Interactive 3D Euler Angles Demonstration with Mouse-Controlled Orientation

In 3D computer graphics, Euler angles serve as a fundamental rotation representation method, using three angles (typically pitch, yaw, and roll) to define an object's spatial orientation. To provide an intuitive understanding of Euler angle rotation effects, interactive 3D demonstration tools enable dynamic adjustment of these angles through mouse interactions, allowing real-time manipulation of object orientation through mouse operations.

The core implementation involves converting Euler angles to a direction cosine matrix for application in 3D model transformations. The direction cosine matrix is a 3x3 matrix where each column represents the directional vector of rotated coordinate axes in the original coordinate system. This conversion ensures mathematical accuracy in rotations while delivering smooth interactive performance. The implementation typically uses matrix multiplication operations where the final transformation matrix is computed as R = Rz(ψ) * Ry(θ) * Rx(φ) for ZYX rotation order.

Through mouse operations (such as dragging or sliding), users can dynamically adjust Euler angle values in real-time, with the 3D model responding immediately to demonstrate how different angle combinations affect object orientation. This interactive learning approach not only helps understand the physical significance of Euler angles but also assists developers in debugging and validating rotation-related algorithms. The implementation typically captures mouse delta movements and maps them to angle increments using sensitivity parameters, updating the rotation matrix on each input event for fluid visual feedback.