Add to ORKGWe extend the notion of a source unfolding of a convex polyhedron P to be based on a closed polygonal curve Q in a particular class rather than based on a point. The class requires that Q “lives on a cone ” to both sides; it includes simple, closed quasigeodesics. Cutting a particular subset of the cut locus of Q (in P) leads to a non-overlapping unfolding of the polyhedron. This gives a new general method to unfold the surface of any convex polyhedron to a simple, planar polygon.
A well-known problem in geometry, which may be traced back to the Renaissance artist Albrecht Durer,...
When studying a 3D convex polyhedron, it is often easier to cut it open and flatten in on the plane. ...
When studying a 3D convex polyhedron, it is often easier to cut it open and flatten in on the plane. ...
Abstract. We extend the notion of a source unfolding of a convex polyhedron P to be based on a close...
We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point....
We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point....
We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point....
We show that cutting shortest paths from every vertex of a convex polyhedron to a simple closed quas...
We extend the notion of a star unfolding to be based on a simple quasigeodesic loop Q rather than on...
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, includ...
We establish that certain classes of simple, closed, polygonal curves on the surface of a convex pol...
An unfolding of a polyhedron is a cutting along its surface such that the surface remains connected ...
We present two algorithms for unfolding the surface of any polyhedron, all of whose faces are triang...
There are two known ways to unfold a convex polyhedron without overlap: the star unfolding and the s...
It is a common conjecture that all convex polyhedra must be edge-unfoldable but to date a valid proo...
A well-known problem in geometry, which may be traced back to the Renaissance artist Albrecht Durer,...
When studying a 3D convex polyhedron, it is often easier to cut it open and flatten in on the plane. ...
When studying a 3D convex polyhedron, it is often easier to cut it open and flatten in on the plane. ...
Abstract. We extend the notion of a source unfolding of a convex polyhedron P to be based on a close...
We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point....
We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point....
We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point....
We show that cutting shortest paths from every vertex of a convex polyhedron to a simple closed quas...
We extend the notion of a star unfolding to be based on a simple quasigeodesic loop Q rather than on...
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, includ...
We establish that certain classes of simple, closed, polygonal curves on the surface of a convex pol...
An unfolding of a polyhedron is a cutting along its surface such that the surface remains connected ...
We present two algorithms for unfolding the surface of any polyhedron, all of whose faces are triang...
There are two known ways to unfold a convex polyhedron without overlap: the star unfolding and the s...
It is a common conjecture that all convex polyhedra must be edge-unfoldable but to date a valid proo...
A well-known problem in geometry, which may be traced back to the Renaissance artist Albrecht Durer,...
When studying a 3D convex polyhedron, it is often easier to cut it open and flatten in on the plane. ...
When studying a 3D convex polyhedron, it is often easier to cut it open and flatten in on the plane. ...