1. To get the exact YPOS of the point on a heightmap, a little bit of trigonometry is needed. Try to draw it on a paper from the front and side view and you should come up with the equations pretty easily yourself (it's just a basic trig - sin/cos and pythagoras)

2. You can also do an approximation through lerping - which works well most of the time (unless the difference in slope between two neighbouring tris is too big).

- Calculate the DeltaY1 for points A,B : DeltaY1 = B.YPOS - A.YPOS

- calc. DeltaY2 for points A,C. DeltaY2 = C.YPOS - A.YPOS

- for a point P, on the triangle ABC:

- PctX = (P.XPOS - A.XPOS) / (B.XPOS-A.XPOS)

- PctZ = (P.ZPOS - A.ZPOS) / (B.ZPOS-A.ZPOS)

- Y1 = A.YPOS + PctX*DeltaY1

- Y2 = A.YPOS + PctZ*DeltaY2

- final YPOS = Y1 + (Y2-Y1)/2