See also: Geometric Linear Transformation (2D), matrix, Simultaneous Linear Equations
The calculator below will calculate the image of the points in three-dimensional space after applying the transformation.
The above transformations (rotation, reflection, scaling, and shearing) can be represented by matrices. To find the image of a point, we multiply the transformation matrix by a column vector that represents the point's coordinate.
The transformation matrices are as follows:
Type of transformation | Transformation matrix |
---|---|
Clockwise rotation by an angle about the origin | |
Counter-clockwise rotation by an angle about the origin | |
Reflection against the -axis | |
Reflection against the -axis | |
Scaling (contraction or dilation) in both and directions by a factor | |
Horizontal shear (parallel to the -axis) by a factor | |
Vertical shear (parallel to the -axis) by a factor |
Examples:
Rotate point clockwise about the origin by an angle .
Reflect point against the -axis.
See also: Geometric Linear Transformation (2D), matrix, Simultaneous Linear Equations