Method for judging position relationship between point and arbitrary polygon by using included angle sum method combining cross multiplication method

Abstract

The invention discloses a method for judging the positional relationship between a point and an arbitrary polygon by using the angle sum method combined with the cross multiplication method, traversing the closed polygon vertices in order, and calculating the azimuth angle between the judging point and the vertices when the traversal is not over; by subtracting the previous vertices The azimuth angle (that is, the azimuth angle difference) to get the included angle value, and the included angle value takes the absolute value; the included angle will not be greater than 180°, and when it is greater than 180°, it will be processed: the included angle value is equal to 360° minus the value obtained in the previous step Angle value; cross product calculation is performed between the judgment point and the two vertex vectors that make up the angle. When the cross product is greater than zero, the direction of the included angle is positive; when it is not greater than zero, the direction of the included angle is negative; the sum of the included angles is added or subtracted according to the direction of the included angle, adding when it is positive and subtracting when it is negative; If the sum is 360°, the judgment point is inside the polygon; if it is not 360°, the judgment point is outside the polygon. The invention judges the direction of the included angle by adding the cross multiplication method, which ensures the judgment of the critical situation of the positional relationship between the judgment point and any polygon.

Description

technical field [0001] The invention relates to a method for judging the positional relationship between a point and an arbitrary polygon, in particular to a method for judging the positional relationship between a point and an arbitrary polygon by an angle sum method combined with a cross multiplication method, and belongs to the technical field of graphic processing. Background technique [0002] In GIS, the topological relationship between points and any polygonal area can be divided into three types: points outside the area, points on the boundary of the area, and points within the area. [0003] The relationship between the judgment point and the position of the polygon is currently mainly based on the cross product judgment method: a convex polygon, each side of which divides the entire 2D screen into left and right sides, and connects the first endpoint of each side with the main test Points to get a vector v, expand the two 2-dimensional vectors into 3-dimensional, a...

AI Technical Summary

Problems solved by technology

[0006] The principle of the cross product judgment method is simple and easy to program, but it is only suitable for convex polygons; the angle sum judgment method is also easy to program, and is suitable for any polygon, but it is not easy to solve the critical situation; the ray method is easy to combine and improve, but it is difficult Handle some critical cases, poor stability

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