Geometry of spiral galaxy arms

The previous work (He, 2001) on image analysis of over one hundred nearby galaxies indicates that for any spiral galaxy image of small inclination there is evidence of two sets of iso-ratio curves in different scales which, like curvilineal coordinate lines, expand over different galaxy components. This result sets constraint on galaxy patterns and a general equation which carries this constraint is presented in the current paper. The equation has clear geometrical meaning. Its much simplified version which applies to galaxy arms, when solved, may be a guidance to understanding galaxy patterns.