Discrete Fourier Transform: Draw Your System of Epicycles
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This example demonstrates how to decompose any hand-drawn curve into a system of rotating circles (epicycles) using the Discrete Fourier Transform (DFT), and reconstruct the original shape in real time. Core mathematical concepts include Fourier series, complex numbers, frequency-domain decomposition, and parametric curve fitting. Construction highlights: GeoGebra buttons (button1-4) control drawing and clearing, a condition (cond) or slider adjusts the number of epicycles, userdraw captures the hand-drawn path, and text objects (text1, txtError) display error metrics. Suitable for high school to university students studying signal processing, complex analysis, or mathematical modeling, as well as for visual demonstrations of the geometric meaning of Fourier transforms.
GeoGebra Commands & Parameters
Boolean txtError(false)false{}false
AI Drawing Prompt Reference
Draw a curve composed of multiple rotating circles, which decompose a hand-drawn path using the Discrete Fourier Transform. Control drawing and clearing with four buttons, and adjust the number of circles with a slider. The hand-drawn path is captured by userdraw, and a text object displays the reconstruction error.
The prompt above was compiled from the original drawing commands and is for reference only.