3D Euler Angle Demonstration with Mouse-Controlled Orientation Adjustment

In this article, we present a comprehensive 3D demonstration of Euler angles where users can modify orientation through mouse interactions. We also provide detailed implementation of code for converting Euler angles to direction cosine matrices. While this process involves some complexity, we will thoroughly explain each step. First, ensure proper mouse configuration to enable 3D object rotation in the virtual space. Next, understand fundamental Euler angle concepts including their mathematical definition and three rotation representation methods (roll, pitch, yaw). The core implementation involves using transformation functions that calculate direction cosine matrices from Euler angles - typically implemented through sequential rotation matrices multiplication around X, Y, and Z axes. This conversion enables effective utilization of Euler angles for describing object rotations in computer programs, with the direction cosine matrix providing a robust mathematical foundation for 3D transformations.