Rotate xy points using multiple angles - python

The problem to be solved is not clear. From what I understand the problem is to make a point rotate around a pivot point with a certain angle theta. The dataframes of pandas are not very suited to the problem, let's use numpy instead. For convenience we first define a class to represent points and vectors in the plane.

class Coord:
    def __init__(self, x, y):
        x, y = np.array(x), np.array(y)
        assert x.shape == y.shape
        self.x, self.y = x, y
        self.shape = x.shape

    @property
    def radius(self):
        return np.sqrt(self.x ** 2 + self.y ** 2)

    def __sub__(self, other):
        return Coord(self.x - other.x, self.y - other.y)

    def __add__(self, other):
        return Coord(self.x + other.x, self.y + other.y)

    def __repr__(self):
        return f"Coord({self.x}, {self.y})"

For instance Coord(2, 3) simply represents a point or a vector with coordinates (2, 3). Additions and subtractions can be performed: Coord(2, 3) + Coord(1, -2) returns Coord(3, 1). Note x and y attributes can be numpy arrays. In this case a Coord instance could be though as a set of points. For example Coord([1, 2, 0],[2, -1, 3]) represents the points/vectors (1, 2), (2, -1) and (0, 3).

Rotation around the origin

Let's add a method _rotate_from_origin to the class Coord that outputs the point after rotation. You can find here an explanation of how to rotate a point.

    def _rotate_from_origin(self, theta):
        return Coord(
            self.x * np.cos(theta) - self.y * np.sin(theta),
            self.x * np.sin(theta) + self.y * np.cos(theta))

Rotation around a given pivot

It seems that you defined the coordinates x_ref and y_ref, with the idea of performing the rotation not around the origin but around this reference point. We can simply achieve this using the following method:

    def rotate(self, theta, pivot=None):
        if not pivot:
            pivot = Coord(0, 0)
        return (self - pivot)._rotate_from_origin(theta) + pivot

That's it! Now you can use this method for any point or set of points.

Example

Let's try on your example (or at least on what I understood of it).

startA = Coord([0, -1], [ 0, -1])  # points that will be rotated with an angle of thetaA
startB = Coord([3,  2], [-1,  0])  # will be rotated with an angle of thetaB
pivot = Coord(1, 1)
thetaA = -np.pi / 4
thetaB = np.pi / 4

## Rotate each set of points with the corresponding angle
rotatedA = startA.rotate(thetaA, pivot=pivot)
rotatedB = startB.rotate(thetaB, pivot=pivot)

## Display the result
plt.plot(pivot.x, pivot.y, 'ko')
plt.plot(startA.x, startA.y, 'o', c='gold')
plt.plot(rotatedA.x, rotatedA.y, 'o', c='gold')
plt.plot(startB.x, startB.y, 'o', c='lightblue')
plt.plot(rotatedB.x, rotatedB.y, 'o', c='royalblue')

Note that here theta parameter is a single integer. In this case each points will be rotated using the same theta value. But several values of thetas can be used to make each point rotate differently. For instance we could have done:

starts = Coord([0, -1, 3, 2], [0, -1, -1, 0])
pivot = Coord(1, 1)
thetas = (np.pi / 4) * np.array([-1, -1, 1, 1])

rotated = starts.rotate(thetas, pivot=pivot)

And the same applies to the pivot parameter. Basically this is the expected behavior when using functions with numpy.