create a program using the graphics.h library in C or C$++$ to perform and visualize a perspective projection of a $3$D cube. The program should:

Input the Cube's Coordinates:

You define the vertices of a cube in $3$D space.

Perform Perspective Projection:

Use a projection matrix to map the $3$D points of the cube onto a $2$D plane. The projection matrix should depend on:

The projection plane $($defined by three points$).$

The center of projection $($COP$).$

The distance $($d$)$ between the COP and the plane.

Find Plane Equation and Projection Matrix:

Create a function to calculate the equation of a plane given three points in $3$D space. Find a reference point RRR in the plane to facilitate the calculation of the projection matrix. Generate the perspective projection matrix.

Calcul vanishing points

Visualize the Cube:

Draw the transformed cube on the screen after applying the perspective projection. Add vanishing points to the visualization to show the effect of perspective.

create an example using the parameters in the image below which are center of projection is the origin $,$plane is the cube diagonals $,$ distance d$=10$

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