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Translate and Rotate Polygon in Matplotlib

I am making a little game with matplotlib (I know, terrible tool for the job but its a meme). I have a polygon that I am trying to translate around the screen, and also let you rotate it. However, I think there is a mix up between pixel coordinates and data coordinates, because once I move the polygon, the center of rotation is very wrong. Here is the code I have so far:
TLDR: Graph is 40x40 in size. I initialize my Polygon at 20,20. Before I move, rotation works fine, once I thrust, the rotation center point is no longer correct and I can see the polygon rotating around some other point
def thrust():
dx = math.cos(self.angle)
dy = math.sin(self.angle)
self.vx += self.acceleration * dx
self.vy += self.acceleration * dy
def update(ax):
self.cx += self.vx # update data coordinates
self.cy += self.vy
ts = ax.transData
coords = ts.transform([self.cx, self.cy])
t = mpl.transforms.Affine2D().translate(self.cx, self.cy)
r = mpl.transforms.Affine2D().rotate_deg_around(coords[0], coords[1], self.angle)
te = t + r
self.shape.set_transform(ts + te)
return self.shape

Handling sprite collisions against an angled rectangular obstacle that is static

So I have this obstacle that I want my sprite to collide with and it is at a particular angle.In this case, we are measuring from the positive x-axis to the top of the rectangle and in this instance it is 333.02 degrees with respect to the positive x-axis or 63.02 degrees with respect to the negative y-axis. So my issue is that how do I set up my pygame sprite to properly collide with the angle rectangle obstacle? Pygame sprite rectangles have no rotation attribute (to my knowledge) and I can't just say, "Hey when the right corner of my sprite collides with top, etc" because of this lack of rotation. My collisions work great for horizontal and even vertical surfaces but I am stuck on how to collide with angled obstacles.
Here is my collision code right now. It uses vectors and checks both x and y independently to see if anything is there. And below is a picture of the object I want to collide with created in the Tile Map Editor. It is at an angle of 333.02 degrees like I mentioned before. I also included a rough sketch of the axis in case that is relevant.
def update(self):
self.animate()
self.acc = vec(0, PLAYER_MASS * GRAVITY)
self.move()
# Equations of Motion
self.acc.x += self.vel.x * PLAYER_FRICTION
self.vel += self.acc
# Collision check in all 4 directions
self.pos.x += (
self.vel.x + 0.5 * self.acc.x * self.game.dt
) # Update x component (Frame-independent motion)
if abs(self.vel.x) < PLAYER_VELX_EPSILON:
self.vel.x = 0
self.rect.x = self.pos.x
hits = pg.sprite.spritecollide(self, self.game.platforms, False)
for hit in hits: # Horizontal collision
if self.vel.x > 0: # Rightward motion
self.rect.right = hit.rect.left
elif self.vel.y < 0: # Leftward motion
self.rect.left = hit.rect.right
self.pos.x = self.rect.x # Update true postion
self.pos.y += self.vel.y + 0.5 * self.acc.y * self.game.dt # Update y component
self.rect.y = self.pos.y + 5
# This prevents double jumping
if self.vel.y > 0:
self.onGnd = False
hits = pg.sprite.spritecollide(self, self.game.platforms, False)
for hit in hits: # Vertical Collision
if self.vel.y > 0: # Downward motion
self.rect.bottom = hit.rect.top
self.vel.y = 0
self.onGnd = True
elif self.vel.y < 0: # Upward motion
self.rect.top = hit.rect.bottom
self.vel.y = 0
self.pos.y = self.rect.y # Update true postion
# Limit Player's movement
if self.rect.bottom > HEIGHT:
self.vel.y = 0
self.rect.bottom = HEIGHT
self.pos.y = self.rect.y
Any help on this problem would be greatly appreciated!

The answer is coordinate translation. Imagine that the rotated object had its own coordinate system, where x runs along the bottom of the rectangle, and y up the side on the left. Then, if you could find the position of your sprite in that coordinate system, you could check for collisions the way you normally would with an unrotated rectangle, i.e., if x >=0 and x <= width and y >=0 and y <= height then there's a collision.
But how do you get the translated coordinates? The answer is matrices. You can use 2d transformation matrices to rotate, scale and translate vectors and coordinates. Unfortunately my experience with these types of transformations is in C#, not python, but this page for instance provides examples and explanations in python using numpy.
Note that this is quite simply the way 2d (and 3d) games work - matrix transformations are everywhere, and are the way to do collision detection of rotated, scaled and translated objects. They are also how sprites are moved, rotated etc: the pygame transform module is a matrix transformation module. So if the code and explanations looks scary at first glance, it is worth investing the time to understand it, since it's hard to write games without it beyond a certain point.
I'm aware this is not a full answer to your question, since I haven't given you the code, but it's too long for a comment, and hopefully points you in the right direction. There's also this answer on SO, which provides some simple code.
EDIT: just to add some further information, a full collision detection routine would check each collidable pixel's position against the object. This may be the required approach in your game, depending on how accurate you need the collision detection to be. That's what I do in my game Magnetar (https://www.youtube.com/watch?v=mbgr2XiIR7w), which collides multiple irregularly shaped sprites at arbitrary positions, scales and rotations.
I note however that in your game there's a way you could possibly "cheat" if all you need is collision detection with some angled slopes. That is you could have a data structure which records the 'corners' of the ground (points it change angle), and then use simple geometry to determine if an x,y point is below or above ground. That is, you would take the x value of a point and check which segment of the ground it is over. If it is over the sloped ground, work out how far along the x axis of the sloped ground it is, then use the sin of the angle times this value to work out the y value of the slope at that position, and if that is greater than the y value of the point you are checking, you have a collision.

The answer from seesharper may be the right way to go. I have no experience with that but it looks interesting and I will have to go read the links and learn something about this approach. I will still provide my immediate reaction to the question before I saw his answer though.
You could use pygames mask and mask collision detection routines. Create a mask that was the shape of the angled rectangle/platform and use the methods to detect collisions with that.
If you add a self.mask attribute to your Sprite subclass, the sprites will automatically use that mask in the collision detection.

Finding proper X/Y coordinate modifiers with given angle in Python/Pygame

I am trying to make a sprite move directly towards the mouse, utilizing the angle between them. This angle is found via the atan2 function. While this angle works fine for rotating the sprite towards the mouse, the sprite moves in the wrong directions depending on the quadrant of the given angle. It will sometimes freeze up in one quadrant, or move directly opposite the mouse.
I am using basic Trig functions to find the angle, and calculate proper additions to the X and Y variables of the sprite. It is also important to note that the angle I calculate, while it doesn't work for movement, does work perfectly for rotation. What's odd is that I pass the X-difference between the two spots, and THEN the Y-difference, which is the opposite of how the inverse tangent function is supposed to be handled. Therefore, I'm not even sure how this angle has been making rotation work correctly.
I've attempted to pass the Y-difference and the X-difference (in that order) into the atan2 function. However, this causes the rotation on my sprite to be wrong, pointing me towards the idea that the angle as a whole is also incorrect. I've also tried following along with numerous other programs, all of which use the same formulas as me. However, these don't work, even when I change the order of the arguments to the atan2 function to match the example programs.
def main():
ExitLoop = False
image = IMAGELOADER.AllImages["Fighter1"]
image2 = IMAGELOADER.AllImages["Fighter2"]
Fighter1 = FighterClass.Fighter(image,(700,700))
Fighter2 = FighterClass.Fighter(image2,(300,300))
while not ExitLoop:
ScreenController.Refresh()
mouse_pos = pygame.mouse.get_pos()
Fighter2.set_x(mouse_pos[0]-32)
Fighter2.set_y(mouse_pos[1]-32)
angle = math.atan2(Fighter1.get_x()-mouse_pos[0]+32, Fighter1.get_y()-mouse_pos[1]+32)
degrees_angle = math.degrees(angle)
Fighter1.rotate(degrees_angle)
xval = Fighter1.get_x()
yval = Fighter1.get_y()
speed = Fighter1.get_speed()
changex = (speed*math.cos(angle))
changey = (speed*math.sin(angle))
Fighter1.set_x(xval+changex)
Fighter1.set_y(yval+changey)
for event in pygame.event.get():
if event.type == pygame.QUIT:
ExitLoop = True
ScreenController.Draw(Fighter1.get_image(),Fighter1.get_rect(),False)
ScreenController.Draw(Fighter2.get_image(),Fighter2.get_rect(),False)
ScreenController.DisplayUpdate()
clock.tick(60)
Class Code (Relevant to the fighter class)
import pygame
import WoodysFunctions
class Fighter(pygame.sprite.Sprite):
def __init__(self,image,XnY):
pygame.sprite.Sprite.__init__(self)
self.image = image
self.__image_source = image
self.rect = self.image.get_rect()
self.__mask = pygame.mask.from_surface(self.image)
self.rect.x = XnY[0]
self.rect.y = XnY[1]
self.__speed = 1
def get_image(self):
return self.image
def get_rect(self):
return self.rect
def get_mask(self):
return self.__mask
def get_x(self):
return self.rect.x
def get_y(self):
return self.rect.y
def get_speed(self):
return self.__speed
def set_image(self,value):
self.image = value
def set_rect(self,value):
self.__rect = value
def set_mask(self,value):
self.__mask = value
def set_x(self,value):
self.rect.x = value
def set_y(self,value):
self.rect.y = value
def set_speed(self,value):
self.__speed = value
def rotate(self,angle):
old_center = self.rect.center
self.image = pygame.transform.rotate(self.__image_source,angle)
self.rect = self.image.get_rect()
self.rect.center = old_center
Expected output: Sprite moves straight towards the mouse
Actual behavior: Sprite moves in wrong directions, with behavior showing patterns depending on quadrant of calculated angle.
Edit:
I changed the program so that the X and Y variables of the sprite are stored in variables separate from the rect object. This prevents decimal truncation. I also recalculated the angle between the sprite and the mouse pointer after the rotation code is finished. In the recalculation, the X and Y difference parameters are swapped to match the inverse tangent function instead of the inverse cotangent function. This recalculated angle is used for angular movement, and the first angle, with the X difference passed first, is used for rotation. It is important to note that after I calculated the changeX and changeY variables using the recalculated angle (with the Y difference passed first), I multiplied them by -1, as otherwise the sprite will move away from the mouse pointer.

I cannot be 100% sure, but I think the problem is that pygame.Rect stores position as integers, because it's supposed to store coordinates and dimensions in pixel unit, and of course you cannot paint half pixel.
Since you are dealing with any angle and trigonometric functions, you end with floats which are truncated when you do:
def set_x(self,value):
self.rect.x = value
Here, if value is 1.4, self.rect.x becomes 1. So you lose "accuracy."
This loss of accuracy is propagated each iteration of the main loop (each frame), resulting in an unexpected motion direction.
The best solution is to store all your value in a separate data structure and update the rect attribute only for drawing in the screen.

Dealing with Sprites and Collisions Using Pygame

I am learning python using pygame and I am working on something that involves sprites and collisions. I've looked at some examples but I still don't quite understand it. What I am attempting to do is to be able to add sprites(a ball) when the user presses the "=" key and also be able to remove the last sprite added when pressing "-". I am not able to remove just the last one, I have only been able to remove all of them.
So far I have been able to add the balls to the window and have them bounce off the walls and one another(sort of). When 2 balls collide, they don't completely touch yet they bounce off. Sometimes the balls get stuck and won't move and sometimes the balls bounce off the frame which they aren't suppose to.
Its my first time working with sprite groups and would appreciate any help/guidance into making this work smoothly.Thanks.
The code:
ball.py
import pygame
from pygame.locals import *
class Ball(pygame.sprite.Sprite):
def __init__(self, x, y, vx, vy):
super().__init__();
self.image = pygame.image.load("ball.png").convert()
self.image.set_colorkey(pygame.Color(0, 0, 0))
self.rect = self.image.get_rect()
self.rect.x = x
self.rect.y = y
self.vx = vx
self.vy = vy
def draw(self, SCREEN):
SCREEN.blit(self.image, (self.rect.x, self.rect.y))
def move(self, SCREEN, balls):
l_collide = self.rect.x + self.image.get_width() + self.vx > SCREEN.get_width()
r_collide = self.rect.x + self.vx < 0
t_collide = self.rect.y + self.vy < 0
b_collide = self.rect.y + self.image.get_height() + self.vy > SCREEN.get_height()
a = pygame.sprite.spritecollide(self, balls, False, False)
if len(a) > 1:
self.vx *= -1
self.vy *= -1
if l_collide or r_collide:
self.vx *= -1
if t_collide or b_collide:
self.vy *= -1
self.rect.x += self.vx
self.rect.y += self.vy
ball_animation.py
import pygame
import sys
import random
import math
from pygame.locals import *
from ball.ball import Ball
from random import randint
def ball_list(num):
ball_list = pygame.sprite.Group()
for x in range(num):
rand_x = random.randint(0,400)
rand_y = random.randint(0,400)
vx = 4
vy = 5
ball_list.add(Ball(rand_x, rand_y, vx, vy))
return ball_list
def main():
pygame.init()
FPS = 30
FPS_CLOCK = pygame.time.Clock()
# COLOR LIST
BLACK = pygame.Color(0, 0, 0)
# Code to create the initial window
window_size = (500, 500)
SCREEN = pygame.display.set_mode(window_size)
# set the title of the window
pygame.display.set_caption("Bouncing Ball Animation")
# change the initial background color to white
SCREEN.fill(BLACK)
balls = ball_list(0)
while True: # <--- main game loop
for event in pygame.event.get():
if event.type == QUIT: # QUIT event to exit the game
pygame.quit()
sys.exit()
if event.type == KEYDOWN:
if event.key == K_EQUALS:
balls.add(Ball(randint(0,400),randint(0,400), 4,5))
if event.key == K_MINUS:
try:
balls.remove()
except IndexError:
print('There is no balls to take!')
SCREEN.fill(BLACK)
for x in balls:
x.move(SCREEN,balls)
x.draw(SCREEN)
pygame.display.update() # Update the display when all events have been processed
FPS_CLOCK.tick(FPS)
if __name__ == "__main__":
main()

Removing Sprites on Press
The problem is sprite.Group.remove(sprites) wants you to specify which sprites it should remove. sprites here should be a sprite/list of sprites that you want to remove from the group. This means to remove the last ball added on key press you need to keep a list of the ball sprites and pop() the most recently added item from it, and then use the result of the pop() as the sprite to remove from the group. sprite.Group has a .sprites() method which returns a list of all sprites in the group, in the order they were added. This list is generated from the group and is not actually an interface with it, so doing things to this list won't affect the group. We can still however use it to get the last added sprite. Here is what it looks like:
elif event.key == K_0:
try:
sprite_list = balls.sprites()
to_remove = sprite_list[-1] # Get last element of list
balls.remove(to_remove)
except IndexError:
print('There is no balls to take!')
Collisions
So this is a bit more involved and not so simple to fix in your code. To understand what the problem is, look at what your collision velocity adjustments are actually doing for the screen border case.
l_collide = self.rect.x + self.image.get_width() + self.vx > SCREEN.get_width()
r_collide = self.rect.x + self.vx < 0
t_collide = self.rect.y + self.vy < 0
b_collide = self.rect.y + self.image.get_height() + self.vy > SCREEN.get_height()
#################
if l_collide or r_collide:
self.vx *= -1
if t_collide or b_collide:
self.vy *= -1
Consider a single time-step in your code. We check to see if the sprite is sitting over the edge of the boundaries by any amount. If its hanging over, we reverse the velocity. There is a case where your edge checking will get you into trouble. If your self.vx is less than the difference between your current position X and the boundary of the x dimension, you will reverse your speed, travel self.vx back towards the boundary, but not make it past. In the next time-step, you will see that you are still over the boundary, and your program will again reverse self.vx, actually sending you away from the boundary. In this case you will bound back and forth each time-step by self.vx. Normally this wouldn't happen in your code, except for when you spawn a new ball sprite over the boundary further than your self.vx or self.vy for that ball. This can be remedied by making sure you don't spawn balls off the edges, or better yet, only reversing your velocity if you need to.
if (l_collide and self.vx>0) or (r_collide and self.vx<0):
self.vx *= -1
if (t_collide and self.vy<0) or (b_collide and self.vy>0):
self.vy *= -1
Notice here we only reverse the velocity if we are over the edge AND the velocity is headed deeper in that direction. Now for your sprites you have two options, just like with the boundaries:
Only initiate a new ball in empty space where it cannot collide.
Implement some way to calculate the correct velocity adjustment and only apply it if the velocity is headed in the opposite direction.
From what I read in the documentation, sprite.Group looks like it is meant for checking if sprites are overlapping, and not for physics simulation. I recommend doing some research on 2d physics simulation to get a nice conceptualization of what information you should want to communicate between objects. I'm sure there are some nice tutorials out there.
Finally, to address your other question about why they are colliding when they don't appear to be touching. sprite.spritecollide is returning which sprites have rectangles that intersect. If your ball.png is color keyed for transparency, this does not affect the rect of the sprite. Pygame appears to have functionality implemented designed to handle this problem in the collided keyword of sprite.spritecollide:
pygame.sprite.spritecollide()
Find sprites in a group that intersect another sprite.
spritecollide(sprite, group, dokill, collided = None) -> Sprite_list
The collided argument is a callback function used to calculate if two sprites >are colliding. it should take two sprites as values, and return a bool value >indicating if they are colliding. If collided is not passed, all sprites must >have a “rect” value, which is a rectangle of the sprite area, which will be >used to calculate the collision.
collided callables:
collide_rect
collide_rect_ratio
collide_circle
collide_circle_ratio
collide_mask
That's from the pygame documentation. The documentation for the collide_circle function states that your sprite should have a radius attribute, or else one will be calculated to fit the entire rectangle inside a circle. As such, in your Ball.__init__ function I would recommend adding:
self.radius = self.rect.width/2
This will make collide_circle use a radius that approximates your ball image, assuming it is centered and circular and occupies the entire image. Next, you must add the collision specification to your collision check by changing:
a = pygame.sprite.spritecollide(self, balls, False, False)
to
a = pygame.sprite.spritecollide(self, balls, False, pygame.sprite.collide_circle)
If you solve the problem of not spawning new ball objects inside each other, this should all work nicely. If you can't get them to spawn inside each other, think about a different data-structure or different way of collision checking to get the results you want. Best of luck!

I can see two questions in your text
You want to only remove one sprite, rather than all the sprites in the spritegroup
If you look at the pygame documentation, you can see that spritegroup.remove has an optional argument. You can remove a single sprite by putting your desired sprite as the argument, such as myspritegroup.remove(mysprite).
You have issues with the colliding
Your collision works for me as long as the balls don't spawn on top of each other on creation which you can simply check. Good luck :)

How do I make the ball bounce off the paddle?

I'm making a basic pong game (paddle is a rectangle on the bottom of the screen and the ball drops from the top of the screen). I want the ball to bounce back up ONLY when it hits the paddle. So far, I've written code that will make the ball bounce off the top and bottom screen, but I'm having trouble with getting the ball to bounce off the paddle.
I have to modify the parameters that are passed to my test_collide_ball method. If it’s current x values are within the range of the paddle, then it bounces back up.
I've been trying to think of a solution for this, and what I'm thinking is that if the ball hits the paddle's y coordinate (the height), then it bounces back up. But it also has to be within the range of x coordinates that make up the paddle (so the width of the paddle).
But when I do this, the ball just gets stuck in place. Any feedback is appreciated! Thanks in advance.
Here is my code for the ball class/methods:
import pygame
class Ball:
def __init__(self, x, y, radius, color, dx, dy):
self.x = x
self.y = y
self.radius = radius
self.color = color
self.dx = dx
self.dy = dy
def draw_ball(self, screen):
pygame.draw.ellipse(screen, self.color,
pygame.Rect(self.x, self.y, self.radius, self.radius))
def update_ball(self):
self.x += self.dx
self.y += self.dy
def test_collide_top_ball(self, top_height):
if (self.y <= top_height):
self.dy *= -1
def test_collide_bottom_ball(self, paddle):
if (self.y == paddle.y) and (self.x >= paddle.x) and (self.x <= paddle.x + paddle.width):
self.dy *= -1

What appears to be happening is your ball enters the collision zone and reverses it's direction. The ball is still in the collision zone, however, and it reverses it's direction again.
What you should look into is a debounce check. Put simply, this is code that prevents something from happening twice or more times (de-bouncing it).
From your code example, the ball's momentum is reversed when it enters the paddle zone. What you might add is a boolean flag to see if you have already detected that the ball entered the zone. When it is first detected, set the flag to true. When the ball moves outside of the zone, set the flag back to false. Only reverse the ball's momentum if the flag is false.
So, (excusing my rusty Python)
def test_collide_bottom_ball(self, paddle):
if (self.y == paddle.y) and (self.x >= paddle.x) and (self.x <= paddle.x + paddle.width) and (!self.hitPaddle):
self.dy *= -1
self.hitPaddle = true
else
self.hitPaddle = false
And in your entity:
self.hitPaddle = false

Just like #MrDoomBringer is saying, you need to prevent it from getting stuck within the pad.
One easy method to solve that is to check whether self.dy is positive - the ball is moving downwards. This way you could also add the same "within" check for the Y-pos as you did with the X-pos. Otherwise, having a collision with an exact Y-coordinate is pretty hard unless you're using the right speed etc.
Another thing - if you have a ball, you most likely want to add it's size to the equation. Then you might want to use some more fancy collision-techniques, such as this: http://www.migapro.com/circle-and-rotated-rectangle-collision-detection/