Circle Inversion Calculator
Calculate the inversion of a point or geometric object with respect to a circle online. Visualize the transformation and understand circle inversion in geometry.
How to Use Circle Inversion Calculator
- Object: Input the object to be inverted. You can enter a point as 'x,y' (e.g., '1,2') or a JSON object for more complex shapes (e.g.,
{"type": "point", "x": 1, "y": 1}or[{"type": "point", "x": 1, "y": 1}, {"type": "point", "x": 2, "y": 2}]for multiple points or lines). - Circle Center (X, Y): Specify the coordinates of the center of the inversion circle. Default is (0,0).
- Circle Radius: Enter the radius of the inversion circle. Must be a positive number. Default is 2.
- Click 'Calculate' to perform the inversion. The inverted object will be displayed below, and visualized on the canvas.
- Use 'Reset' to clear all inputs and start fresh.
- Click 'Copy' to copy the JSON output of the inverted object to your clipboard.
Enter a point as 'x,y' or a JSON array of points/objects.
Inverted Object (JSON):
Visualization:
About Circle Inversion
Inversion in a circle is a transformation of the plane that "inverts" points with respect to a given circle. Specifically, for a circle centered at O with radius r, the inversion of a point P is a point P' on the ray OP such that the product of the distances from the center O to P and P' is equal to the square of the radius, i.e., OP ⋅ OP' = r2.
Points closer to the center of the circle are mapped to points farther away, and vice versa. Points on the circle are mapped to themselves. Inversion in a circle is a fundamental concept in geometry and has applications in complex analysis, physics, and computer graphics. This tool helps visualize and calculate this transformation for points and geometric objects.
For further reading, you can explore resources on Inversive Geometry on Wikipedia.