八叉树编码的三维物体截面之比计算

Calculating the Ratio of Section′s Area of 3D Object in Octree Coding

三维物体截面面积之比反映了形体几何结构，是一种常用的指标，不同三维形体编码方式采取的截面面积估算方法不同。本文提出了空间八叉树编码表示的三维物体截面面积之比的计算方法，根据截面轴的类型分两种方法进行讨论，一种是垂直于坐标轴的截面；一种是垂直于任意方向轴的截面。两种方法都要进行八叉树到截面四叉树的转换。第一种转换直接通过遍历八叉树而生成特殊截面四叉树；第二种方法根据截面轴的方向，将八叉树进行三维变换，使截面轴与某个坐标轴重合，从而产生新的八叉树，然后利用第一种方法，产生截面四叉树，最后计算截面面积之比。

The ratio of section′s area of 3D object may describe the geometric structure and it is a index in common use. The calculation method is different in different coding. This paper presents a way for calculating the ratio of section′s area of 3D object in octree coding. The two kinds of methods based on the type of section′s axis are discussed. The one is the axis perpendicular to coordination axis and the other is in any direction. The two methods need the transformation from octree to section quadtree. The first method directly traverse the octree, the second is to rotate and move the octree for that the axis of section coincide with coordination axis and then it produces a new octree,then produces section quadtree by the first method. The ratio of section′s area is calculated from section quadtree.