The Chord Length Distribution Function Of The Changing Convex Domain

Integral Geometry is a subject which originated from the famous problem of Buffon needle.Another called of Integral Geometry is Geometric Probability, belonged to the category ofdifferential geometry essentially, with the natures that investigating of a graphic through avariety of integral. The development has always been linked with geometric probability. The ideaof Integral Geometry is to use the methods of probability to discuss convex body and geometry.The application and development have relationship with algebra, partial differential equation,geometric analysis, convex geometry, geometric inequality and so on. A lot of elderships made agreat contribution to geometry, such as Santalo, Yan Zhida, Wu Daren, Ren Delin.The chord length distribution function of convex domain is one of the most importantsubjects of convex body theory. It has much application background such as Pattern Recognition,Statistical analysis of materials. But now, there is not provide a unified approach to obtain thechord length distribution function for convex domain in existing literature. In this paper we takeregular hexagon for example to discuss the approach to calculate the exact analytical formula ofchord length distribution function in using generalization support function technique and limitedchord function. The method provided in this paper is simple and innovative. Also do a littlepromotion that the studying of chord length distribution function in a stretching regular hexagonon the basis of regular hexagons, and get the appropriate results, while later studies onhigh-dimensional convex bodies have laid the foundations of chord length distribution function.