SAMPLING → TRANSPORT
Check the weights. Check the total.
Two browser-recomputed references connect chapters 3, 6 and 7. Each control evaluates the displayed equations immediately; no animation advances a hidden fluid solver.
01 / 02
Put the sample on its own lattice
Inspect eight donors of q(x,y,z) = 1.2 + 0.7x − 1.1y + 0.4z. Select cell, x-, y- or z-face storage, then move the sample. The physical grid spacing stays (0.2, 0.3, 0.4).
Predict, then compare
Matching lattice offsets reproduce the direct affine value to roundoff. Now keep x-face storage and use a cell-centre sampling offset: the signed error becomes −0.07. Positive weights summing to one do not detect this geometry mistake. Orange marks the requested point; the teal point is the weighted donor position. They coincide only with the matching offset.
Scope. This browser recomputes the existing companion affine fixture with a complete regular stencil. It does not test obstacle extensions, native sampling execution or IEEE proof obligations. The donor table exposes all eight weights and values.
02 / 02
Bound the result, then check its total
Compare the linear departure sample, an unlimited forward/backward correction, and replacement by the linear value whenever the correction leaves its two-donor bounds. With the six-sample symmetric edge and Courant 0.5, predict the overshoot before inspecting the curves.
Predict, then compare
The raw result reaches −0.125 and 1.125; two cells fall back. Now use the asymmetric edge at Courant 0.25: one fallback restores bounds, but the sum changes from 1.6 to 1.61875. Range preservation is not conservation. Try smooth sine, 64 samples, Courant 0.5 and 128 steps for one period; linear RMS error is about 0.101090 and limited error about 0.009022.
Scope. Periodic 1D scalar reference with prescribed constant velocity, independently recomputed from the companion equations. The 3D depth axis only separates curves; it is not a third fluid dimension. Every method has the same fixed value scale. RMS uses analytic sine translation, or translation of the initial piecewise-linear interpolant for edge fixtures. Sum is unweighted; divide its change by sample count for a unit-period integral. No native midpoint/clamped transport or corrected native API is claimed.