Incrementing Area Of Convex Hull

I want to use convex hull to draw a line around a list of points. However, I would like for the area to be larger than just minimum convex hull. How do I achieve that. P.S. I am us

Solution 1:

from scipy.spatial  import ConvexHull
import matplotlib.pyplot as plt
import numpy as np
import math

def PointsInCircum(eachPoint,r,n=100):
    return [(eachPoint[0] + math.cos(2*math.pi/n*x)*r,eachPoint[1] + math.sin(2*math.pi/n*x)*r) for x in range(0,n+1)]


def bufferPoints (inPoints, stretchCoef, n):
    newPoints = []
    for eachPoint in inPoints:
        newPoints += PointsInCircum(eachPoint, stretchCoef, n)
    newPoints = np.array(newPoints)
    newBuffer = ConvexHull (newPoints)

    return newPoints[newBuffer.vertices]


if __name__ == '__main__':
    points = np.array([[-2,3], [2,4], [-2,-2], [2,-1], [1,-1], [-0.5, 0.5]])
    plt.scatter(points[:,0], points[:,1])
    plt.show()
    convh = ConvexHull(points)#Get the first convexHull (speeds up the next process)

    stretchCoef = 1.2
    pointsStretched = bufferPoints (points[convh.vertices], stretchCoef, n=10)
    plt.scatter(points[:,0], points[:,1])
    plt.scatter(pointsStretched[:,0], pointsStretched[:,1], color='r')
    plt.show() 

So I updated the above code. It creates a circle of points around each of the first set of ConvexHull vertices and then creates a new ConvexHull.

Here is the output of this code Plot View

Solution 2:

Here is an idea to solve the exact problem you have on paper:

from scipy.spatial  import ConvexHull
import matplotlib.pyplot as plt
import numpy as np

if __name__ == '__main__':
    points = np.array([[-2,3], [2,4], [-2,-2], [2,-1], [1,-1], [-0.5, 0.5]])
    plt.scatter(points[:,0], points[:,1])
    plt.show()
    convh = ConvexHull(points)

    stretchCoef = 1.2
    pointsStretched = points[convh.vertices]*stretchCoef
    plt.scatter(points[:,0], points[:,1])
    plt.scatter(pointsStretched[:,0], pointsStretched[:,1], color='r')
    plt.show()

pointsStretched find the new points for your new convex hull. Using a stretching coefficient works here because you have the points on each of the vertices of the convexhull on different quadrants, but I think you get the idea of how to solve this. One way is to find the points in your stretched convexhull, which will be along the same vector as the initial points.