Rotate point about another point in degrees python

Rotate point about another point in degrees python

To rotate a point about another point in Python, you can use trigonometric functions to calculate the new coordinates after applying a rotation transformation. Here's how you can do it:

Let's assume you want to rotate point P around point A by a given angle in degrees.

import math # Function to rotate a point about another point def rotate_point(point, angle_degrees, pivot): # Convert the angle to radians angle_radians = math.radians(angle_degrees) # Translate the point to the origin by subtracting the pivot translated_point = (point[0] - pivot[0], point[1] - pivot[1]) # Apply rotation using trigonometric formulas x_new = translated_point[0] * math.cos(angle_radians) - translated_point[1] * math.sin(angle_radians) y_new = translated_point[0] * math.sin(angle_radians) + translated_point[1] * math.cos(angle_radians) # Translate the rotated point back to its original position by adding the pivot rotated_point = (x_new + pivot[0], y_new + pivot[1]) return rotated_point # Example points and pivot point_P = (3, 4) pivot_A = (1, 1) angle_degrees = 45 # Rotate point P around pivot A by the specified angle new_point = rotate_point(point_P, angle_degrees, pivot_A) print("Original Point P:", point_P) print("Rotated Point P:", new_point)

In this example, the rotate_point function takes the point to be rotated, the angle of rotation in degrees, and the pivot point as arguments. It then performs the translation, rotation, and translation back to the original position using trigonometric formulas.

Make sure to adjust the point coordinates and pivot as needed for your specific use case.

Examples

  1. "How to rotate a point about another point in degrees in Python"

    • Description: This query discusses how to rotate a given point around another point by a specified angle in degrees.
    • Code:
      import math def rotate_point(point, origin, angle_degrees): angle_radians = math.radians(angle_degrees) px, py = point ox, oy = origin # Apply rotation matrix qx = ox + math.cos(angle_radians) * (px - ox) - math.sin(angle_radians) * (py - oy) qy = oy + math.sin(angle_radians) * (px - ox) + math.cos(angle_radians) * (py - oy) return (qx, qy) # Example usage point = (1, 0) # Point to be rotated origin = (0, 0) # Origin around which to rotate angle_degrees = 90 # Angle in degrees new_point = rotate_point(point, origin, angle_degrees) print(new_point) # Output: (0.0, 1.0)

  2. "Rotate point about another point with a given distance in Python"

    • Description: This query explores rotating a point around another point by a specific angle, considering a given distance.
    • Code:
      import math def rotate_point(point, origin, angle_degrees, distance): angle_radians = math.radians(angle_degrees) ox, oy = origin # Calculate new coordinates based on angle and distance qx = ox + distance * math.cos(angle_radians) qy = oy + distance * math.sin(angle_radians) return (qx, qy) # Example usage origin = (0, 0) # Origin point distance = 1 # Distance from origin angle_degrees = 45 # Rotation angle in degrees rotated_point = rotate_point(origin, origin, angle_degrees, distance) print(rotated_point) # Output: (0.7071, 0.7071)

  3. "Rotate point around another point with a specific angle in Python"

    • Description: This query discusses rotating a point around another point with a given angle.
    • Code:
      import math def rotate_point(point, origin, angle_degrees): angle_radians = math.radians(angle_degrees) px, py = point ox, oy = origin # Apply rotation formula qx = ox + math.cos(angle_radians) * (px - ox) - math.sin(angle_radians) * (py - oy) qy = oy + math.sin(angle_radians) * (px - ox) + math.cos(angle_radians) * (py - oy) return (qx, qy) # Example usage point = (1, 1) # Point to rotate origin = (0, 0) # Origin of rotation angle_degrees = 45 # Rotation angle rotated_point = rotate_point(point, origin, angle_degrees) print(rotated_point) # Output: (0.0, 1.4142)

  4. "Rotate a point by degrees using numpy in Python"

    • Description: This query explores how to use numpy to rotate a point by a given angle.
    • Code:
      import numpy as np def rotate_point(point, origin, angle_degrees): angle_radians = np.radians(angle_degrees) rotation_matrix = np.array([ [np.cos(angle_radians), -np.sin(angle_radians)], [np.sin(angle_radians), np.cos(angle_radians)] ]) translated_point = np.array(point) - np.array(origin) rotated_point = np.dot(rotation_matrix, translated_point) + np.array(origin) return tuple(rotated_point) # Example usage point = (1, 0) # Point to rotate origin = (0, 0) # Origin of rotation angle_degrees = 90 # Rotation angle new_point = rotate_point(point, origin, angle_degrees) print(new_point) # Output: (0.0, 1.0)

  5. "Calculate angle between two points in Python"

    • Description: This query discusses how to calculate the angle between two points in degrees.
    • Code:
      import math def angle_between_points(point1, point2): dx = point2[0] - point1[0] dy = point2[1] - point1[1] angle_radians = math.atan2(dy, dx) angle_degrees = math.degrees(angle_radians) return angle_degrees # Example usage point1 = (0, 0) point2 = (1, 1) angle = angle_between_points(point1, point2) print(angle) # Output: 45.0

  6. "Rotate point in 3D space in Python"

    • Description: This query discusses how to rotate a point in 3D space about a given axis.
    • Code:
      import math import numpy as np def rotate_point_3d(point, axis, angle_degrees): angle_radians = math.radians(angle_degrees) # Define the rotation matrix for the given axis if axis == 'x': rotation_matrix = np.array([ [1, 0, 0], [0, math.cos(angle_radians), -math.sin(angle_radians)], [0, math.sin(angle_radians), math.cos(angle_radians)] ]) elif axis == 'y': rotation_matrix = np.array([ [math.cos(angle_radians), 0, math.sin(angle_radians)], [0, 1, 0], [-math.sin(angle_radians), 0, math.cos(angle_radians)] ]) elif axis == 'z': rotation_matrix = np.array([ [math.cos(angle_radians), -math.sin(angle_radians), 0], [math.sin(angle_radians), math.cos(angle_radians), 0], [0, 0, 1] ]) else: raise ValueError("Axis must be 'x', 'y', or 'z'.") point_np = np.array(point) rotated_point = np.dot(rotation_matrix, point_np) return tuple(rotated_point) # Example usage point = (1, 0, 0) # Point to rotate axis = 'y' # Axis of rotation angle_degrees = 90 # Rotation angle in degrees new_point = rotate_point_3d(point, axis, angle_degrees) print(new_point) # Output: (0.0, 0.0, 1.0)

  7. "Rotate point around another point using transformation matrix in Python"

    • Description: This query explores using transformation matrices to rotate a point around another point.
    • Code:
      import numpy as np def rotate_point(point, origin, angle_degrees): angle_radians = np.radians(angle_degrees) rotation_matrix = np.array([ [np.cos(angle_radians), -np.sin(angle_radians)], [np.sin(angle_radians), np.cos(angle_radians)] ]) # Translate point to origin, apply rotation, then translate back translated_point = np.array(point) - np.array(origin) rotated_point = np.dot(rotation_matrix, translated_point) final_point = rotated_point + np.array(origin) return tuple(final_point) # Example usage point = (1, 0) # Point to rotate origin = (0, 0) # Origin of rotation angle_degrees = 90 # Rotation angle rotated_point = rotate_point(point, origin, angle_degrees) print(rotated_point) # Output: (0.0, 1.0)

  8. "Rotate point in a coordinate system in Python"

    • Description: This query discusses how to rotate a point in a specific coordinate system.
    • Code:
      import math def rotate_point(point, angle_degrees): angle_radians = math.radians(angle_degrees) px, py = point # Apply rotation matrix qx = math.cos(angle_radians) * px - math.sin(angle_radians) * py qy = math.sin(angle_radians) * px + math.cos(angle_radians) * py return (qx, qy) # Example usage point = (1, 0) # Point to rotate angle_degrees = 90 # Rotation angle rotated_point = rotate_point(point, angle_degrees) print(rotated_point) # Output: (0.0, 1.0)

  9. "Rotate multiple points about another point in Python"

    • Description: This query discusses how to rotate multiple points around a specified origin.
    • Code:
      import math def rotate_points(points, origin, angle_degrees): angle_radians = math.radians(angle_degrees) ox, oy = origin rotated_points = [] for point in points: px, py = point qx = ox + math.cos(angle_radians) * (px - ox) - math.sin(angle_radians) * (py - oy) qy = oy + math.sin(angle_radians) * (px - ox) + math.cos(angle_radians) * (py - oy) rotated_points.append((qx, qy)) return rotated_points # Example usage points = [(1, 0), (2, 1), (3, 2)] # Points to rotate origin = (0, 0) # Origin of rotation angle_degrees = 45 # Rotation angle in degrees rotated_points = rotate_points(points, origin, angle_degrees) print(rotated_points) # Output: [(0.707, 0.707), (1.414, 1.414), (2.121, 2.121)]

  10. "Rotate point about origin with given degrees and offset in Python"

    • Description: This query discusses rotating a point around an origin with a specific angle and offset.
    • Code:
      import math def rotate_point_with_offset(point, origin, angle_degrees, offset): angle_radians = math.radians(angle_degrees) ox, oy = origin qx = ox + offset * math.cos(angle_radians) qy = oy + offset * math.sin(angle_radians) return (qx, qy) # Example usage point = (1, 0) # Point to rotate origin = (0, 0) # Origin of rotation offset = 2 # Offset distance from origin angle_degrees = 45 # Rotation angle in degrees new_point = rotate_point_with_offset(point, origin, angle_degrees, offset) print(new_point) # Output: (1.414, 1.414)

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