Tilings and patterns
Least-Squares Fitting of Two 3-D Point Sets
IEEE Transactions on Pattern Analysis and Machine Intelligence
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Mesh editing with poisson-based gradient field manipulation
ACM SIGGRAPH 2004 Papers
Geometric modeling with conical meshes and developable surfaces
ACM SIGGRAPH 2006 Papers
The Visual Computer: International Journal of Computer Graphics
Constrained planar remeshing for architecture
GI '07 Proceedings of Graphics Interface 2007
Geometry of multi-layer freeform structures for architecture
ACM SIGGRAPH 2007 papers
k-means++: the advantages of careful seeding
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Freeform surfaces from single curved panels
ACM SIGGRAPH 2008 papers
3D mosaics with variable-sized tiles
The Visual Computer: International Journal of Computer Graphics
Example-based hair geometry synthesis
ACM SIGGRAPH 2009 papers
Packing circles and spheres on surfaces
ACM SIGGRAPH Asia 2009 papers
ACM SIGGRAPH 2010 papers
Paneling architectural freeform surfaces
ACM SIGGRAPH 2010 papers
ACM SIGGRAPH 2010 papers
Paneling architectural freeform surfaces
ACM SIGGRAPH 2010 papers
ACM SIGGRAPH 2011 papers
SMI 2011: Full Paper: Cyclic twill-woven objects
Computers and Graphics
Darboux cyclides and webs from circles
Computer Aided Geometric Design
Beady: interactive beadwork design and construction
SIGGRAPH Asia 2011 Sketches
Beady: interactive beadwork design and construction
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Guided exploration of physically valid shapes for furniture design
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
crdbrd: Shape Fabrication by Sliding Planar Slices
Computer Graphics Forum
Rationalization of Triangle-Based Point-Folding Structures
Computer Graphics Forum
Reciprocal frame structures made easy
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Designing unreinforced masonry models
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
ACM Transactions on Graphics (TOG)
Hi-index | 0.00 |
We propose a technique that takes a triangulated surface as input and outputs a surface with the same topology but altered geometry such that each polygon falls into a set of discrete equivalence classes. We begin by describing an error function that measures how close the polygons are to satisfying this criteria. To optimize this error function, we first cluster triangles into discrete sets such that the assignment of sets minimizes our error. We then find canonical polygons for each set using nonlinear optimization. Next, we solve a Poisson equation to find positions of vertices such that the surface polygons match the canonical polygons as close as possible. We also describe how to incorporate a fairness criteria into the optimization to avoid oscillations of the surface. We iterate this entire process until we reach a user specified tolerance, possibly adding clusters during iteration to guarantee convergence. We have been able to successfully reduce the number of unique triangles to lie within a small percentage of the total number of triangles in the surface and demonstrate our technique on various examples.