Derivation and simulation verification of the relationship between world coordinates and local coordinates under virtual reality engine

Yan-An Yao, Zhibin Du, Xiaoyan Huang, Ran Li

Abstract: 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.