PyGameExamplesAndAnswers

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Move towards target

Shoot a bullet in a certain direction - Rotate player and shoot bullet towards faced direction

Shoot bullets towards target or mouse

Related Stack Overflow questions:

pygame.transform.rotate does not transform the object itself, but creates a new rotated surface and returns it.

If you want to fire a bullet in a certain direction, the direction is defined the moment the bullet is fired, but it does not change continuously.
When the bullet is fired, set the starting position of the bullet and calculate the direction vector to the mouse position:

self.pos = (x, y)
mx, my = pygame.mouse.get_pos()
self.dir = (mx - x, my - y)

The direction vector should not depend on the distance to the mouse, but it has to be a Unit vector. Normalize the vector by dividing by the Euclidean distance

length = math.hypot(*self.dir)
if length == 0.0:
    self.dir = (0, -1)
else:
    self.dir = (self.dir[0]/length, self.dir[1]/length)

Compute the angle of the vector and rotate the bullet. In general, the angle of a vector can be computed by atan2(y, x). The y-axis needs to be reversed (atan2(-y, x)) as the y-axis generally points up, but in the PyGame coordinate system the y-axis points down (see How to know the angle between two vectors?):

angle = math.degrees(math.atan2(-self.dir[1], self.dir[0]))

self.bullet = pygame.Surface((7, 2)).convert_alpha()
self.bullet.fill((255, 255, 255))
self.bullet = pygame.transform.rotate(self.bullet, angle)

To update the position of the bullet, it is sufficient to scale the direction (by a velocity) and add it to the position of the bullet:

self.pos = (self.pos[0]+self.dir[0]*self.speed,
            self.pos[1]+self.dir[1]*self.speed)

To draw the rotated bullet in the correct position, take the bounding rectangle of the rotated bullet and set the center point with self.pos (see How do I rotate an image around its center using PyGame?):

bullet_rect = self.bullet.get_rect(center = self.pos)
surf.blit(self.bullet, bullet_rect)  

Follow target or mouse

Enemy follow

Related Stack Overflow questions:

For a more sophisticated solution, you’ve to compute the Euclidean distance form the point to the target. Use pygame.math.Vector2 for the computation.

Compute the distance from between the follower and the sprite and the unit direction vector from (follower_x, follower_y) to (mainsprite_x, mainsprite_y). The Unit Vector can be computed by dividing the direction vector by the distance or by normalizing (normalize()) the direction vector:

target_vector = Vector2(mainsprite_x, mainsprite_y)
follower_vector = Vector2(follower_x, follower_y)

distance = follower_vector.distance_to(target_vector)
direction_vector = target_vector - follower_vector
if distance > 0:
    direction_vector /= distance

Now you can define an exact step_distance and move to follower int direction of the sprite:

if distance > 0:
    new_follower_vector = follower_vector + direction_vector * step_distance.

Define a maximum_distance and a minimum_distance. The minimum step distance is:

min_step = max(0, distance - maximum_distance)

The maximum step distance is

max_step = distance - minimum_distance

Put it all together:

minimum_distance    = 0
maximum_distance    = 10000
target_vector       = Vector2(mainsprite_x, mainsprite_y)
follower_vector     = Vector2(follower_x, follower_y)
new_follower_vector = Vector2(follower_x, follower_y)

distance = follower_vector.distance_to(target_vector)
if distance > minimum_distance:
    direction_vector    = (target_vector - follower_vector) / distance
    min_step            = max(0, distance - maximum_distance)
    max_step            = distance - minimum_distance
    step_distance       = min_step + (max_step - min_step) * LERP_FACTOR
    new_follower_vector = follower_vector + direction_vector * step_distance