Self-Intersection Detection for Fourier Polynomial Curves via Polyline Approxima

This example demonstrates how to locate self-intersecting points on a planar curve generated from a Fourier-type polynomial (parametric Fourier construction) using a polyline (piecewise linear) approximation. The key phenomenon is that, after discretizing the parameter and connecting consecutive samples into line segments, self-intersections can be detected where different segments cross. It focuses on parameterized curve evaluation, Fourier coefficients/synthesis, discretization with a parameter sequence, and geometric segment–segment intersection logic (secant/chord-like comparisons) to produce and filter candidate intersection points. The GeoGebra construction relies on commands and structures such as CurveCartesian to build the curve, Sequence to generate the sampling parameter t, Element to access corresponding constructed quantities, and utilities like Div, Mod, LaTeX for indexing/formatting. Conditional logic (if, rf, and related parameters such as n0, q_fc, mod_fc) is used to decide which segment pairs are relevant and to filter valid intersection points. Lists like lPoints_y, lPoly_y, and lX_y organize polyline segments and the resulting intersection data for visualization. Suitable for advanced high school, university pre-calculus/engineering math, computational geometry, and graphing-focused learning or projects.