本研究針對過去四面體元素接觸判斷的相關論文中接觸形態分類進行了歸納整理，新增了針對面對面與稜邊對面的接觸判斷方式，並將接觸形式判斷流程樹狀圖可清楚的展示判斷過程和知道不同的判斷過程所可以到達的分支結果。本研究中以C++程式語言編寫模擬程式，並以物件導向程式的設計方式去建立程式架構，釐清程式裡各個類別物件之間的關係，並為後續的程式擴增與修改增加了方便性，讓此架構可以成為之後離散元素接觸判斷的程式基礎架構。
本論文在多個多面體之間的接觸碰撞判斷，將多面體離散成四面體元素之集合，兩個多面體的接觸判斷就可以看成是兩組四面體元素群之間的接觸判斷。而四面體元素群中需要接受接觸判斷的只有位在多面體外表面的頂點、稜邊與面，所以經過篩選，將位在多面體內部的內接面排除在判斷過程外，簡化計算流程。
四面體元素之間的接觸可劃分為六類，頂點對面、頂點對稜邊、頂點對頂點、稜邊對面、稜邊對稜邊與面對面，而這些分類中又可以分為一般情況與特殊情況兩類，一般情況是指自然碰撞中最常發生的情況，有頂點對面與稜邊對稜邊這兩種情況，而這種情況也是本研究其他四種接觸判斷理論的基礎判斷。

This research summarizes the classification of contact morphology in related papers on the contact judgment of tetrahedral elements in the past, and added new judgment methods for face-to-face judgment and edge-to-face judgment. The entire judgment process is drawn as a tree diagram, so that people can clearly see the judgment process and know The branch results that can be reached by different judgment processes. In this study, the simulation program was written in C++ programming language, and the program structure was established by the design method of object-oriented program, to clarify the relationship between the various types of objects in the program, and to increase the convenience for subsequent program expansion and modification. This structure can become the program infrastructure for subsequent contact judgments of discrete elements.
In this paper, the contact and collision judgment between multiple polyhedrons is to discretize the polyhedron into tetrahedral elements. The contact judgment of two polyhedrons can be regarded as the contact judgment between two groups of tetrahedral element groups. In the tetrahedral element group, only the vertices, edges, and faces on the outer surface need to be judged by contact. Therefore, after filtering, the inscribed faces inside the polyhedron are excluded from the judgment process, simplifying the calculation process.
The contact between tetrahedral elements can be divided into six categories, vertex-to-face, vertex-to-edge, vertex-to-vertex, edge-to-face, edge-to-edge and face-to-face, and these categories can be divided into general cases and special cases. Two types, the general cases refer to more frequently occurring cases in natural collision, there are two cases of vertex-to-face and edge-to-edge, and thess cases are also basic judgments of the contact judgment theory in this research. Other special contact cases are only after special conditions are met.

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