golang computational geometry

In recent years, computational geometry has received more and more attention in the field of computer science, and the Go language (Golang) has also received widespread attention from developers due to its efficient running speed and simple and easy-to-learn syntax. There are many excellent libraries in Golang that can implement computational geometry functions, such as Go-geo, Gonum, etc. The emergence of these libraries has greatly reduced the workload of programmers and made computational geometry an easier field to implement.

Go-geo is one of the commonly used computational geometry libraries in Golang. It provides many common computational geometry algorithms and data structures, including: convex hull of plane point set, triangulation, half-plane intersection, The nearest point pair, the positional relationship between points and polygons, etc. Below we will introduce the geometric calculation function in Go-geo in detail.

1. Convex hull of a plane point set

The convex hull of a plane point set is the smallest convex polygon on the plane that surrounds a set of points inside. Go-geo provides the most common algorithm implementations: Graham Scan algorithm and fast convex hull algorithm. The Graham Scan algorithm is based on polar angle sorting, and the time complexity is O(nlogn); while the fast convex hull algorithm is based on the divide and conquer idea, and the time complexity is O(nlogh), where h is the number of vertices of the convex hull. .

By calling the function provided by the Go-geo library, you can easily solve the convex hull of a set of plane points. For example, the following code:

<code>import (
    "github.com/paulmach/go.geo"
)

func main() {
    // 创建平面点集
    points := []geo.Point{
        geo.Point{X: 0, Y: 0},
        geo.Point{X: 0, Y: 1},
        geo.Point{X: 1, Y: 0},
        geo.Point{X: 1, Y: 1},
    }
    // 求解凸包
    hull := geo.NewConvexHull(points)
    hull.Calculate()
    // 访问凸包的各个顶点
    for _, point := range hull.Points {
        fmt.Println(point)
    }
}</code>

In the above code, we first create a plane point set containing four points, then call the NewConvexHull function to create a convex hull object, and finally call the Calculate method to solve the convex hull, and pass Accessing the Points member of the convex hull accesses the individual vertices of the convex hull.

2. Triangulation

Triangulation is the process of dividing a plane point set into several non-intersecting triangles. In the field of computational geometry, triangulation is usually used to represent polygons, shells, calculate the properties of curves, etc. Go-geo provides the implementation of a variety of triangulation algorithms, including the Delaunay triangulation algorithm based on the insertion strategy and the convex hull triangulation algorithm based on the incremental strategy.

The following code demonstrates how to implement triangulation based on the Delaunay strategy:

<code>import (
    "github.com/paulmach/go.geo"
)

func main() {
    // 创建平面点集
    points := []geo.Point{
        geo.Point{X: 0, Y: 0},
        geo.Point{X: 0, Y: 1},
        geo.Point{X: 1, Y: 0},
        geo.Point{X: 1, Y: 1},
    }
    // 剖分三角形
    triangles := geo.NewDelaunayTriangulation(points)
    triangles.Triangulate()
    // 访问三角形的各个顶点
    for _, triangle := range triangles.Triangles {
        fmt.Println(triangle.V1, triangle.V2, triangle.V3)
    }
}</code>

In the above code, we first create a plane point set containing four points, and then call NewDelaunayTriangulation The function creates a triangulation object, and finally calls the Triangulate method to perform triangulation, and accesses each vertex of the triangle by accessing the Vertices member of the triangle.

3. Half-plane intersection

Half-plane intersection refers to the intersection of several half-planes on the plane. In the field of computational geometry, half-plane intersection is often used to solve maximum coverage problems, shortest path problems, minimum circle coverage problems, etc. Go-geo provides common half-plane intersection algorithm implementations, including: kernel line method, fast half-plane intersection and inversion half-plane intersection.

The following code demonstrates how to use the fast half-plane intersection algorithm to solve the intersection of two planar regions:

<code>import (
    "github.com/paulmach/go.geo"
)

func main() {
    // 创建第一个平面区域
    poly1 := geo.NewPolygon()
    poly1.Points = []geo.Point{
        geo.Point{X: 0, Y: 0},
        geo.Point{X: 0, Y: 1},
        geo.Point{X: 1, Y: 1},
        geo.Point{X: 1, Y: 0},
    }
    // 创建第二个平面区域
    poly2 := geo.NewPolygon()
    poly2.Points = []geo.Point{
        geo.Point{X: 0.5, Y: 0.5},
        geo.Point{X: 0.5, Y: 1.5},
        geo.Point{X: 1.5, Y: 1.5},
        geo.Point{X: 1.5, Y: 0.5},
    }
    // 求解两个区域的交集
    overlap, _ := geo.Overlap(poly1, poly2)
    // 访问交集的各个顶点
    for _, point := range overlap.Points {
        fmt.Println(point)
    }
}</code>

In the above code, we use the NewPolygon function to create two planar regions poly1 and poly2, then solve the intersection of the two regions by calling the Overlap function, and access the individual vertices of the intersection by accessing the Points member of the intersection.

4. Nearest Point Pair

The nearest point pair problem refers to a set of points on a given plane and finding the distance between the two closest points. In the field of computational geometry, the nearest point pair problem is often used to solve state estimation problems, route planning problems, etc. Go-geo provides an implementation of the nearest point pair algorithm based on the divide-and-conquer strategy, with a time complexity of O(nlogn).

The following code demonstrates how to use the Go-geo library to solve the problem of the nearest point pair on the plane:

<code>import (
    "github.com/paulmach/go.geo"
)

func main() {
    // 创建平面点集
    points := []geo.Point{
        geo.Point{X: 0, Y: 0},
        geo.Point{X: 0, Y: 1},
        geo.Point{X: 1, Y: 0},
        geo.Point{X: 1, Y: 1},
    }
    // 求解最近点对
    d := geo.ClosestPoints(points)
    fmt.Println(d)
}</code>

In the above code, we use the ClosestPoints function to solve the problem of the closest point pair on the plane. , and output the result.

5. The positional relationship between points and polygons

The positional relationship between points and polygons refers to determining whether a point on the plane is inside or outside the polygon, or It's on the border. In the field of computational geometry, the positional relationship between points and polygons is often used to solve intersection problems, construction problems, geographic information system problems, etc. Go-geo provides a function implementation for judging the position relationship between points and polygons, which can be called as needed.

The following code demonstrates how to use the Go-geo library to determine whether a point is inside a polygon:

<code>import (
    "github.com/paulmach/go.geo"
)

func main() {
    // 创建多边形
    poly := geo.NewPolygon()
    poly.Points = []geo.Point{
        geo.Point{X: 0, Y: 0},
        geo.Point{X: 0, Y: 2},
        geo.Point{X: 2, Y: 2},
        geo.Point{X: 2, Y: 0},
    }
    // 判断点是否在多边形内部
    point := geo.Point{X: 1, Y: 1}
    if poly.Contains(point) {
        fmt.Println("Point is inside polygon")
    } else {
        fmt.Println("Point is outside polygon")
    }
}</code>

In the above code, we create a polygon containing four points and then call Contains Function determines whether a point is inside a polygon.

Conclusion

Go language is an efficient programming language. With the assistance of computational geometry libraries such as Go-geo, we can easily implement various complex computational geometry algorithms in Go language. In the future, with the continuous research and development of computational geometry algorithms, Golang will surely become one of the major programming languages ​​in the field of computational geometry.

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