3D Rotations and Quaternions vs ER3D Euler Rotations in 3D

3D Rotations and Quaternions is an interactive tool for users who work with 3D orientation math in graphics, roboticsor simulation. It provides precise computations, clean visualizations, and fast conversions between the standard rotation representations. Features include: • Conversion between Euler angles, axis–angle, quaternions, and rotation matrices • Interactive 3D visualization and rotation animation • Quaternion interpolation (LERP and SLERP) • Rotation of user-defined points by user-defined quaternions • Determination of a quaternion that rotates vector v into vector w • Composition of up to 10 sequential quaternion rotations • Quaternion generation from constant angular velocity and time • Reflection of a point across a plane Feedback and suggestions: graphmath@aol.com

Three-dimensional (3D) rotational kinematics are one of the most important, and yet also one of the most easily misunderstood topics of advanced mechanical engineering dynamics and trajectory simulation modeling. The ER3D mobile app aims to be a teaching aid for students and interested learners who want to understand these fundamental kinematics in an interactive and visually appealing setting, including in Augmented Reality (AR). Features of the app include: - Space Shuttle model for teaching a 3-2-1 rotation sequencee - Gyroscope model for teaching a 3-1-3 rotation sequence - Sliders to update 3-2-1 (yaw, pitch, and roll) or 3-1-3 (procession, nutation, and spin) angles - Globe Earth that may be rotated to visualize locations at different latitudes and longitudes - Context menus with text descriptions of the kinematic properties ER3D is free and open source, developed for iPhone, iPad, macOS, and VisionOS using SwiftUI and RealityKit.