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Multi-level Partition of Unity Implicits

Multi-level Partition of Unity Implicits. Alexander Belyaev. Marc Alexa. Greg Turk. Hans-Peter Seidel. Yutaka Ohtake. Adaptive Distance Function from Point-Cloud. f=0 approximates the given point-set. Visualized by Polygon mesh Ray-tracing Particles ….

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Multi-level Partition of Unity Implicits

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  1. Multi-level Partition of Unity Implicits Alexander Belyaev Marc Alexa GregTurk Hans-PeterSeidel Yutaka Ohtake

  2. Adaptive Distance Function from Point-Cloud f=0 approximatesthe given point-set • Visualized by • Polygon mesh • Ray-tracing • Particles • … Implicit (Solid) f(x,y,z)>0:inside f(x,y,z)<0:outside Point-cloud +Oriented normals

  3. Implicit Modeling to Point-Set Surfaces Blending Space transformation Boolean operations Morphing

  4. Zipper reconstruction[Turk 95] Our reconstruction Reconstruction from Range Scans Polygonization of f=0 Points form 10 range surfaces Filling holes Merging overlapped range surfaces

  5. Q(x)=0 (quadric) Weighted average of the local functions f(x)=0 Support of Q(x)(B-spline) Multi-level partition of unity (Octree based) Large error region is subdivided Multi-level Partition of Unity Partition of unity

  6. With decreasing error

  7. Original mesh(David head 1mm) Approximation by MPU with 10-4 accuracy Advantages of MPU 4M points10-4 error • Local and Adaptive • Much faster than RBF based methods • Very large point-sets (Millions of points) • No limit for out-of-core

  8. Corner function Local analysis of points and normals Edge function Piecewise quadric functions Standard quadric Sharp Features Ray-traced f=0

  9. 57 min. Fast RBF [Carr SIG01] 1/3 • Model • # points • error • RAM • # tri. • time • 433K • 8.0×10-4 • 306MB • - • 170 min. Dragon (Pentium3 550MHz) Timing and Demo Bunny Dragon David (Pentium4 1.6GHz)

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