sa2014.siggraph.org sponsored by. sa2014.siggraph.org sponsored by approximate pyramidal shape...
TRANSCRIPT
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- SA2014.SIGGRAPH.ORG SPONSORED BY
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- SA2014.SIGGRAPH.ORG SPONSORED BY Approximate Pyramidal Shape Decomposition Ruizhen Hu Honghua Li Hao Zhang Daniel Cohen-Or Simon Fraser UniversityZhejiang UniversityTel Aviv University
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- SA2014.SIGGRAPH.ORG SPONSORED BY Pyramidal shape 3 Terrain 2.5D Heightfield
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- SA2014.SIGGRAPH.ORG SPONSORED BY Pyramidal shape 4
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- SA2014.SIGGRAPH.ORG SPONSORED BY Various applications 5
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- SA2014.SIGGRAPH.ORG SPONSORED BY Various applications 6 3D layered printing
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- SA2014.SIGGRAPH.ORG SPONSORED BY Various applications 7 3D layered printing Molding/casting
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- SA2014.SIGGRAPH.ORG SPONSORED BY Various applications 8 3D layered printing Molding/casting Point inside/outside testing
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- SA2014.SIGGRAPH.ORG SPONSORED BY Various applications 9 3D layered printing Molding/casting Point inside/outside testing
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- SA2014.SIGGRAPH.ORG SPONSORED BY However, 10 Many common objects are not pyramidal Pyramidal decomposition
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- SA2014.SIGGRAPH.ORG SPONSORED BY Pyramidal decomposition Exact pyramidal decomposition Minimum number of pyramidal parts 11 NP-hard NP-hard [Fekete and Mitchell 2001]
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- SA2014.SIGGRAPH.ORG SPONSORED BY Pyramidal decomposition Approximate pyramidal decomposition Parts being only approximately pyramidal Still aiming to produce as few parts as possible 12
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- SA2014.SIGGRAPH.ORG SPONSORED BY Key idea 13 Exact Cover Problem {1234}
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- SA2014.SIGGRAPH.ORG SPONSORED BY Key idea 14 {1234} Exact Cover Problem
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- SA2014.SIGGRAPH.ORG SPONSORED BY Key idea 15 {1234} 1 2 3 4 Over-segmentation Candidate parts by merging segments Exact Cover Problem
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- SA2014.SIGGRAPH.ORG SPONSORED BY Key idea 16 {1234} Pyramidal decomposition Pyramidal Final decomposition Over-segmentation Candidate parts by merging segments Exact Cover Problem
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- SA2014.SIGGRAPH.ORG SPONSORED BY Find an appropriate over-segmentation of the shape Build an appropriate set of candidate pyramidal parts Main challenge 17 Infinite possible pyramidal parts
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- SA2014.SIGGRAPH.ORG SPONSORED BY Intuition Large pyramidal parts Minimum-sized decompositions Easier to generate 18
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- SA2014.SIGGRAPH.ORG SPONSORED BY Intuition Large pyramidal parts May not be enough 19 1 2 34 5 6
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- SA2014.SIGGRAPH.ORG SPONSORED BY Intuition Large pyramidal parts May not be enough Combination of intersections 20 1 2 34 5 6
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- SA2014.SIGGRAPH.ORG SPONSORED BY Intuition Large pyramidal parts May not be enough Combination of intersections 21 1 2 34 5 6
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- SA2014.SIGGRAPH.ORG SPONSORED BY Intuition Large pyramidal parts May not be enough Combination of intersections 22 1 2 34 5 6
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- SA2014.SIGGRAPH.ORG SPONSORED BY Algorithm overview 23 Set Collection of subsets Exact cover Intersections
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- SA2014.SIGGRAPH.ORG SPONSORED BY Cell generation Base sampling Sample a set of directions Sample a set of bases along each direction 24
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- SA2014.SIGGRAPH.ORG SPONSORED BY Cell generation Base sampling Base selection Capacity measure 25 Total pyramidal areas Number of decomposed parts
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- SA2014.SIGGRAPH.ORG SPONSORED BY Cell generation Base sampling Base selection Capacity measure 26
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- SA2014.SIGGRAPH.ORG SPONSORED BY Cell generation Base sampling Base selection Capability measure Base voting 27
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- SA2014.SIGGRAPH.ORG SPONSORED BY Cell generation Base sampling Base selection Cell formation Points voted for the same set of bases 28 Estimation of intersections
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- SA2014.SIGGRAPH.ORG SPONSORED BY Block construction To further reduce the number of candidate parts Cluster cells into blocks Find the boundaries 29
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- SA2014.SIGGRAPH.ORG SPONSORED BY Candidate parts & decomposition Parts are formed by merging blocks Decomposition can be found by solving ECP 30 Blocks Decompositions Candidate parts
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- SA2014.SIGGRAPH.ORG SPONSORED BY Results Datasets 149 2D shapes 80 3D shapes 31
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- SA2014.SIGGRAPH.ORG SPONSORED BY Results 2D shapes 32
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- SA2014.SIGGRAPH.ORG SPONSORED BY Results 3D shapes 33
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- SA2014.SIGGRAPH.ORG SPONSORED BY Evaluations 2-pyramidality 25 2D shapes & 30 3D shapes 34
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- SA2014.SIGGRAPH.ORG SPONSORED BY Evaluations Comparison to greedy approach 2-pyramidality (2D shapes) 35 Ours: Greedy:
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- SA2014.SIGGRAPH.ORG SPONSORED BY Evaluations Comparison to human judgement 30 users & 20 2D shapes 36 OursUser decomposition
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- SA2014.SIGGRAPH.ORG SPONSORED BY 3D Printing 37
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- SA2014.SIGGRAPH.ORG SPONSORED BY Conclusion A relatively new and unexplored shape property. The first construction algorithm for approximate pyramidal decomposition. The key insight is to turn the problem into a exact cover problem. The bottom-up clustering-based approach is both general and versatile. 38
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- SA2014.SIGGRAPH.ORG SPONSORED BY Limitation & further work Realistic waste estimation for 3D printing Pyramidalization Minimal modification to maximally reduce the size of its pyramidal decomposition 39
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- SA2014.SIGGRAPH.ORG SPONSORED BY Set Collection of subsets Exact cover Intersections Thank you! Approximate Pyramidal Shape Decomposition Ruizhen Hu Honghua Li Hao Zhang Daniel Cohen-Or