stored, in the respective octant
Normals of Sharp Edges
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SamplingBack to Our Example
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SamplingBack to Our Example
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Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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SamplingResult
1 Position Image (9x9) 8 Normal Images (9x9)
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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RemeshingAlgorithm
Remeshing from geometry images is very similar to the original method
A vertex is created for each image pixelFor each group of four pixels, two triangles
are created…But since we have up to 8 normals per
vertex, more vertices may need to be createdFaces must also be connected to the
appropriate vertices
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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Remeshing
1. For each image pixel, we create as many vertices as there are different normals (up to 8) and store them in an array[8]
2. When creating the faces, we use the following rule to select which vertex to connect.
Algorithm
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RemeshingExample
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ResultsSquare Torus (Original Model)
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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ResultsSquare Torus (Comparison)
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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ResultsSquare Torus (Position and Normal images)
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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ResultsFandisk (Original Model)
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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ResultsFandisk (Remeshings)
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
129×129 Geometry Images33×33 Geometry Images
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ResultsFandisk (129×129 Position and Normal images)
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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ResultsCSG (Orignal Model and 257×257 Remeshing)
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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Results257×257 Positon and Normal Geometry Images
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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Results
Start!
Video
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Conclusion
Simple and efficient techniqueDoes not over-constrain the parameterization
processCan be added to any geometry image
generation pipelineCan only encode a maximum of 8 normalsMust store these 8 normals and 1 uv
coordinates
Wrap up
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Future Work
Once the grid is snapped to sharp features, it may be possible to add an extra relaxation step to deform the parameterization and bring back the grid to a regular shape
Try something other than a greedy algorithm, maybe something like a quadric error metric could help find a better overall solution
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work
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Thank You!
Questions? Comments?
Geometry Images Motivation Grid Alignment Sampling Remeshing Results Video Conclusions & Future Work