How to determine a point within the polygon

Thesis need to use a point

Self-reference　

https://solos.im/2015/3/27/%E6%80%8E%E6%A0%B7%E5%88%A4%E6%96%AD%E4%B8%80%E4%B8%AA%E7%82%B9%E5%9C%A8%E5%A4%9A%E8%BE%B9%E5%BD%A2%E5%86%85/

 

origin

Recently dizzy, suddenly want to study how the next judge after a coordinate point is within a polygon, this issue is resolved we can calculate the administrative division according to this point where the coordinates of a point.

algorithm

From the Internet to find a bit and found a very clever algorithm, the algorithm is as follows:

• The entire surface is divided into two portions (x> 0 && y == 0 || y> 0 section and x <0 && y == 0 || y <0 portion)
• Sequential scanning polygons each vertex when a vertex and the preceding vertex in the different parts, determine what the previous point to the origin point with respect to the direction of clockwise or counterclockwise (as determined by the cross-product), if it is clockwise r ++, or r - (r initially 0)
• If the result of r == 2 || r == - 2, the interior of the polygon is at the origin, otherwise not.

python achieve

def is_point_in(x, y, points):
    count = 0
    x1, y1 = points[0]
    x1_part = (y1 > y) or ((x1 - x > 0) and (y1 == y)) # x1在哪一部分中
    x2, y2 = '', ''  # points[1]
    points.append((x1, y1))
    for point in points[1:]:
        x2, y2 = point
        x2_part = (y2 > y) or ((x2 > x) and (y2 == y)) # x2在哪一部分中
        if x2_part == x1_part:
            x1, y1 = x2, y2
            continue
        mul = (x1 - x)*(y2 - y) - (x2 - x)*(y1 - y)
        if mul > 0:  # 叉积大于0 逆时针
            count += 1
        elif mul < 0:
            count -= 1
        x1, y1 = x2, y2
        x1_part = x2_part
    if count == 2 or count == -2:
        return True
    else:
        return False


if __name__ == '__main__':
    points = [[117.1510864068032,40.0705150448258],[117.2866776871509,40.10934259697606], ... ]
    y = 39.99
    x = 116.468006
    for i in xrange(10000):
        is_point_in(x + i * 0.01, y + i * 0.01, points)

operation hours

time python point.py

real    0m8.746s
user    0m8.680s
sys 0m0.034s

Performed 10,000 times, takes 8.746 seconds, too slow a wood there, try to go into

 

package main

import (
    //"fmt"
)


func is_point_in(x float64, y float64, points [][]float64) bool {
    count := 0
    x1, y1 := points[0][0], points[0][1]
    x1_part := (y1 > y) || ((x1 - x > 0) && (y1 == y))
    var a = []float64{x1, y1}
    p := append(points, a)
    for i := range p {
        if (i == 0) {
            continue
        }
        point := p[i]
        x2, y2 := point[0], point[1]
        x2_part := (y2 > y) || ((x2 > x) && (y2 == y))
        if (x2_part == x1_part){
            x1, y1 = x2, y2
            continue
        }
        mul := (x1 - x)*(y2 - y) - (x2 - x)*(y1 - y)
        if mul > 0 {
            count += 1
        } else {
            if( mul < 0) {
                count -= 1
            }
        }
        x1, y1 = x2, y2
        x1_part = x2_part
    }

    if (count == 2 || count == -2){
        return true
    } else {
        return false
    }
}

func main() {
    points := [][]float64{{117.1510864068032,40.0705150448258},{117.2866776871509,40.10934259697606}, ... ,}
    y := 39.99
    x := 116.468006
    for i:=1; i < 10000; i++ {
        _ = is_point_in(x + float64(i)*0.01, y + float64(i) * 0.01, points)
    }
}

execution time:

go build point.go
time ./point

real    0m0.038s
user    0m0.035s
sys 0m0.005s