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We have the real system coordinates with the observer placed in the points .The projection screen plane is placed in and the screen coordinates are . We have for simplicity the coincidence within the axis and

We can transform from the real to the screen coordinates via the formulas:

Triangle decomposition

The extremes of the triangle chord have equations: and with

A point of the chord has equation : with .

So ,developing the calculus:

These are the barycentric coordinates of the point in the triangle: with

Edge walking

(A) Divide the triangle into 2 triangles with a common side parallel to the X axis.
You must identify by the y coordinate an upper corner (U) ,lower corner (L) and middle corner (M) ,then locate the second middle point (M')

(B) For each triangle locate on the edges wich are not in common a start point (S) and an end point (E) with the same Y coordinate.Then you can easily manage every pixel from S to E.

Axonometric projection

I use an oblique projection,where the projection plane for simplicity coincide with the real plane , with and .

The real point is mapped in the projection point via the formulas:

Where and are the measure unit on the projection axes , and is the angle between the projection of the x and z axes,and are the coordinate of the projection of the real origin O.