rotateZ

rotateZ is a function commonly found in 2D graphics and 3D graphics libraries and frameworks. Its primary purpose is to apply a rotation transformation around the Z-axis to a given object, point, or set of vertices. This transformation is fundamental in computer graphics for orienting objects in a virtual space.

When rotateZ is applied, it alters the orientation of an object by pivoting it around the Z-axis. In a standard right-handed coordinate system, the Z-axis typically points out of the screen or towards the viewer. A positive rotation around the Z-axis usually corresponds to a counter-clockwise rotation when viewed from the positive Z-axis. Conversely, a negative rotation results in a clockwise rotation.

The mathematical basis for rotateZ is a rotation matrix. For a point (x, y) in 2D, applying a rotation by an angle θ around the origin results in new coordinates (x', y') where x' = x * cos(θ) - y * sin(θ) and y' = x * sin(θ) + y * cos(θ). In 3D, if the rotation is purely around the Z-axis, the X and Y coordinates are transformed similarly, while the Z coordinate remains unchanged. The corresponding 3D rotation matrix for rotation around the Z-axis by an angle θ is:

[[cos(θ), -sin(θ), 0],

[sin(θ), cos(θ), 0],

[0, 0, 1]]

Implementations of rotateZ often take the angle of rotation as an argument, typically in degrees or radians. This function is a building block for more complex transformations, allowing for sophisticated scene manipulation and animation in various applications, including video games, simulations, and design software.