orthogonality #

Shows two vectors whose angle oscillates through 90°, with a live dot-product bar that hits zero exactly at perpendicularity. In the same orthonormal (axis-aligned) basis, a moving vector v is decomposed into components c1 and c2 using dot products (c_i = e_i·v), and a tiny 2×2 Kronecker-delta grid reinforces e_i·e_j = δ_ij.

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

01.Checking perpendicular directions in geometry/physics (work = force·displacement).
02.Projecting signals onto orthonormal bases (Fourier/orthogonal transforms).
03.Extracting coordinates in an orthonormal basis for graphics, robotics, and numerical linear algebra.

technical notes #

Single-loop time-based animation (3.8–4.2s cycles) with eased highlight when |u·v|≈0. Uses snap-to-grid (4–6px) for a blocky aesthetic, green-on-black palette, and pure Canvas2D drawing (no dependencies).

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