Rotation Formula:
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Rotation around a point is a geometric transformation that moves a point around a fixed center by a specified angle while maintaining the distance from the center. This operation is fundamental in computer graphics, robotics, and physics.
The rotation formula consists of three steps:
Where:
Explanation: The formula translates the point to the origin, performs the rotation, then translates back to the original center.
Details: Point rotation is used in computer graphics for object transformations, in robotics for joint movements, in physics for angular motion calculations, and in game development for character movements.
Tips: Enter the point coordinates, rotation center coordinates, and rotation angle in degrees. The calculator will automatically convert the angle to radians and compute the new position.
Q1: What's the difference between rotation around origin and arbitrary point?
A: Rotation around origin is simpler (xc=0, yc=0). Rotation around arbitrary point requires the full translation-rotation-translation process.
Q2: Does the rotation angle direction matter?
A: Yes, positive angles typically represent counter-clockwise rotation, while negative angles represent clockwise rotation.
Q3: Can this be extended to 3D rotation?
A: Yes, but 3D rotation requires more complex mathematics using rotation matrices or quaternions.
Q4: How precise are the calculations?
A: The calculator provides results rounded to 4 decimal places, sufficient for most applications.
Q5: What if I need multiple rotations?
A: You can chain rotations by using the output of one rotation as input to the next rotation calculation.