Matrix for orthographic projection, Computer Graphics

Matrix for Orthographic Projection

Orthographic projections are projections into one of the coordinate planes x=0, y=0or z=0. The matrix for orthographic projection on the z=0 planes that is xy-plane as:  

1965_Matrix for Orthographic Projection 2.png

Remember here that the third-column i.e. z-column in this matrix is all zeros. For orthographic projection on the z=0 plane, such the z-coordinates of a position vector is set to zero. Correspondingly, we can also obtain the matrices for orthographic projection on the x=0 and y=0 planes as given below:

2065_Matrix for Orthographic Projection.png

For illustration, seems the object specified in Figure. The orthographic projections of this object on the x=0, y=0 as well as z=0 planes from center of projection at infinity on the +x-, +y- and +z-axes.

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