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References: Polar Coordinates, Oscillation & Easing

  1. Polar coordinate system - Wikipedia - Two-dimensional coordinate system defined by radius and angle, including conversion formulas to Cartesian coordinates. Vital for spiral generation, radial symmetry, and circular particle rings.

  2. Atan2 - Wikipedia - Mathematical and computational derivation of the two-argument arctangent function, resolving quadrant ambiguities. Fundamental for calculating directional heading angles toward target points in interactive systems.

  3. Lissajous curve - Wikipedia - Parametric curves generated by orthogonal sinusoidal inputs with varying frequency ratios and phase shifts. Invaluable for creating intricate harmonograph patterns and oscilloscope generative sketches in p5.js.

  4. The Animator's Survival Kit: A Manual of Methods, Principles and Formulas for Classical, Computer, Games, Stop Motion and Internet Animators - Richard Williams - Faber and Faber - Williams formulated the foundational slow-in and slow-out easing principles, providing the classic visual timing charts that inspire computational easing curve algorithms in interactive animation.

  5. Foundation Actionscript 3.0 Animation: Making Things Move! - Keith Peters - Friends of ED / Apress - Peters pioneered the canonical Spring and Easing code algorithms for interactive designers, reducing complex calculus into intuitive proportional velocity formulas for interactive visual projects.

  6. Polar Coordinates in p5.js - The Coding Train - Visual video lesson demonstrating how radius and theta convert via x = r * cos(theta) and y = r * sin(theta) to create spirals, orbital motion, and algorithmic flowers.

  7. Easing Functions Cheat Sheet - Andrey Sitnik & Ivan Solovev - Interactive visualization and mathematical formulas for quadratic, cubic, elastic, and bounce easing curves with copy-paste JavaScript snippets for smooth UI animation and motion graphics.

  8. Understanding atan2() and Directional Rotation - MDN Web Docs - Technical guide explaining Math.atan2 parameter order, return range in radians (-PI to PI), and practical applications for tracking mouse cursor angles accurately in graphics.

  9. Harmonograph and Lissajous Curve Generator - Walking Randomly - Mathematical exploration of mechanical harmonographs, phase offsets, and decay envelopes for plotting complex resonant waveforms in procedural code sketches and generative patterns.

  10. p5.js Trigonometric Calculations Reference - p5.js Foundation - Documentation for atan2(), angleMode(DEGREES/RADIANS), and polar math functions used to position elements radially around a center point on the interactive canvas viewport.