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Vector overlay is an operation (or class of operations) in a geographic information system (GIS) for integrating two or more vector spatial data sets. Terms such as polygon overlay, map overlay, and topological overlay are often used synonymously, although they are not identical in the range of operations they include.
The + and invariants keep track of how curves change under these transformations and deformations. The + invariant increases by 2 when a direct self-tangency move creates new self-intersection points (and decreases by 2 when such points are eliminated), while decreases by 2 when an inverse self-tangency move creates new intersections (and increases by 2 when they are eliminated).
A key example of self-intersection numbers is the exceptional curve of a blow-up, which is a central operation in birational geometry. Given an algebraic surface S, blowing up at a point creates a curve C. This curve C is recognisable by its genus, which is 0, and its self-intersection number, which is −1. (This is not obvious.)
A Noetherian local ring is called a complete intersection ring if its embedding dimension is the sum of the dimension and the first deviation: emb dim(R) = dim(R) + ε 1 (R). There is also a recursive characterization of local complete intersection rings that can be used as a definition, as follows. Suppose that R is a complete Noetherian local ...
(Here the qualification "simple" means that the geodesic closes on itself without an intervening self-intersection.) This follows from the equations for the geodesics given in the previous section. All other geodesics are typified by Figs. 8 and 9 which show a geodesic starting on the equator with α 0 = 45° .
Cause, Prevention, Repair [ edit ] Sliver polygons are typically created when polygons are automatically generated from lines that should be coincident (e.g., an international boundary following a river de jure , or two adjacent counties) but are not, due to the natural discrepancies that arise from manual or automated digitization .
These are commonly specified according to some form of the 9-Intersection Model, [4] which is incorporated into the international Simple Feature Access specification (ISO 19125-2). [ 5 ] A Metric relation is a quantitative (measurable) relationship between two shapes in a coordinate space, most commonly a distance or direction.
GPC can compute the following clip operations: difference, intersection, exclusive-or and union. Polygons may comprise multiple disjoint contours. Contour vertices may be specified as clockwise or anticlockwise. Contours may be convex, concave or self-intersecting. Contours may be nested. In other words, polygons may have holes.