pygame.math.Vector2: Movement with Vectors

pygame.Vector2 is a pair of floats, x and y, with the math you need for movement built in. Positions, velocities and directions are all vectors:

pos = pygame.Vector2(100, 200)
velocity = pygame.Vector2(3, -1)
pos += velocity          # (103, 199)

Because a vector holds floats, it also avoids the Rect rounding trap: keep the position in a Vector2 and copy it into the Rect for drawing and collisions.

Same speed in every direction

Pressing Right and Down together moves (1, 1) per step, which is about 1.41 long, so diagonal movement is 41% faster. Normalize the direction first, which keeps it pointing the same way but makes its length 1:

import pygame

pygame.init()
screen = pygame.display.set_mode((480, 360))
clock = pygame.time.Clock()

pos = pygame.Vector2(240, 180)
speed = 4
running = True

while running:
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            running = False

    keys = pygame.key.get_pressed()
    direction = pygame.Vector2(
        keys[pygame.K_RIGHT] - keys[pygame.K_LEFT],
        keys[pygame.K_DOWN] - keys[pygame.K_UP],
    )
    if direction.length() > 0:
        direction = direction.normalize()
    pos += direction * speed
    pos.x = max(20, min(460, pos.x))
    pos.y = max(20, min(340, pos.y))

    screen.fill((22, 26, 40))
    pygame.draw.circle(screen, (110, 220, 160), pos, 20)
    pygame.display.flip()
    clock.tick(60)

pygame.quit()

Press Play, click the game and steer with the arrows. The if matters: normalizing (0, 0) raises ValueError: Can't normalize Vector of length zero.

Chasing a target

Subtract two positions to get the arrow from one to the other. Normalize it and multiply by a speed to take one step along it. This enemy follows the mouse:

import pygame

pygame.init()
screen = pygame.display.set_mode((480, 360))
clock = pygame.time.Clock()

enemy = pygame.Vector2(60, 60)
speed = 2.5
running = True

while running:
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            running = False

    target = pygame.Vector2(pygame.mouse.get_pos())
    to_target = target - enemy
    if to_target.length() > speed:
        enemy += to_target.normalize() * speed
    else:
        enemy = target

    screen.fill((30, 24, 36))
    pygame.draw.circle(screen, (240, 90, 90), enemy, 16)
    pygame.draw.circle(screen, (200, 200, 220), target, 6, width=2)
    pygame.display.flip()
    clock.tick(60)

pygame.quit()

Move the pointer over the game. When the enemy is closer than one step, it lands on the target instead of overshooting and jittering. pygame-ce does the same in one call: enemy.move_towards_ip(target, speed).

Useful methods

+, -, * by a number, / by a number, == and v.x, v.y all work as you would expect. A Vector2 can be passed anywhere pygame wants a position: pygame.draw.circle(screen, color, pos, 10) or rect.center = pos (the Rect rounds it).

Aiming and rotation

To point a ship at the mouse, get the angle of the direction and rotate the image by it. as_polar() returns the length and the angle in degrees:

direction = pygame.Vector2(pygame.mouse.get_pos()) - ship_pos
_, angle = direction.as_polar()
rotated = pygame.transform.rotate(ship_image, -angle - 90)

The minus sign is there because pygame's y axis points down while rotate turns counterclockwise; the - 90 depends on which way the image faces. pygame.transform shows how to blit the rotated image around its center.