Unlock the power of linear transformations with our online Matrix Transformation Calculator. Easily apply scaling, rotation, translation, and shearing operations to 2D matrices or sets of points. Ideal for students, engineers, and developers working with linear algebra, computer graphics, or geometric transformations. Simplify complex matrix operations instantly and visualize their effects.
Formula:
Matrix transformations modify the elements of a matrix or coordinates of points, applying operations like scaling, rotation, translation, or shearing. For a 2D transformation using homogeneous coordinates (x, y, 1), the general process involves multiplying an original point vector by a 3x3 transformation matrix (T):
P' = T * P
- P is the original point vector (e.g.,
[x, y, 1]T) - P' is the transformed point vector (e.g.,
[x', y', 1]T) - T is the 3x3 transformation matrix, which varies based on the type of transformation:
- Scaling (by sx, sy):
[[sx, 0, 0], [0, sy, 0], [0, 0, 1]] - Rotation (by θ degrees):
[[cos(θ), -sin(θ), 0], [sin(θ), cos(θ), 0], [0, 0, 1]] - Translation (by tx, ty):
[[1, 0, tx], [0, 1, ty], [0, 0, 1]] - Shearing (by shx, shy):
[[1, shx, 0], [shy, 1, 0], [0, 0, 1]]
- Scaling (by sx, sy):