Art gallery theorems and algorithms
Art gallery theorems and algorithms
Joint triangulations and triangulation maps
SCG '87 Proceedings of the third annual symposium on Computational geometry
A physically based approach to 2–D shape blending
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Shape transformation for polyhedral objects
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
On compatible triangulations of simple polygons
Computational Geometry: Theory and Applications
2-D shape blending: an intrinsic solution to the vertex path problem
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Shape Blending Using the Star-Skeleton Representation
IEEE Computer Graphics and Applications
As-rigid-as-possible shape interpolation
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Controllable morphing of compatible planar triangulations
ACM Transactions on Graphics (TOG)
Vertex correspondence between polygons in different applications
Machine Graphics & Vision International Journal
Technical Section: Point-in-polygon tests by convex decomposition
Computers and Graphics
Technical section: 2D point-in-polygon test by classifying edges into layers
Computers and Graphics
Tweening boundary curves of non-simple immersions of a disk
Proceedings of the Eighth Indian Conference on Computer Vision, Graphics and Image Processing
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We introduce the notion of compatible star decompositions of simple polygons. In general, given two polygons with a correspondence between their vertices, two polygonal decompositions of the two polygons are said to be compatible if there exists a one-to-one mapping between them such that the corresponding pieces are defined by corresponding vertices. For compatible star decompositions, we also require correspondence between star points of the star pieces. Compatible star decompositions have applications in computer animation and shape representation and analysis.We present two algorithms for constructing compatible star decompositions of two simple polygons. The first algorithm is optimal in the number of pieces in the decomposition, providing that such a decomposition exists without adding Steiner vertices. The second algorithm constructs compatible star decompositions with Steiner vertices, which are not minimal in the number of pieces but are asymptotically worst case optimal in this number and in the number of added Steiner vertices. We prove that some pairs of polygons require 驴(n2) pieces, and that the decompositions computed by the second algorithm possess no more than O(n2) pieces.In addition to the contributions regarding compatible star decompositions, the paper also corrects an error in the only previously published polynomial algorithm for constructing a minimal star decomposition of a simple polygon, an error which might lead to a nonminimal decomposition.