The build area is essentially a Venn diagram of the maximum reach of each arm. The central, intersecting set is the build area. If the reach of an arm is less than the pillar-to-pillar spacing, then there are cutouts in the set where the arms cannot reach.You can see that as the reach of the arms increases, the build area becomes a triangle. As the reach of the arms decreases, the build area becomes a rounded triangle. There is an optimal range in the middle, where the build area is a rough hexagon (pictured above)I am assuming, in that diagram, that the arms can reach a full 180deg arc, but that may not be the case; it could be significantly less, in which case, the shape will become somewhat more complex.Here's the math for converting x,y,z to ha,hb,hc, the three pillar heights, using arbitrary placement of the pillars:A quick definition, the length of some vector, V, is the square root of the vector dotted with itself:|V| = sqrt( V.V )|V| = sqrt( Vx^2 + Vy^2 + Vz^2 )In the x-y plane:First define three vectors from the origin to each support/drive pillar: A,B,CDefine a vector from the origin to the desired location of the print head: WDefine the length of an arm: rDefine the height of each carriage on its pillar: ha, hb, hcThen the horizontal distance from each pillar to the print head is:a = |W-A|b = |W-B|c = |W-C|(note that the subtractions here are vector subtractionsIn 3D space:Then, knowing the length of the arm, each height is defined as:ha = z + sqrt(r^2 – a^2)hb = z + sqrt(r^2 – b^2)hc = z + sqrt(r^2 – c^2)Substituting to get rid of one square and one square root operation,ha = z + sqrt( r^2 – ( W-A )^2 )hb = z + sqrt( r^2 – ( W-B )^2 )hc = z + sqrt( r^2 – ( W-C )^2 )Note that ( W-A )^2 = ( Wx-Ax )^2 + ( Wy-Ay )^2 + ( Wz-Az )^2 since this is a vector subtraction and a vector square.