Limb Length Determinations Using 3D coordinates

by Edward Frank and Robert Leverett

The length of a limb segment can be determined by measuring the position of the end points of the branch in 3-dimensional space from an external reference position. The length is then calculated by applying Pythagorean’s Theorem. The following diagram illustrates the process.

From the external reference position O, the direct distance to L1 is measured to P1 along with the vertical angle V1 and azimuth A1. The coordinates x1, y1, and z1 are then computed. The same process is followed for P2.

This sequence is carried out as follows:

1) The horizontal distance d1 from the initial reference point O to a target point P1 is computed as d1 = cos(inclination) x laser distance = L1sinV1

The value of x at the first point is: x1 = sin(azimuth) x horizontal distance = d1sinA1

The value of y at the first point is: y1 = cos(azimuth) x horizontal distance = d1cosA1

The value of z at the first point is: z1 = sin(inclination) x laser distance = L1sinV1

This process is repeated for P2 to get x2, y2, z2

The final step is to compute the distance from P1 to P2 (L) using the following formula.

L = [(X2-X1)2+(Y2-Y1)2+(Z2-Z1)2] 1/2

Note that we are squaring the changes in the x, y, and z values, adding these squares together and taking the square root of the sum.