CODEWITHSUNDEEP
pythonmathpygame
Bramwell Simpson
Bramwell Simpson

Reputation: 63

How to find points on a circumference

How do I find a user defined amount of points on a circumference of a circle. Then when it has been found, place it in a 2 dimensional array for later use. For a slightly better view of it:

enter image description here

Thanks for all the help :)

Upvotes: 3

Views: 3859

Answers (3)

skrx
skrx

Reputation: 20438

You could also use pygame's Vector2 class. Just rotate a vector with the length of the radius and add it to the center of the circle to get a point on the circumference.

import pygame as pg
from pygame.math import Vector2


def points(number, center, radius):
    angle = 360/number
    point_list = []
    for i in range(number):
        # Create a vector with the length of the radius, rotate it
        # and add it to the center point to get a point on the circumference.
        vec = center + Vector2(radius, 0).rotate(i*angle)
        # pygame.draw.circle needs ints, so we have to convert the vector.
        point_list.append([int(vec.x), int(vec.y)])
    return point_list


def main():
    screen = pg.display.set_mode((640, 480))
    clock = pg.time.Clock()
    center = (320, 240)
    radius = 150
    number = 2
    point_list = points(number, center, radius)

    done = False

    while not done:
        for event in pg.event.get():
            if event.type == pg.QUIT:
                done = True
            elif event.type == pg.KEYDOWN:
                if event.key == pg.K_c:
                    number += 1 # Increment the number and generate new points.
                    point_list = points(number, center, radius)

        screen.fill((30, 30, 30))
        pg.draw.circle(screen, (220, 120, 0), center, radius, 2)
        for pos in point_list:
            pg.draw.circle(screen, (0, 120, 250), pos, 20, 2)
        pg.display.flip()
        clock.tick(30)


if __name__ == '__main__':
    pg.init()
    main()
    pg.quit()

Upvotes: 1

Jake
Jake

Reputation: 637

Im assuming you want the points evenly spaced.

A circle has 360 degrees about the center, or 2pi radians.

you need to divide 2pi by the number of points that you want. say 4 -> 2pi/4

that is the number of radians from one point to the next.

to compute x and y coordinates use these two equations r = sqrt( x2 + y2 ), and θ = tan-1 ( y / x )

where θ1 = 0*2*pi/4, θ2 = 1*2*pi/4, θ3 = 2*2*pi/4, and θ4 = 3*2*pi/4

some code would look like this:

import numpy as np

def get_points(radius, number_of_points):
    radians_between_each_point = 2*np.pi/number_of_points
    list_of_points = []
    for p in range(0, number_of_points):
        list_of_points.append( (radius*np.cos(p*radians_between_each_point),radius*np.sin(p*radians_between_each_point)) )
    return list_of_points

Upvotes: 4

ChuckCottrill
ChuckCottrill

Reputation: 4444

You want to find points (x,y) which are points which are solutions to the equation x^2 + y^2 = R^2.

First note that both x and y must be in [-R,R], and when you pick x (or y), the other can be found by solving y = sqrt(R^2 - x^2).

An alternative is to use the angle, theta, and x = R * cos(theta), y = R * sin(theta). You need only solve for theta in [0,2*PI) radians (sin, cos typically use radians, PI radians is 180 degrees). Which depends upon whether you want to use trignometry (sin/cos are transcedental functions).

You can translate these points (x,y) to a new center (xc,yc) simply by adding (x1,y1) to (x,y) to get translated points (xt,yt) = (x+xc,y+yc).

Upvotes: 0

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