multimed: correct mmlut lookups at the table edges and on the axis; deterministic test_volumedimension

[alexlib]

Two bugs in the multimedia look-up table (mmlut) and one flaky test.

1. get_mmf_from_mmlut used the table's edge rows

The bilinear lookup needs all four corners (ir..ir+1, iz..iz+1) inside the table, but the bounds test was

if (ir > nr) return 0;
if (iz < 0 || iz > nz) return 0;
... if (v4[i] < 0 || v4[i] > nr*nz) return 0;

That accepts the top row (iz = nz-1) and the row above it (iz = nz). There the "z+1" corners wrap into the next radial row, and at one corner the read is data[nr*nz], one past the end. The result is used as the radial shift, so points near the top of the volume got a wrong refraction factor and no fallback to the iterative solve.

Fix: return 0 unless all four corners are table entries. multimed_r_nlay then falls back to the iterative solve.

2. The R = 0 row held a placeholder (commit 80aa038)

multimed_r_nlay returns 1.0 at r == 0. That is a placeholder: the factor multiplies r there, so any value is exact for that point. init_mmlut tabulated it as the R = 0 row, so interpolation across the first radial cell pulled every point within rw of the glass-normal axis toward 1.0.

Fix: the factor is even in r, so the row is now (4 f(rw) − f(2 rw)) / 3.

3. test_volumedimension was flaky

It passed uninitialized xmax/xmin/ymax/ymin to volumedimension(), which only widens them. The result depended on stack leftovers; I saw xmax = 100.0 instead of 73.02. They now start empty.

Tests

test_mmlut_matches_iterative (new): compares the LUT with the iterative solve over the whole table.

region	master	this PR
away from the axis	up to 0.53	< 1e-4
within one cell of the axis	up to 0.12	< 5e-4

Near the axis the reference's own fixed 0.001 mm stop limits accuracy, which is why that region has a looser tolerance.

Three existing tests encoded the first-cell error and now check converged values:

test	old expectation	new expectation
test_init_mmLUT	data[0] == 1	data[0] is the r → 0 limit
test_get_mmf_mmLUT at (1,1,1), R = 1.41 < rw	1.00382	1.005406 (converged solve, tol 1e-9)
test_multimed_nlay (Xq, Yq)	(0.74811917, 0.75977975)	(0.67565088, 0.68906505), from the converged mmf; tolerance 5e-4 for the LUT's interpolation error scaled by the camera distance

Full local run (all check_*.c compiled against liboptv/src with a minimal stand-in check.h, since libcheck isn't available here):

	ok	fail
master	84	3
this PR	86	2

The 2 remaining failures, track3d_test_cavity and track3d_test_burgers, also fail on master.

The same three fixes are in openptv2 main (76c4416a and earlier).

Related: #230 (trafo scx), #231 (orient glass fit, .addpar precision), #233 (trackback Y limits).

🤖 Generated with Claude Code

[Copilot]

🟡 Changes recommended

Points slightly below the LUT origin still bypass fallback due to C’s truncation of negative fractional indices.

1 open finding

• Reject negative relative Z before LUT interpolation · New

What changed in this PR

Fixes multimedia LUT edge access and stabilizes volume-dimension testing.

Changes:

• Restricts bilinear interpolation to valid LUT cells.
• Adds iterative-solver comparison coverage.
• Initializes volume extrema deterministically.

File	Description
liboptv/​src/​multimed.c	Tightens LUT interpolation bounds.
liboptv/​tests/​check_multimed.c	Adds regression coverage and deterministic initialization.

🧠 Review effort: Balanced

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