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To: python-list@python.org
From: Peter Otten <__peter__@web.de>
Subject: Re: Beginner. 2d rotation gives unexpected results.
Date: Tue, 23 Jul 2013 15:11:43 +0200
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enmce@yandex.ru wrote:

> This is my first post, nice to meet you all!

Welcome!

> I`m biology student from Russia, trying to learn python to perform some
> 
> simple simulations.
> 
> Here`s my first problem.
> I`m trying to perform some simple 2d vector rotations in pygame, in order
> 
> to learn the basics of linear algebra and 2d transformations. So far i
> 
> understand matrix multiplication pretty well, and probably all my math is
> 
> right. Eventually i`m planning to write Poly class, and use it to rotate
> 
> and translate some simple shapes. But when i try and write it in the
> 
> program, i get very weird results, like all points of rectangle with
> 
> coordinates [0,0],[0,100],[100,0],[100,100] start to go spiral and
> 
> eventually shrink to the center. Although even Excel calculations with
> 
> this formulas give me right result.
> I use Python 3.3 on Windows Xp.
> What is wrong with my code?

>     def rotate(self): # rotation method
>         sin = m.sin(self.rot) #calculationg sin and cos
>         cos = m.cos(self.rot)
>         x_rot = int(self.pos[0]*cos-self.pos[1]*sin) #mulpitplicating

The conversion to int introduces a rounding error that accumulates over 
time.

> vector to rotation matrix
>         y_rot = int(self.pos[0]*sin+self.pos[1]*cos)
> 
>         self.pos[0] = x_rot #set new coordinates to a point
>         self.pos[1] = y_rot

One way to keep the error low is to keep the float values in self.pos and do 
the rounding on the fly when you display the point:

class Poly():
    def __init__(self, color, pos, rot=m.radians(1)):
        self.color = color
        self.pos = pos
        self.rot = rot
    def draw(self):
        x, y = self.pos
        pygame.draw.circle(screen, self.color, [350+int(x), 250+int(y)], 10, 
0)
    def rotate(self):
        sin = m.sin(self.rot)
        cos = m.cos(self.rot)
        x_rot = self.pos[0]*cos-self.pos[1]*sin
        y_rot = self.pos[0]*sin+self.pos[1]*cos

        self.pos = [x_rot, y_rot]

a = Poly(white, [100, 100])
b = Poly(green, [0, 100])
c = Poly(blue, [100, 0])
d = Poly(red, [0, 0])