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  • Calculation of 2D Angles ('CAST' problem)

    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):
    259-268.

    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...

    Chris
    --
    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
    http://engineering.cua.edu/biomedical/faculty/kirtley

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