ACE (Breiman & Friedman, 1985) estimates transformations of the response Y and the predictors X so that an additive model fits as tightly as possible:

Θ(Y)  ≈  Σ_j Φ_j(X_j)

For the single-predictor example Y = exp(sin X), the slider walks through the geometry:

1. the raw data on the front face;
2. its conditional-expectation smooth E[Y | X];
3. the predictor transform Φ(X) laid flat on the floor;
4. an additive surface raised vertically over that floor curve;
5. the smooth projected onto the surface at height Θ(Y);
6. and, read on the right face, the linearized Θ(Y)–Φ(X) line.

The very visual projection reading of the algorithm I learned from Clara MJJ. Roth, thank you.