Become as Skilled as Iq in Distance Functions and Shapes

Become as Skilled as Iq in Distance Functions and Shapes

Become as Skilled as Iq in Distance Functions and Shapes

  1. Solidify the mathematical foundations

    Signed Distance Functions (SDFs) are grounded in geometry, not mere tricks. Deepen these areas:

    • Euclidean geometry (distance formulas for points, lines, circles, spheres)
    • Analytic geometry (equations and distances for planes, lines, circles, ellipses)
    • Linear algebra (projections, rotation matrices, orthonormal bases)
    • Metric spaces & norms (not only L2, but also L1, Lp, etc.)

  2. Master an SDF “repertoire”

    Iq’s strength is combining a vast library of shape SDFs. Grow your repertoire in this order:

    1. Primitives: sphere, box, cylinder, torus
    2. Transforms: translation, rotation, reflection, scaling
    3. Composition: min (union), max (intersection), smooth-min (smooth union)
    4. Applications: metaballs, repetition (tiling via mod), folding (fractalization)

  3. Bridge theory and implementation

    • Theoretical: prove/derive general forms for distance functions (e.g., point–plane distance via a normal dot product).
    • Practical: render SDFs in GLSL or p5.js (advance a ray and draw the hit point via ray marching).

  4. Trace the history and ideas

    Understanding the lineage before and after Iq deepens insight:

    • History of geometry (Euclid, Descartes, Gauss)
    • Evolution of computer graphics (Blinn’s implicit surfaces, Perlin noise)
    • Modern SDF uses (game collision, font rendering, physics simulation)

  5. Practical ways to learn

    • On Shadertoy, copy and modify code by Iq and other authors.
    • In p5.js, try 2D SDFs to build the intuition of “drawing with a distance field.”
    • Study with both math and CG books:
      • Math: Convex Optimization (Boyd); Geometry and the Imagination (Hilbert)
      • CG: Ray Tracing in One Weekend (Peter Shirley); Real‑Time Rendering (Akenine‑Möller)

  6. Build thinking habits

    Keep asking: “How can I express any given shape as a distance function?” Examples:

    • Star shape → min over several rays
    • Heart shape → combine a circle with a sine function
    • Outline of the Japanese archipelago → a circle SDF distorted with noise

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