Shear Matrix Generator
Create shear transformation matrices for 2D and 3D spaces. Visualize the shear effect and easily copy the resulting matrix.
Shear Parameters
Resulting Shear Matrix
Shear Visualization
Visual representation of the shear transformation applied to a square. Original shape in blue, sheared shape in coral.
About Shear Matrix
In linear algebra, a shear matrix is a transformation matrix that distorts shapes by shifting points parallel to an axis or plane, while keeping the axis or plane fixed. It's like tilting a stack of cards – the base remains in place, but the top shifts. Shear matrices are fundamental in computer graphics, geometric modeling, and various engineering applications. They are defined by a shear factor and the axis or plane along which the shear is applied. For example, in 2D, shearing along the x-axis changes the x-coordinates proportionally to the y-coordinate, and vice versa for shearing along the y-axis. In 3D, shear can occur along axes or planes, offering more complex transformations.
- 2D Shear along X-axis: [[1, s], [0, 1]], where 's' is the shear factor.
- 2D Shear along Y-axis: [[1, 0], [s, 1]], where 's' is the shear factor.
- 3D Shear along X-axis: [[1, 0, 0], [0, 1, 0], [s, 0, 1]].
- 3D Shear along XY-plane: [[1, 0, 0], [0, 1, s], [0, 0, 1]].
Learn more about shear matrices on resources like Wikipedia and Khan Academy's linear algebra sections.