Calculate lens BC (base curve) and diameter based on K readings (keratometry readings).

# Custom Toric Contact Lenses Calculation.md

Custom Toric Contact Lenses Calculation

Calculate lens base curve and diameter based on keratometry readings.

BC and dia calculation algorithm is based on Soft Special Edition – Base Curve.

contacts.py

#!/usr/bin/env python
"""
Calculate lens BC (base curve) and diameter based on K readings (keratometry readings).
BC and dia calculation based on http://softspecialedition.com/base_curve

Glossary:
CL - Contact Lenses
OD - right patient's eye
OS - left patient's eye
HVID - horizontal visible iris diameter
K1 - flat meridian from keratometric readings
K2 - steep meridian from keratometric readings
VD - vertex distance
D - diopters
"""
import math


# Refractive readings (used to adjust prescription from glasses to contacts)
VD = 12.00  # mm. Set to 0 if it is your contact lens prescription

OD_Sph = +2.00
OD_Cyl = -0.75
OD_Axis = 20

OS_Sph = +3.50
OS_Cyl = -1.25
OS_Axis = 176

# Keratometry readings (used to calculate Base Curve and Diameter)
OD_HVID = 11.96  # mm
OD_Anterior_3mm_K1 = 38.72  # D
OD_Anterior_3mm_K2 = 39.17  # D
OD_Anterior_3mm_K_Avg = 38.94  # D, None if not specified
# OD_Anterior_3mm_K1_Axis = 20  # degrees
# OD_Anterior_3mm_K2_Axis = 110  # degrees

OS_HVID = 12.01
OS_Anterior_3mm_K1 = 38.12
OS_Anterior_3mm_K2 = 39.45
OS_Anterior_3mm_K_Avg = 38.77
# OS_Anterior_3mm_K1_Axis = 172
# OS_Anterior_3mm_K2_Axis = 82


# Constants
n0 = 1       # Refractive index of air
n1 = 1.3375  # Keratometric index
HVID_Avg = 11.8  # Average HVID discussed in the last issue of Soft Special Edition


def clamp(minimum, x, maximum):
    return max(minimum, min(x, maximum))


def round4(x):
    """ 0.25 step """
    return round(x*4)/4


def round8(x):
    """ 0.125 step """
    return round(x*8)/8


def main():
    OD_Toric = OD_Cyl is not None and OD_Axis is not None
    OS_Toric = OS_Cyl is not None and OS_Axis is not None

    def glassToContacts(sph, cyl):
        # F_c = (F^(-1) - x)^(-1), where
        #  F_c is the power corrected for vertex distance,
        #  F is the original lens power, and
        #  x is the change in vertex distance in meters.
        F_c1 = 1/((1/sph) - VD*0.001)
        F_c2_uncorrected = sph + cyl
        F_c2 = 1/((1/F_c2_uncorrected) - VD*0.001)
        F_cyl = F_c2 - F_c1
        return F_c1, F_cyl

    OD_CL_Sph, OD_CL_Cyl = glassToContacts(OD_Sph, OD_Cyl)
    OS_CL_Sph, OS_CL_Cyl = glassToContacts(OS_Sph, OS_Cyl)
    OD_CL_Axis, OS_CL_Axis = OD_Axis, OS_Axis


    # Calculating CL Diameter
    """
    Once the HVID is determined we add 2.0mm to the HVID to determine our overall lens diameter for a spherical lens
     (eg. HVID = 12.0mm, overall lens diameter = 14.0mm). For a toric contact lens we add 2.5mm 
     (eg. HVID = 12.0mm, overall lens diameter = 14.5mm) to provide adequate limbal coverage and to aid in lens stabilization.
    """
    OD_CL_Diameter = OD_HVID + (2.5 if OD_Toric else 2)
    OS_CL_Diameter = OS_HVID + (2.5 if OS_Toric else 2)

    # Calculating mean keratometric reading
    OD_K_Mean = OD_Anterior_3mm_K_Avg or (OD_Anterior_3mm_K1 + OD_Anterior_3mm_K2) / 2
    OS_K_Mean = OS_Anterior_3mm_K_Avg or (OS_Anterior_3mm_K1 + OS_Anterior_3mm_K2) / 2

    # Calculating effective keratometric reading
    """
    Determine the “effective K,” which is a number that embodies both the central keratometric readings and the HVID. 
    This is done be adding 1D to the mean K for every 0.2mm that the HVID is larger than 11.8mm 
    (this was the average HVID discussed in the last issue of Soft Special Edition) 
    and subtracting 1D from the mean K for every 0.2mm that the HVID is smaller than 11.8mm.
    """
    OD_K_Effective = OD_K_Mean + (OD_HVID - HVID_Avg) * 5
    OS_K_Effective = OS_K_Mean + (OS_HVID - HVID_Avg) * 5

    # Convert Effective K to BC
    OD_CL_BC_Calculated = (n1 - n0) * 1000 / OD_K_Effective
    OS_CL_BC_Calculated = (n1 - n0) * 1000 / OS_K_Effective

    # "Nomogram" impl.
    def fitFlatter(lens_dia):
        lens_dia = clamp(12, lens_dia, 16.5)
        lens_dia = round(lens_dia * 2) / 2  # round to 0.5
        if math.isclose(lens_dia, 12):
            return 0
        return (lens_dia - 12.5) * 2 * 0.20 + 0.10

    # Adjust
    OD_CL_BC = OD_CL_BC_Calculated + fitFlatter(OD_CL_Diameter)
    OS_CL_BC = OS_CL_BC_Calculated + fitFlatter(OS_CL_Diameter)


    print(f"---")
    print(f"OD_Sph: {OD_Sph:.2f}, OD_CL_Sph: {OD_CL_Sph:.2f}, rounded: {round4(OD_CL_Sph):+.2f} {round8(OD_CL_Sph):+.3f}")
    print(f"OS_Sph: {OS_Sph:.2f}, OS_CL_Sph: {OS_CL_Sph:.2f}, rounded: {round4(OS_CL_Sph):+.2f} {round8(OS_CL_Sph):+.3f}")
    print(f"OD_Cyl: {OD_Cyl:.2f}, OD_CL_Cyl: {OD_CL_Cyl:.2f}, rounded: {round4(OD_CL_Cyl):+.2f} {round8(OD_CL_Cyl):+.3f}")
    print(f"OS_Cyl: {OS_Cyl:.2f}, OS_CL_Cyl: {OS_CL_Cyl:.2f}, rounded: {round4(OS_CL_Cyl):+.2f} {round8(OS_CL_Cyl):+.3f}")

    print(f"OD_HVID: {OD_HVID:.2f} mm, OD_CL_Diameter: {OD_CL_Diameter:.2f} mm. BC will be flatter by {fitFlatter(OD_CL_Diameter):.2f} mm.")
    print(f"OS_HVID: {OS_HVID:.2f} mm, OS_CL_Diameter: {OS_CL_Diameter:.2f} mm. BC will be flatter by {fitFlatter(OS_CL_Diameter):.2f} mm.")

    print(f"OD_K_Mean: {OD_K_Mean:.2f} D, OD_K_Effective: {OD_K_Effective:.2f} D.")
    print(f"OS_K_Mean: {OS_K_Mean:.2f} D, OS_K_Effective: {OS_K_Effective:.2f} D.")

    print(f"OD_CL_BC_Calculated: {OD_CL_BC_Calculated:.2f} mm, OD_CL_BC: {OD_CL_BC:.2f} mm.")
    print(f"OS_CL_BC_Calculated: {OS_CL_BC_Calculated:.2f} mm, OS_CL_BC: {OS_CL_BC:.2f} mm.")

    print(f"---")
    print(f"Based on your readings, your soft contact lenses should be:")
    print(f"OD (right eye):")
    print(f"  Base Curve: {OD_CL_BC:.1f} mm")
    print(f"  Diameter:   {OD_CL_Diameter:.1f} mm")
    print(f"  Sphere:   {OD_CL_Sph:+.2f} (0.25 D step: {round4(OD_CL_Sph):+.2f}) (0.125 D step: {round8(OD_CL_Sph):+.3f})")
    print(f"  Cylinder: {OD_CL_Cyl:.2f} (0.25 D step: {round4(OD_CL_Cyl):+.2f}) (0.125 D step: {round8(OD_CL_Cyl):+.3f})")
    print(f"  Axis:     {OD_CL_Axis:.0f}° (10° step: {round(OD_CL_Axis/10)*10})")
    print(f"  Based on nominal {VD:.0f} mm vertex distance")
    print(f"OS (left eye):")
    print(f"  Base Curve: {OS_CL_BC:.1f} mm")
    print(f"  Diameter:   {OS_CL_Diameter:.1f} mm")
    print(f"  Sphere:   {OS_CL_Sph:+.2f} D (0.25 D step: {round4(OS_CL_Sph):+.2f}) (0.125 D step: {round8(OS_CL_Sph):+.3f})")
    print(f"  Cylinder: {OS_CL_Cyl:.2f} D (0.25 D step: {round4(OS_CL_Cyl):+.2f}) (0.125 D step: {round8(OS_CL_Cyl):+.3f})")
    print(f"  Axis:     {OS_CL_Axis:.0f}° (10° step: {round(OS_CL_Axis/10)*10})")
    print(f"  Based on nominal {VD:.0f} mm vertex distance")
    # Order custom lens: https://www.eyemaxxoutlet.com/c-vue-55-custom-toric-contact-lenses


if __name__ == '__main__':
    main()

output.md

---
OD_Sph: 2.00, OD_CL_Sph: 2.05, rounded: +2.00 +2.000
OS_Sph: 3.50, OS_CL_Sph: 3.65, rounded: +3.75 +3.625
OD_Cyl: -0.75, OD_CL_Cyl: -0.78, rounded: -0.75 -0.750
OS_Cyl: -1.25, OS_CL_Cyl: -1.34, rounded: -1.25 -1.375
OD_HVID: 11.96 mm, OD_CL_Diameter: 14.46 mm. BC will be flatter by 0.90 mm.
OS_HVID: 12.01 mm, OS_CL_Diameter: 14.51 mm. BC will be flatter by 0.90 mm.
OD_K_Mean: 38.94 D, OD_K_Effective: 39.74 D.
OS_K_Mean: 38.77 D, OS_K_Effective: 39.82 D.
OD_CL_BC_Calculated: 8.49 mm, OD_CL_BC: 9.39 mm.
OS_CL_BC_Calculated: 8.48 mm, OS_CL_BC: 9.38 mm.
---
Based on your readings, your soft contact lenses should be:
OD (right eye):
  Base Curve: 9.4 mm
  Diameter:   14.5 mm
  Sphere:   +2.05 (0.25 D step: +2.00) (0.125 D step: +2.000)
  Cylinder: -0.78 (0.25 D step: -0.75) (0.125 D step: -0.750)
  Axis:     20° (10° step: 20)
  Based on nominal 12 mm vertex distance
OS (left eye):
  Base Curve: 9.4 mm
  Diameter:   14.5 mm
  Sphere:   +3.65 D (0.25 D step: +3.75) (0.125 D step: +3.625)
  Cylinder: -1.34 D (0.25 D step: -1.25) (0.125 D step: -1.375)
  Axis:     176° (10° step: 180)
  Based on nominal 12 mm vertex distance