As a new human–computer interaction technology, virtual reality technology has been widely used in education, military, industry, art and entertainment, etc. Unity3D is one of the most popular virtual reality product development engines in the world. Coordinate transformation is the mathematical basis for space transformation in virtual reality technology. This paper explains the mechanism of Euler rotation causing the phenomenon of gimbal lock from the perspective of mathematical principles and derives the importance of Unity3D using quaternion for rotation calculation. Based on the Unity3D quaternion rotation calculation, the world–local coordinate transformation relationship of the child object under the Unity3D engine is deeply deduced and verified, which lays a theoretical foundation for the in-depth development of virtual reality products based on Unity3D.

中文翻译：

---

虚拟现实引擎下世界坐标与局部坐标之间关系的推导与仿真验证

作为一种新的人机交互技术，虚拟现实技术已广泛应用于教育，军事，工业，艺术和娱乐等领域。Unity3D是世界上最受欢迎的虚拟现实产品开发引擎之一。坐标变换是虚拟现实技术中空间变换的数学基础。本文从数学原理的角度解释了欧拉旋转引起万向节锁定现象的机理，并得出了使用四元数进行旋转计算的Unity3D的重要性。基于Unity3D四元数旋转计算，深入推导并验证了Unity3D引擎下子对象的世界-局部坐标转换关系，