How do I find the coordinates of a point on a circle in PyGame?

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If a sprite is in the centre of a circle at the point 250,250 in pygame what is the equation to find the edge of the circle in any direction relative to the original point. Could the equation have the angle (as X) in the equation?

math pygame python
1 Answers

The general formula is (x, y) = (cx + r * cos(a), cy + r * sin(a)).

However, in your case ° is at the top and the angle increases clockwise. Therefore the formula is:

angle_rad = math.radians(angle)
pt_x = cpt[0] + radius * math.sin(angle_rad)
pt_y = cpt[1] - radius * math.cos(angle_rad)

Alternatively, you can use the pygame.math module and pygame.math.Vector2.rotate:

vec = pygame.math.Vector2(0, -radius).rotate(angle)
pt_x, pt_y = cpt[0] + vec.x, cpt[1] + vec.y

Minimal example:

import pygame
import math

pygame.init()
window = pygame.display.set_mode((500, 500))
font = pygame.font.SysFont(None, 40)
clock = pygame.time.Clock()
cpt = window.get_rect().center
angle = 0
radius = 100

run = True
while run:
    clock.tick(60)
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False  

    # solution 1
    #angle_rad = math.radians(angle)
    #pt_x = cpt[0] + radius * math.sin(angle_rad)
    #pt_y = cpt[1] - radius * math.cos(angle_rad)    
    
    # solution 2
    vec = pygame.math.Vector2(0, -radius).rotate(angle)
    pt_x, pt_y = cpt[0] + vec.x, cpt[1] + vec.y
    
    angle += 1     
    if angle >= 360:
        angle = 0

    window.fill((255, 255, 255))
    pygame.draw.circle(window, (0, 0, 0), cpt, radius, 2)
    pygame.draw.line(window, (0, 0, 255), cpt, (pt_x, pt_y), 2)
    pygame.draw.line(window, (0, 0, 255), cpt, (cpt[0], cpt[1]-radius), 2)
    text = font.render(str(angle), True, (255, 0, 0))
    window.blit(text, text.get_rect(center = cpt))
    pygame.display.flip()

pygame.quit()
exit()
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