Polygons with holes, with simply connected brown regions and interior boundaries, including degenerate cases of single vertices and edges, (a,b,f).
Circular
Pentagonal
An annulus can be approximated by two n-sided boundaries with the same center, but different radius.
In geometry, a polygon with holes is an area-connected planar polygon with one external boundary and one or more interior boundaries (holes).[1] Polygons with holes can be dissected into multiple polygons by adding new edges, so they are not frequently needed.
An ordinary polygon can be called simply-connected, while a polygon-with-holes is multiply-connected. An H-holed-polygon is H-connected.[2]
^Somerville, D. M. Y. (1929), "IX.4: Polyhedra with ring-shaped faces", An Introduction To The Geometry Of Dimensions, Methuen & Co., pp. 144–145
^O'Rourke, Joseph (1987), "Chapter 5: Holes" (PDF), Art Gallery Theorems and Algorithms, International Series of Monographs on Computer Science, vol. 3, Oxford University Press, pp. 125–145, ISBN 0-19-503965-3
and 27 Related for: Polygon with holes information
triangulate a simple polygon is based on the two ears theorem, as the fact that any simple polygonwith at least 4 vertices without holes has at least two...
is concerned only with simple and solid polygons, a polygon may refer only to a simple polygon or to a solid polygon. A polygonal chain may cross over...
convex polygons (n-gons), since this simplifies rendering, but may also be more generally composed of concave polygons, or even polygonswithholes. The...
using dynamic programming.: 166–167 If the raw polygon might have holes, even if they are degenerate holes (i.e., single points), the problem is NP-hard...
In geometry, a simple polygon is a polygon that does not intersect itself and has no holes. That is, it is a piecewise-linear Jordan curve consisting of...
ones if the obstacle is a simple polygon or if there are a fixed number of polygonalholes). Given a simple polygon P {\displaystyle {\mathcal {P}}} and...
For polygons which may contain holes, finding a minimum such covering is NP-hard. This sharp difference between hole-free and general polygons can be...
input polygon as it shrinks. The following algorithms consider an input that forms a polygon, a polygonwithholes, or a PSLG. For a polygonal input we...
restrict the types of polygons that can be used as subjects or clips. Even complex (self-intersecting) polygons, and polygonswithholes can be processed....
endpoints are concave corners. A rectilinear polygon that is also simple is also called hole-free because it has no holes - only a single continuous boundary....
this property does not characterize star-shaped polygons, as there also exist polygonswithholes in which the link diameter is two. Maheshwari, Anil;...
many more places. The two-dimensional meshing includes simple polygon, polygonwithholes, multiple domain and curved domain. In three dimensions there...
geometry, the point-in-polygon (PIP) problem asks whether a given point in the plane lies inside, outside, or on the boundary of a polygon. It is a special...
weakly simple polygon can arise in computer graphics and CAD as a computer representation of polygonal regions withholes: for each hole a "cut" is created...
graphics, polygonal modeling is an approach for modeling objects by representing or approximating their surfaces using polygon meshes. Polygonal modeling...
The Scale Axis Transform – a generalization of the medial axis Straight Skeleton for polygonwithholes – Straight Skeleton builder implemented in java....
nested. In other words, polygons may have holes. The clip operation output from GPC is a set of polygon contours or tristrips. Holes and external contours...
In mathematics, a fundamental polygon can be defined for every compact Riemann surface of genus greater than 0. It encodes not only the topology of the...
stone chips in the holes' upper fills supports this. That none of the other antiquarians who visited the site noticed any such holes implies that they...
typically shaped as regular polygons, withholes near each vertex and possibly at the center, as well. The number of holes in the tablets used is a limiting...
polygon can mean two different things: In geometry, a polygon in the unitary plane, which has two complex dimensions. In computer graphics, a polygon...
with the -1 (0xFFFFFFFF) separator, which is followed by one or more lists of indices that form bounding polygons (outer boundaries) and maybe holes (inner...
operate with primitives which are curves (segments of straight lines, circles and more complicated curves), as well as shapes (boxes, arbitrary polygons, circles)...
Wormhole Allows Information to Escape Black Holes". Quanta Magazine. 23 October 2017. Thorne, Kip S. (1994). Black Holes and Time Warps. W. W. Norton. ISBN 978-0-393-31276-8...
and ἕδρον (-hedron) 'base, seat') is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron...
polynomial time when the area to be guarded is a simple polygon. The problem is NP-hard for polygonswithholes, but may be approximated in polynomial time by...
Global Information
