How your 3D PCA coordinates are computed

Every user receives three principal-component coordinates (PC1, PC2, PC3) that place them in the same 3D space as the reference populations and as every other Haeckel user. The coordinates power the "Genetically Similar" recommendations, the Networks 3D visualisation, and the kinship heuristics that precede full KING-robust inference.

Centroid-based projection

The reference panel contains pre-computed PCA centroids for each of the reference subpopulations, derived from a one-time PCA on the full reference VCF. Each user's coordinates are the weighted average of the relevant centroids, weighted by the user's inferred ancestry components.

A user who is 70% European and 30% East Asian sits at 0.7 × EUR_centroid + 0.3 × EAS_centroid in 3D space. An admixed user with components across many populations sits at the appropriate convex combination. The centroids themselves were placed so that the 3D Euclidean distance between any two of them is calibrated against the published Fst between those two reference populations, which means that pairwise distances between users approximate √Fst.

Jitter for visualisation only

Two users with identical inferred ancestry would otherwise project to exactly the same 3D point. To prevent visual overlap in the Networks 3D scene, the projector adds a small isotropic jitter (default magnitude 0.02) to the coordinates used for rendering. The unjittered coordinates are stored separately and used for any quantitative comparison such as kinship pre-screening.