AI Generated finetuned for the visualisation and not code quality.

Interactive C + Raylib viewer for exploring how complex polynomial roots, values, and zero contours behave across a small set of preset equations. The app shows the roots on a 2D complex plane, lifts the polynomial magnitude into a colourful 3D surface, and animates a smooth morph between one preset polynomial and the next.

• Displays preset complex polynomials and their roots
• Cycles between presets with a smooth homotopy instead of a hard cut
• Matches roots between presets by angle order and best cyclic shift
• Evaluates the mixed polynomial across a dense complex grid
• Turns |p(z)| into a 3D height field so roots become visible valleys
• Draws the zero-locus curves for Re(p_t(z)) = 0 and Im(p_t(z)) = 0
• Lets you orbit the surface, zoom in, and probe any point under the mouse
• Shows an explanation panel for the currently hovered complex sample

The viewer interpolates between two preset polynomials:

p_t(z) = (1 - t) P_a(z) + t P_b(z)

It then converts the mixed value into a surface height:

height(z) = -2.25 * tanh(0.58 * ln(|p_t(z)| + 1e-6))

That gives the app three linked ways to understand the same point:

• location in the complex plane
• complex value p_t(z)
• height and colour on the rendered surface

flowchart LR
    A["Preset A Roots<br/>current equation"]
    B["Preset B Roots<br/>next equation"]
    C["Root Matching<br/>sort by argument + best cyclic shift"]
    D["Root Interpolation<br/>mixed root positions"]
    E["Polynomial Evaluation<br/>sample p_t(z) over a grid"]
    F["Height Mapping<br/>ln(|p_t(z)|) -> surface"]
    G["Contour Extraction<br/>Re=0 and Im=0"]
    H["Render Views<br/>3D surface + mini plane + probe panel"]

    A --> C
    B --> C
    C --> D
    D --> E
    E --> F
    E --> G
    F --> H
    G --> H

    classDef roots fill:#15263d,stroke:#8fd3ff,color:#f3fbff,stroke-width:2px;
    classDef match fill:#45215f,stroke:#ff9de1,color:#fff6fd,stroke-width:2px;
    classDef math fill:#173f32,stroke:#9ff5b8,color:#f3fff7,stroke-width:2px;
    classDef render fill:#5a3300,stroke:#ffd166,color:#fff8eb,stroke-width:2px;

    class A,B roots;
    class C,D match;
    class E,F,G math;
    class H render;

flowchart TB
    M["Mini Complex Plane<br/>roots and probe position"]
    S["Surface Mesh<br/>colour and height from p_t(z)"]
    C["Mirror Floor<br/>zero contours"]
    P["Probe / Hover<br/>chosen z"]
    R["Cyan Curves<br/>Re(p_t(z)) = 0"]
    I["Gold Curves<br/>Im(p_t(z)) = 0"]
    H["Height Panel<br/>z -> p_t(z) -> |p_t(z)| -> y"]

    M --> P
    P --> S
    P --> H
    S --> C
    C --> R
    C --> I

    classDef panel fill:#11243a,stroke:#8ecae6,color:#eef8ff,stroke-width:2px;
    classDef probe fill:#4f1f63,stroke:#ff99d7,color:#fff6fd,stroke-width:2px;
    classDef contour fill:#204d38,stroke:#9fe5a8,color:#f5fff6,stroke-width:2px;
    classDef detail fill:#5b3f06,stroke:#ffd166,color:#fff9ed,stroke-width:2px;

    class M,S,C panel;
    class P probe;
    class R,I contour;
    class H detail;

• z^2 + 1 = 0
• z^2 - 5z + 6 = 0
• z^4 - 1 = 0
• z^5 - 1 = 0
• z^3 - 8 = 0
• z^6 + 1 = 0
• (z-1)(z+2i)(z+1-i)=0
• z^7 - 1 = 0

These give a mix of real roots, roots on the unit circle, asymmetric configurations, and degree changes during transitions.

• q: quit
• 1: open the roots visualizer page
• 2: open the empty placeholder page
• space: pause or resume the animation
• p: advance to the next preset and start the morph

• left drag: orbit the 3D camera around the surface
• mouse wheel: zoom in or out
• hover the 3D surface: probe the corresponding complex coordinate
• hover the mini complex plane: inspect root positions or choose a custom complex sample

This repo is doing more than drawing roots as static dots. It links together:

• algebra: the factorised roots that define the polynomial
• geometry: the complex plane location z = x + iy
• analysis: the value p_t(z) and its real and imaginary zero sets
• shape: a 3D surface whose valleys reveal where the polynomial gets close to zero

That makes it easier to see how roots move, how zero contours cross, and how the local behaviour around a root changes as the polynomial morphs from one preset to another.

• raylib
• pkg-config
• a C compiler such as cc or clang

make
make run