View Full Version : Calculation of 2D Angles ('CAST' problem)

Dr. Chris Kirtley
12-18-2002, 06:00 AM
Dear all,

Many years ago, Ray Smith and I developed a software package for
digitizing marker locations from digital movies of patients. We then
calculated the segment angles and derived the joint angles. It was
published here: Kirtley C & Smith RA (2001) Application of Multimedia to
the study of Human Movement. Multimedia Tools and Applications: 14 (3):

I recall that at the time, Ray and I were fairly new to motion analysis
and we agonized for quite some time about how to cope with the
sectorization ('CAST') problem. For example, say you have a shank
segment that's almost vertical. The ATAN function of (Yknee -
Yankle)/(Xknee - Xankle) returns the correct angle of the shank when the
angle with the floor is less than 90 degrees, but returns a negative
value when it's at more than 90 degrees. For example, 120 degrees would
come out -30 degrees.

Eventually, Ray came up with a method of laboriously checking which
sector (quadrant) the segment is in and thereby correcting the angle.
This works fine, but I have always thought that there must be a more
elegant solution. I wonder if anyone can enlighten me?

I may as well take the opportunity to wish everyone Happy holidays...

Dr. Chris Kirtley MD PhD
Associate Professor
Dept. of Biomedical Engineering
Catholic University of America
620 Michigan Ave NE, Washington, DC 20064
Tel. 202-319-6247, fax 202-319-4287
Email: kirtley@cua.edu

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