Triangle Area Representation for Profiled Fiber Shape

A multi-shape representation approach for measuring geometrical properties of profiled fibers was presented.From closed edge chains of a fiber cross section,three evenly spaced vertices were selected to form a triangle by changing the vertices＇ spacing,or the step length,the Triangle Area Representation（TAR）was calculated with a special determinant.The bend direction of the two consecutive lines drawn by three vertices determined the sign of the TAR.TARN and TARP were negative and positive extensions of TAR,and used to analyze concave and convex segments on the boundary.The length of TARN measured the size of concaveness.Multi-scale TARPs together with TARN can help to detect fiber conglutinations.