# Beginner. 2d rotation gives unexpected results.

Peter Otten __peter__ at web.de
Tue Jul 23 15:11:43 CEST 2013

```enmce at 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*cos-self.pos*sin) #mulpitplicating

The conversion to int introduces a rounding error that accumulates over
time.

> vector to rotation matrix
>         y_rot = int(self.pos*sin+self.pos*cos)
>
>         self.pos = x_rot #set new coordinates to a point
>         self.pos = 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():
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*cos-self.pos*sin
y_rot = self.pos*sin+self.pos*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])

```