Unleash Geometric Transformations

Explore affine transformations in 2D and 3D space. Transform points and shapes with ease and visualize the magic unfold.

Configuration

Dimension:

Select the dimension for transformation (2D or 3D).

Object (JSON Array):

Enter the object as a JSON array of points or a single point. E.g., [[1, 2], [3, 4]] for multiple 2D points or [1,2] for a single 2D point.

Transformation Matrix (JSON Array):

Enter the transformation matrix as a JSON array. For 2D, use a 3x3 matrix; for 3D, use a 4x4 matrix. E.g., [[1, 0, 0], [0, 1, 0], [0, 0, 1]] for 2D identity.

Transformed Object:

Visualization

About Affine Transformations

Affine transformations are fundamental in geometry and computer graphics, preserving collinearity and ratios of distances. They include translations, scaling, rotations, reflections, and shears. In 2D, an affine transformation can be represented by a 3x3 matrix, and in 3D by a 4x4 matrix, allowing for transformations in homogeneous coordinates.

This tool helps visualize how objects are transformed when you apply these matrices. Use it to understand geometric manipulations, from simple shifts to complex distortions. Experiment with different matrices to see real-time effects on your shapes!

For further reading, check out resources on linear algebra and geometric transformations.