> I will take some times to see your code.
> If I understand, the point D is not in the same plane as the triangle,
> the torus is - but I may be wrong - the equator of the sphere on which D
> is.

Correct - D is NOT in the same plane of the triangle.  It is a point H units
away from the triangular plane.
#declare PointD  =  vtransform (Middle, transform {translate Normal*Height});

The center you are using, the "centroid"
#local TMC = Triangle_Mass_Center(Corner_A_1, Corner_A_2, Corner_A_3);
is not the center used for finding the tangent circle.

The "circumcenter"
#declare Middle =  Triangle_M_out (Corner_A_1, Corner_A_2, Corner_A_3);
is the one to use - it also happens to lie on the midpoint between Corner_A_1
and Corner_A_3, because it is is a right triangle, and so it bisects the
hypotenuse.

I think maybe the rotation vectors I'm using are incorrect, or the trigonometry
is off, but I cannot see how.   Hopefully I can do more to understand what is
wrong tonight.

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