Disjoint Convex Shell
Yun-hyeong Kim and Zhonghua Xi and Jyh-Ming Lien
Abstract
In this work, we study a geometric structure called disjoint convex shell or simply DC-shell. A DC-shell of a polyhedron is a set of pairwise interior disjoint convex objects that collectively approximate the given polyhedron.
- Preventing convex objects from overlapping enables faster and robust collision response and more realistic fracturing simulation.
- Without disjointness constraint, a physical realization of the approximation becomes impossible.
This paper investigates multiple approaches that construct DC-shells from shapes that are either composed of overlapping components or segmented into parts. We show theoretically that, even under this rather simplified setting, constructing DC-shell is difficult.
Left: input composed shape. Middle: overlapping convex hulls. Right: disjoint convex shell (DC-Shell)
To demonstrate the power of DC-shell, we studied how DC-shell can be used in mesh unfolding, an important computational method in manufacturing 3D shape from the 2D material. Approximating a given polyhedron model by DC-shells provides two major benefits.
- First, they are much easier to unfold using the existing unfolding methods.
- Second, they can be folded easily by both human folder or self-folding machines. Consequently, DC-shell makes paper craft creation and design more accessible to younger children and provides chances to enrich their education experiences.
Left: Folded convex components. Right: Assembled DC-Shell.
Publication
Disjoint Convex Shell and its Applications in Mesh Unfolding, Yun-Hyeong Kim and Zhonghua Xi and Jyh-Ming Lien, Symposium on Solid and Physical Modeling (SPM), also appears in Journal of Computer-Aided Design, Jun. 2017
Web Site / Paper(pdf) / BibTeX
Web Site / Paper(pdf) / BibTeX
- Supplementary materials of the SPM 2017 paper
Software and Dataset
- Our implementation can be found here: Go to Github repository
- Models and results will be available soon.
Video
This video shows a realistic fracturing simulation created via DC-shells and blender, and paper craft fabrications enabled by DC-shells.
Remeshing
Existing methods do not ensure convexity after remeshing, we proposed a method that guarantees convexity and volume bound via Laplacian smoothing.
From left to right: (a) original hull, (b) isotropic remesh of (a), (c) convex hulls of (b), (d) Our remesh
Paper Crafting
The DC shells can be folded easily by school kids and have been used in class to enrich their learning experiences.
Built by 9-12 year-old school students from South Korea.
3D Printing
As every component is now convex, DC-shell also makes 3D printing easier and faster.
From left to right: (a) original input, (b) 3D prints of DC-shells, (c) Assembled model
Related Works
Learning to Segment and Unfold Polyhedral Mesh from Failures, Zhonghua Xi and Yun-Hyeong Kim and Young J. Kim and Jyh-Ming Lien, Shape Modeling International (SMI); also appears in Journal of Computers & Graphics, Jun. 2016
Web Site / Paper(pdf) / BibTeX
Web Site / Paper(pdf) / BibTeX
Nearly Convex Segmentation of Polyhedra Through Convex Ridge Separation, Guilin Liu and Zhonghua Xi and Jyh-Ming Lien, Symposium on Solid & Physical Modeling (SPM); also appears in Journal of Computer-Aided Design, Jun. 2016
Web Site / Paper(pdf) / BibTeX
Web Site / Paper(pdf) / BibTeX
Continuous Unfolding of Polyhedra - a Motion Planning Approach, Zhonghua Xi and Jyh-Ming Lien, 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Sep. 2015
Web Site / Paper(pdf) / BibTeX
Web Site / Paper(pdf) / BibTeX