Don't worry, I learned how to solve it now. since you can find the projection matrix pretty easily then you just plug in the values from the given vector, here W (unit vector of v) the squares cancel the square roots and you're left with that matrix in solution P. But i was wondering how do you add a matrix into the text?StoneTemplePython said:
##P = \mathbf{ww}^T = \frac{1}{5}\begin{bmatrix}UOAMCBURGER said:
A projection matrix is a square matrix used to transform points in a three-dimensional space onto a two-dimensional plane. It is important because it allows us to represent 3D objects on a 2D surface, which is useful for computer graphics and other applications.
To calculate a projection matrix, you need to know the dimensions of the 3D space and the plane onto which you want to project the points. The projection matrix is a combination of a translation matrix and a scaling matrix, which can be calculated using the coordinates of the points and the dimensions of the space and plane.
A projection matrix is always a square matrix with a size of (n+1)x(n+1), where n is the number of dimensions in the 3D space. It is also an idempotent matrix, meaning that when multiplied by itself, it results in the same matrix. Additionally, the determinant of a projection matrix is always 0.
In computer graphics, a projection matrix is used to transform 3D points onto a 2D screen for display. This is essential for creating realistic 3D images and animations in video games, movies, and other digital media. It is also used for various rendering techniques, such as perspective and orthographic projections.
A perspective projection matrix creates the illusion of depth by making objects appear smaller as they move farther away from the viewer. On the other hand, an orthographic projection matrix does not take distance into account and keeps the size of objects consistent, resulting in a more flat and distorted image. Perspective projection is commonly used in most 3D rendering applications, while orthographic projection is often used for technical drawings and engineering applications.
