What is the formula or function that describes the movement of a figure around an arbitrary point?

Question

Geometry

Good afternoon.
What I have: a geometric figure (it can be any), a point, the coordinates of the point, the coordinates of the figure relative to its center.
What can I do: Rotate the shape to any of the 360 ​​degree angles around its own axis.
What I need: rotate any of the 360 ​​degrees around the point, which is set to any point strictly within this figure.

Answer 1

You have several points - they are all on the circle, the
basic formulas are:
x = r*cos(fi)
y = r*sin(fi)
you only need to calculate their initial positions, and here we recall a right triangle and its angles.
abs(a)/abs(b)=tan(fi)
a=x-x0
b=y-y0
y0,x0 - coordinates of the desired point (around which we rotate)
x,y - point near the rectangle,
well, from the sign a and b depends on which quarter of the angle.
a>0 and b>0 - such as is fi=fi
a>0 and b<0 fi=180-fi
a<0 and b<0 fi=180+fi
a<0 and b>0 fi=-fi
is you get a zero angle for one of the points and you need to add 1 to it, and so 4 points and then look for them as points on a circle.
If it's hard to imagine, draw on paper (in a drawing tool).