Easy

Rotate 2D Points

~12 mincode completion

Implement rotate_points(points, theta).

  • points has shape (N, 2).
  • theta is in radians, counterclockwise.
  • Return an array of shape (N, 2).

Examples

theta = 0 leaves the points unchanged

Input
rotate_points([[1, 0], [0, 1]], 0)
Output
[[1, 0], [0, 1]]

90 degrees counterclockwise: (1,0) -> (0,1), (0,1) -> (-1,0)

Input
rotate_points([[1, 0], [0, 1], [1, 1]], 1.5707963267948966)
Output
[[0, 1], [-1, 0], [-1, 1]]

45 degrees sends (1,0) onto the diagonal

Input
rotate_points([[1, 0]], 0.7853981633974483)
Output
[[0.70711, 0.70711]]

Hints

Hint 1

Use a matrix product rather than nested loops, and check which operand transposes.

Hint 2

Reach for counterclockwise rather than clockwise.

Requirements

  • points: (N, 2) array of (x, y) rows

  • theta: rotation angle in radians

  • Return (N, 2) array of rotated points

Constraints

  • Allowed library: NumPy only

  • Time limit: 200 ms, Memory: 64 MB

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Python
import numpy as np


def rotate_points(points, theta):
    """
    Rotate 2D points counterclockwise by theta radians.

    Args:
        points: (N, 2) array of (x, y) rows
        theta:  rotation angle in radians

    Returns:
        (N, 2) array of rotated points
    """
    # YOUR CODE HERE
    pass
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