Step by Step solution about How to resolve the algorithm Convex hull step by step in the Go programming language

The provided Go code defines a ConvexHull function for finding the convex hull of a set of points in two-dimensional space. A convex hull is the smallest convex polygon that encloses all the points in a set. It is often used to approximate the shape of a point set.

Here's a detailed breakdown of the code:

• Point and Points Types:

  • image.Point from the image package is used to represent a point in two-dimensional space.
  • points is a custom type defined as a slice of image.Point. It provides methods for sorting and comparing points.

• ConvexHull Function:

  • The ConvexHull method takes a points slice as input and returns a new points slice representing the convex hull of the input points.
  • It essentially uses the "Monotone Chain" algorithm to construct the convex hull as follows:
    • The points are sorted in ascending order of x-coordinates, and then in ascending order of y-coordinates for points with the same x-coordinate.
    • The algorithm creates two "hulls": one for the lower boundary and one for the upper boundary of the convex hull.
    • It iterates through the sorted points and checks if the current point creates a clockwise turn (i.e., a concave corner) with the last two points in the lower hull. If it does, it removes those points from the hull.
    • It then adds the current point to the lower hull.
    • After processing all points, the algorithm reverses the direction and starts from the last point in the lower hull. It performs the same checks and updates the upper hull.
    • Finally, it joins the lower and upper hulls to form the convex hull.

• ccw Function:

  • The ccw function takes three image.Point as input and returns a boolean indicating whether the points make a counter-clockwise (CCW) turn.
  • It calculates the cross product of the two vectors formed by the three points to determine the direction of the turn.

• Main Function:

  • The main function initializes a points slice with some example points.
  • It calls the ConvexHull method on the points slice to compute the convex hull.
  • Finally, it prints the resulting convex hull points.

In summary, this code demonstrates an efficient algorithm for constructing the convex hull of a set of points, which can be useful in various applications such as computer graphics, computational geometry, and data visualization.

package main

import (
	"fmt"
	"image"
	"sort"
)


// ConvexHull returns the set of points that define the
// convex hull of p in CCW order starting from the left most.
func (p points) ConvexHull() points {
	// From https://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain
	// with only minor deviations.
	sort.Sort(p)
	var h points

	// Lower hull
	for _, pt := range p {
		for len(h) >= 2 && !ccw(h[len(h)-2], h[len(h)-1], pt) {
			h = h[:len(h)-1]
		}
		h = append(h, pt)
	}

	// Upper hull
	for i, t := len(p)-2, len(h)+1; i >= 0; i-- {
		pt := p[i]
		for len(h) >= t && !ccw(h[len(h)-2], h[len(h)-1], pt) {
			h = h[:len(h)-1]
		}
		h = append(h, pt)
	}

	return h[:len(h)-1]
}

// ccw returns true if the three points make a counter-clockwise turn
func ccw(a, b, c image.Point) bool {
	return ((b.X - a.X) * (c.Y - a.Y)) > ((b.Y - a.Y) * (c.X - a.X))
}

type points []image.Point

func (p points) Len() int      { return len(p) }
func (p points) Swap(i, j int) { p[i], p[j] = p[j], p[i] }
func (p points) Less(i, j int) bool {
	if p[i].X == p[j].X {
		return p[i].Y < p[i].Y
	}
	return p[i].X < p[j].X
}

func main() {
	pts := points{
		{16, 3}, {12, 17}, {0, 6}, {-4, -6}, {16, 6},
		{16, -7}, {16, -3}, {17, -4}, {5, 19}, {19, -8},
		{3, 16}, {12, 13}, {3, -4}, {17, 5}, {-3, 15},
		{-3, -9}, {0, 11}, {-9, -3}, {-4, -2}, {12, 10},
	}
	hull := pts.ConvexHull()
	fmt.Println("Convex Hull:", hull)
}