projiceringsmatris

A projection matrix, often referred to as a "projection matrix" or "projection transformation matrix," is a mathematical tool used in computer graphics and linear algebra to transform vectors or points from one coordinate system to another. It is typically a 4x4 matrix used in 3D graphics to project 3D coordinates onto a 2D plane, such as a computer screen.

The projection matrix is used to perform perspective or orthographic projection. In perspective projection, objects that are farther away appear smaller, mimicking the way the human eye perceives depth. Orthographic projection, on the other hand, maintains the size of objects regardless of their distance from the viewer, which is useful in applications like architectural drawings or engineering blueprints.

The projection matrix is derived from the camera's position, orientation, and field of view. It is used in the rendering pipeline to transform the vertices of 3D models from world space to screen space. The resulting 2D coordinates are then used to rasterize the model onto the screen.

In linear algebra, a projection matrix is a square matrix that projects a vector onto a subspace. It is an idempotent matrix, meaning that applying the projection matrix twice to a vector yields the same result as applying it once. Projection matrices are used in various applications, including signal processing, data analysis, and machine learning.