Original Model

Convex Hull

Original Model

Reconstructed Surface

Snaking  Spiking 
• Uses bounding planes for quick and efficient culling • Like sweeping a polygon along its normal to create a prism • Points within prism use distance to plane • Points outside prism are given infinite distance 

• Using orthogonal bounding planes can cause spiking • Caused when point lies near concave edge • Attempted to fix by using averaged split plane when concave edge detected • Didn't fix all conditions (point directly above edge) • Worsened problems with 'snaking' 

• An attempt to eliminate all spiking • Rotated bounding slabs 45 degrees away from the normal • Results too chaotic to properly examine • Extreme problems with snaking and sliding 

• Much smarter attempt to eliminate spiking • Calculate clipped distances to polygon, edges, and vertices, and take minimum • Polygon slabs are built orthogonal to face normal • Edges are clipped by testing against two of three bounding slabs • Still experienced moderate amounts of snaking and sliding 
• An attempt to prioritize larger triangles for refinement • Attempt to decimate convex hull by forcing even refinement • Preserved convex hull lines quite nicely • Still experiencing problems with snaking and sliding 
• Holds true to our heuristic of shortest possible edges • Nicely decimated features created by convex hull • Alpha variable allowed us to test various edge length biases • We found that alpha = 1/4 provides nice results • Still experienced moderate amounts of snaking and sliding 
• Our most stable metric • Causes distance metric to smoothly fall off as candidate approaches coplanar • Candidates that are actually coplanar are given infinite distance • Candidates which lie within prism region are unaffected • Utilizes same large edge bias as previously • Fixes many problems with snaking and sliding • Still experiences problems with inverted reconstruction • Performs poorly on large coplanar regions (cube) 
• Designed to improve results on mostly coplanar input data • Divides by dot product between normal and (candidate  centroid) • Causes distance to approach infinity as point approaches coplanar • Biases candidates closer to the centroid higher then edges • Greatly improves cube example, but in general performs worse 
Original  Reconstructed 
[1] M. Kass, A. Witkin, and D. Terzopoulos, "Active contour models," International Journal of Computer Vision 1(4), pp. 321331, 1987 [2] W. Schroeder, J. Zarge, and W. Lorensen. Decimation of Triangle Meshes. Computer Graphics, Volume 25, No. 3, (Proc. SIGGRAPH `92), July, 1992 [3] F. Bernardini, C. Bajaj, J. Chen, D. Shikore, "A TriangulationBased Object Reconstruction Method," In 6th Annual Video Review of Computational Geometry, 13th ACM Symposium on Computational Geometry, pp. 14, 1997 [4] Rick Parent, Computer Animation: Algorithms and Techniques, Morgan Kaufmann Publishers, pp. 437447. 2002 [5] Andrea Bottino, Wim Nuij and Kees van Overveld, How to Shrinkwrap through a Critical Point: an Algorithm for the Adaptive Triangulation of IsoSurfaces with Arbitrary Topology, 1996 [6] Leif P. Kobbelt, Jens Vorsatz, Ulf Labsik and HansPeter Seidel, A Shrink Wrapping Approach to Remeshing Polygonal Surfaces, 1999 