Geometric Rotation Tool
Visualize and calculate the rotation of geometric objects around a central point.
Input Parameters
Enter the coordinates of the object, the rotation center, and the rotation angle to perform the rotation.
Enter coordinates as comma-separated values or a JSON array.
Specify the point around which to rotate.
Enter angle in degrees (deg) or radians (rad).
Rotated Object Coordinates:
Rotation Visualization
Understanding Geometric Rotation
Geometric rotation is a fundamental transformation in geometry where an object is moved in a circular motion around a fixed point, known as the center of rotation. The object turns through a specified angle, maintaining its shape and size.
In 2D space, rotation can be defined by the rotation center (a point) and the angle of rotation. Positive angles denote counter-clockwise rotation, while negative angles indicate clockwise rotation.
This tool helps visualize and calculate the new coordinates of a shape after rotation, which is useful in various fields like computer graphics, engineering, and mathematics for spatial reasoning and design.
Formula
For a point (x, y) rotated by an angle θ around the origin (0, 0), the new coordinates (x', y') are given by:
- x' = x * cos(θ) - y * sin(θ)
- y' = x * sin(θ) + y * cos(θ)