3D Rotations and Quaternions vs HelixPlot

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

Discover the beauty of mathematics with HelixPlot, the ultimate 3D graphing calculator for parametric equations and complex numbers. Whether you are a student visualizing calculus concepts, a teacher demonstrating vector functions, or an engineer analyzing waveforms, HelixPlot turns abstract formulas into interactive 3D visualizations instantly. ▸ REAL-TIME 3D RENDERING Type your equation and watch it come to life. HelixPlot renders parametric curves, surfaces, and complex functions in stunning 3D with smooth animations and glowing tracer effects. ▸ THREE VISUALIZATION MODES - Parametric Curves: r(t) = (x, y, z) rendered as smooth 3D tubes - Surfaces: z = f(x,y) with height-based color mapping - Complex Functions: Visualize complex numbers in 3D space ▸ 47 BUILT-IN PRESETS Explore famous equations across five scientific fields: - Mathematics: Lissajous curves, Rose curves, Archimedean spirals - Physics: Damped oscillators, Kepler orbits, Wave packets - Chemistry: Arrhenius curves, Lennard-Jones potential - Biology: Logistic growth, Michaelis-Menten kinetics - Earth Science: Tidal patterns, Seismic waves ▸ PROFESSIONAL LATEX EDITOR Input equations naturally with our visual LaTeX editor. Supports fractions, roots, integrals, Greek letters, and all standard mathematical notation. ▸ INTERACTIVE PARAMETER CONTROL Adjust constants with real-time sliders and see how parameters affect your graph instantly. Perfect for understanding mathematical relationships. ▸ MULTIPLE VIEW MODES - Diagram View: Full 3D perspective with projection shadows - Quad View: See 3D + XY + XZ + YZ planes simultaneously - Projection Planes: Customizable colors and transparency ▸ ANIMATION PLAYBACK Watch curves draw themselves with smooth animations. Control playback speed (0.5x to 5x), scrub through time, and track coordinates in real-time. ▸ EXPORT & SHARE - Save high-resolution PNG images for reports and presentations - Generate shareable links so others can view your exact visualization - Copy equation code for use in other projects ▸ CUSTOMIZATION - Light and Dark themes - Customizable projection plane colors - Adjustable grid, axis labels, and tick marks ▸ OPTIMIZED PERFORMANCE - Web Worker parallel processing for smooth UI - GPU-accelerated rendering with custom shaders - Handles complex equations without lag PERFECT FOR: - Students learning trigonometry, vectors, and calculus - Teachers creating visual demonstrations - Researchers generating publication-quality graphics - Artists exploring mathematical beauty HelixPlot brings the hidden beauty of mathematics to your fingertips. Download now and see equations like never before.