Add bioER plate height volume calcs

pylabrobot/resources/bioer/plates.py

@@ -1,3 +1,6 @@
+# BioER 2.2 mL deepwell with polynomial height<->volume mapping
+# Uses fit: h(V) = a3*V^3 + a2*V^2 + a1*V + a0   (V in µL, h in mm)
+
 from pylabrobot.resources.plate import Plate
 from pylabrobot.resources.utils import create_ordered_items_2d
 from pylabrobot.resources.well import (
@@ -6,33 +9,88 @@
   WellBottomType,
 )
 
+# Measured the height of vols in the plate. Graphed and then fitted polynomial.
+# Polynomial more accurate than circular conical frustum.
+
+# ---- Polynomial coefficients from your fit (units: µL -> mm) ----
+_A3 = 2.34770904e-09
+_A2 = -9.12279010e-06
+_A1 = 2.68872240e-02
+_A0 = 2.06530412e00
+
+# ---- Geometry / limits (from your earlier spec & measurements) ----
+_WELL_TOP_SIDE_MM = 8.25  # inner opening (square), mm
+_WELL_DEPTH_MM = 42.4  # well depth, mm
+_MAX_VOL_UL = 2200.0  # vendor spec, µL
+
+
+# Monotone cubic on [0, MAX_VOL] from your data — use binary search for inversion
+def _height_from_volume_poly(vol_ul: float) -> float:
+  """Height (mm) from volume (µL) using the fitted cubic."""
+  v = max(0.0, min(float(vol_ul), _MAX_VOL_UL))
+  h = ((_A3 * v + _A2) * v + _A1) * v + _A0
+  # Clamp to physical depth
+  if h < 0.0:
+    return 0.0
+  if h > _WELL_DEPTH_MM:
+    return _WELL_DEPTH_MM
+  return h
+
+
+def _volume_from_height_poly(h_mm: float, *, tol: float = 1e-6, max_iter: int = 64) -> float:
+  """Volume (µL) from height (mm) by inverting the cubic with binary search."""
+  h_target = max(0.0, min(float(h_mm), _WELL_DEPTH_MM))
+  lo, hi = 0.0, _MAX_VOL_UL
+  # Quick outs
+  if h_target <= _height_from_volume_poly(lo):
+    return 0.0
+  if h_target >= _height_from_volume_poly(hi):
+    return _MAX_VOL_UL
+  for _ in range(max_iter):
+    mid = 0.5 * (lo + hi)
+    h_mid = _height_from_volume_poly(mid)
+    if abs(h_mid - h_target) <= tol:
+      return mid
+    if h_mid < h_target:
+      lo = mid
+    else:
+      hi = mid
+  return 0.5 * (lo + hi)
+
 
 def BioER_96_wellplate_Vb_2200uL(name: str) -> Plate:
   """BioER Cat. No. BSH06M1T-A (KingFisher-compatible)
   Spec: https://en.bioer.com/uploadfiles/2024/05/20240513165756879.pdf
   """
+  well_kwargs = {
+    "size_x": _WELL_TOP_SIDE_MM,
+    "size_y": _WELL_TOP_SIDE_MM,
+    "size_z": _WELL_DEPTH_MM,
+    "bottom_type": WellBottomType.V,  # physical bottom shape
+    "cross_section_type": CrossSectionType.RECTANGLE,
+    "material_z_thickness": 0.8,  # measured
+    "max_volume": _MAX_VOL_UL,
+    # ---- height<->volume mapping used by PLR ----
+    "compute_height_from_volume": lambda vol_ul: _height_from_volume_poly(vol_ul),
+    "compute_volume_from_height": lambda h_mm: _volume_from_height_poly(h_mm),
+  }
+
   return Plate(
     name=name,
-    size_x=127.1,  # from spec
-    size_y=85.0,  # from spec
-    size_z=44.2,  # from spec
+    size_x=127.1,  # spec
+    size_y=85.0,  # spec
+    size_z=44.2,  # spec
     lid=None,
     model=BioER_96_wellplate_Vb_2200uL.__name__,
     ordered_items=create_ordered_items_2d(
       Well,
-      size_x=8.25,  # from spec (inner well width)
-      size_y=8.25,  # from spec (inner well length)
-      size_z=42.4,  # measured (well depth)
+      num_items_x=12,  # spec
+      num_items_y=8,  # spec
       dx=9.5,  # measured (column pitch)
       dy=7.5,  # measured (row pitch)
-      dz=6,  # measured (expected to be 44.2-42.4-0.8=1, but 6 optimal on Hamilton_MFX_plateholder_DWP_metal_tapped  )
-      material_z_thickness=0.8,  # measured
+      dz=6.0,  # calibrated (mounting offset for your deck)
       item_dx=9.0,  # measured
       item_dy=9.0,  # measured
-      num_items_x=12,  # from spec
-      num_items_y=8,  # from spec
-      cross_section_type=CrossSectionType.RECTANGLE,
-      bottom_type=WellBottomType.V,
-      max_volume=2200,  # from spec (2.2 mL)
+      **well_kwargs,
     ),
   )