Unital (geometry)

Template:Unclear J.M.Tienstra (1895-1951) was a professor of the Delft university of Technology where he taught the use of barycentric coordinates in solving the resection problem. It seems most probable that his name became attached to the procedure for this reason. Nevertheless, precisely when and by whom this formula was first proposed is an open question. In orienteering and surveying, the Tienstra formula is used to solve the resection problem to determine the location of a given point based on observations of known landmarks from that point.

$E_{p}={\frac {K_{1}E_{a}+K_{2}E_{b}+K_{3}E_{c}}{K_{1}+K_{2}+K_{3}}}$

$N_{p}={\frac {K_{1}N_{a}+K_{2}N_{b}+K_{3}N_{c}}{K_{1}+K_{2}+K_{3}}}$

Where:
$K_{1}={\frac {1}{cot(A)-cot(\alpha )}}$
$K_{2}={\frac {1}{cot(B)-cot(\beta )}}$
$K_{3}={\frac {1}{cot(C)-cot(\gamma )}}$

References

• http://www.vermessungsseiten.de/englisch/vermtech/positioning.htm
• 3-Point Resection Solver Using Tienstra's Method