Mathematical Axis Resampling & Bilinear Interpolation

Tuning engineers frequently need to port proven calibration parameters across generational boundaries (e.g. converting an M52TUB28 tune from MS42 to an M54B30 MS43, or porting an MS43 tune to an MS45.1).

In the user’s database, ms42_to_ms43_common_tables.csv maps hundreds of shared calibration symbols between generations:

┌──────────────────────────────────────────────────────────────────────────────────────────────────┐  
│                   MS42 TO MS43 CROSS-GENERATIONAL SYMBOL TRANSLATION EXCERPT                     │  
├───────────────────────────────────┬───────────────────────────────────┬──────────────────────────┤  
│ Siemens MS42 Calibration Symbol   │ Siemens MS43 Calibration Symbol   │ Translation Classification│  
├───────────────────────────────────┼───────────────────────────────────┼──────────────────────────┤  
│ id_add_knk__n                     │ id_add_knk__n                     │ DIRECT_COPY (Exact Match) │  
│ id_crlc_maf_diag__n               │ id_crlc_maf_diag__n               │ DIRECT_COPY (Exact Match) │  
│ id_cycnr_dly_iga_tra__n           │ id_cycnr_dly_iga_tra__n           │ DIRECT_COPY (Exact Match) │  
│ id_dly_st_ivvt__toil              │ id_dly_st_ivvt__toil              │ DIRECT_COPY (Exact Match) │  
│ id_dri_n_sp_min_vb__vb_mmv        │ id_dri_n_sp_min_vb__vb_mmv        │ DIRECT_COPY (Exact Match) │  
│ id_ecfpwm_igk_off__temp_cat       │ id_ecfpwm_igk_off__temp_cat       │ DIRECT_COPY (Exact Match) │  
│ id_ectpwm_add__n__tco_sp          │ id_ectpwm_add__n__tco_sp          │ DIRECT_COPY (Exact Match) │  
│ id_fac_knks_thd__tia              │ id_fac_knks_thd__tia              │ DIRECT_COPY (Exact Match) │  
│ id_gear__n_vs_cru                 │ id_gear__n_vs_cru                 │ DIRECT_COPY (Exact Match) │  
│ id_iga_dec_knk_1__n               │ id_iga_dec_knk_1__n               │ DIRECT_COPY (Exact Match) │  
│ id_iga_inc_knk__n                 │ id_iga_inc_knk__n                 │ DIRECT_COPY (Exact Match) │  
│ id_knkwb_0__n__maf                │ id_knkwb_0__n__maf                │ DIRECT_COPY (Exact Match) │  
│ id_maf_tab__v_maf_1__v_maf_2      │ id_maf_tab__v_maf_1__v_maf_2      │ MANUAL_REVIEW (Rescaling) │  
│ id_n_max_cycnr__vs                │ id_n_max_cycnr__vs                │ DIRECT_COPY (Exact Match) │  
│ id_pvs_fl__n                      │ id_pvs_fl__n                      │ DIRECT_COPY (Exact Match) │  
│ id_t_sap_on__tco_st               │ id_t_sap_on__tco_st               │ DIRECT_COPY (Exact Match) │  
└───────────────────────────────────┴───────────────────────────────────┴──────────────────────────┘  

15.1 Mathematical Axis Resampling & Bilinear Interpolation#

When migrating maps between firmware builds where axis break points differ, direct byte copying causes severe calibration distortion. The translation pipeline applies 2D Bilinear Resampling:

f(x, y) \approx \frac{(x_2 - x)(y_2 - y)}{(x_2 - x_1)(y_2 - y_1)} Q_{11} + \frac{(x - x_1)(y_2 - y)}{(x_2 - x_1)(y_2 - y_1)} Q_{21} + \frac{(x_2 - x)(y - y_1)}{(x_2 - x_1)(y_2 - y_1)} Q_{12} + \frac{(x - x_1)(y - y_1)}{(x_2 - x_1)(y_2 - y_1)} Q_{22}