Limb Length Using 3D coordinates

General discussions of measurement techniques and the results of testing of techniques and equipment.

Moderators: edfrank, dbhguru, edfrank, dbhguru

#1)  Limb Length Using 3D coordinates

Postby edfrank » Fri Mar 29, 2013 5:57 pm

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.

               
                       
XYZ Coordinates.gif
                                       
               


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.
"I love science and it pains me to think that so many are terrified of the subject or feel that choosing science means you cannot also choose compassion, or the arts, or be awe by nature. Science is not meant to cure us of mystery, but to reinvent and revigorate it." by Robert M. Sapolsky
User avatar
edfrank
Site Admin
 
Posts: 4101
{ IMAGES }: 0
Joined: Sun Mar 07, 2010 6:46 pm
Location: Reynoldsville, Pennsylvania, USA
Has Liked: 823 times
Has Been Liked: 600 times
Blog: View Blog (3)
Print view this post

Return to Measurement and Dendromorphometry

Who is online

Users browsing this forum: No registered users and 1 guest

cron