The Coordinate Transformation Calculator is a powerful tool used to convert coordinates from one system to another. It employs mathematical formulas to accurately transform coordinates, allowing users to manipulate spatial data effectively. By inputting the original coordinates and relevant parameters such as rotation angles and translation values, users can obtain the corresponding coordinates in the new system.
Formula of Coordinate Transformation Calculator
The transformation of coordinates is governed by the following formulas:
new_x = (old_x * cos(theta)) - (old_y * sin(theta)) + translation_x new_y = (old_x * sin(theta)) + (old_y * cos(theta)) + translation_y
In these formulas:
- (old_x, old_y, old_z) are the coordinates in the original system.
- (new_x, new_y, new_z) are the coordinates in the new system.
- theta is the rotation angle in the XY plane.
- phi is the rotation angle in the XZ plane.
- (translation_x, translation_y, translation_z) are the translation values along each axis.
These formulas efficiently handle coordinate transformations, making complex spatial computations accessible to users.
General Terms Table
| Term | Description |
|---|---|
| Coordinate | A set of values that represent a point’s position in space. |
| Transformation | The process of converting coordinates from one system to another. |
| Rotation Angle | The angle by which coordinates are rotated around an axis. |
| Translation Value | The distance by which coordinates are shifted along an axis. |
This table provides a handy reference for users, offering definitions of common terms related to coordinate transformation.
Example of Coordinate Transformation Calculator
Suppose we have a point with coordinates (2, 3) in the original system. We want to rotate it by 45 degrees clockwise and then translate it by (1, 1) units along the X and Y axes. Using the Coordinate Transformation Calculator, we can determine the new coordinates as follows:
- Calculate the new_x coordinate:
new_x = (2 * cos(45°)) - (3 * sin(45°)) + 1 ≈ (1.414) - (2.121) + 1 ≈ 0.293 - Calculate the new_y coordinate:
new_y = (2 * sin(45°)) + (3 * cos(45°)) + 1 ≈ (2.121) + (1.414) + 1 ≈ 4.535
Therefore, the new coordinates are approximately (0.293, 4.535).
Most Common FAQs
A: Yes, the Coordinate Transformation Calculator supports negative coordinates, allowing users to work with points in any quadrant.
A: Rotation angles are typically specified in degrees, while translation values are in units consistent with the coordinate system (e.g., meters, feet).
A: The calculator can handle coordinates of any magnitude, ensuring flexibility for various applications.