   Simplify reference system and vector movement
Greetings, Well, I spend a whole afternoon trying to implement a simple navigation system using vectors. Finally it worked, here's a fragment of what I did (from a Spaceship class): def moveForward(self):    self.center -= self.step * Vector2D(1,0).rotate(self.angle).invX()    self.rect.center = self.center.toPoint()Basically, I use right and left arrow keys to rotate the spaceship to right or left direction, respectly. And, I have the previous fragmente code to move forward. Due the fact that (0,0) grows from left to right (x-coordinate) and from top to bottom, I have to invert the x-coordinate (invX() method) from the rotated vector in order to "correct" the spaceship navigation. Is there another way to make this simpler, for example, changing the origin or somewhat like that? Thank you
  That looks a bit awkward. Instead of keeping an angle to indicate where the spaceship is pointing, use a vector of length 1. The code would then look something like this (ignoring the issue of the flipped x coordinate, which I think should be dealt with in the rendering code, not the scene update code):def moveForward(self):    self.center += self.step * self.heading    self.rect.center = self.center.toPoint() # I don't know what this line doesWhat is self.rect.center? And why do you need to call `toPoint' on self.center? What is self.center if not a point?EDIT: Oh, the tricky part with using heading as a length-one vector is how to rotate it when the user presses a key. Instead of adding something to the angle, rotate the vector by some amount (you seem to already have code for that). You may have to normalize the vector every so often (like every frame, for simplicity) so that it doesn't end up being much longer or shorter by accumulated floating-point errors.   ;What is self.rect.center? And why do you need to call `toPoint' on self.center? What is self.center if not a point?self.rect.center is a python tuple. I need to set it to render the spaceship later, and it doesn't accept a "vector". toPoint() method converts a vector in a tuple. I know, it seems ugly but i couldn't figure out how deal with it. EDIT: I hadn't understood your full answer but now it's clear to me. Thank you very much!;You may have to normalize the vector every so often (like every frame, for simplicity) so that it doesn't end up being much longer or shorter by accumulated floating-point errors. Have you got any additional information (websites, books) of what you wrote it? Thanks;  I don't, but what I describe in that particular sentence you quoted (you need to normalize your vector every so often) is the standard thing to do when controlling a 3D attitude using a quaternion (which has to be kept with length 1 as well). The situation here is analogous.If you want to know something else about how to do 2D geometry without using angles, I love to evangelize about it. ;Hahaha, OK. Thanks!