Perhaps the finest exponents of the art of calculating and flying to a TDP is demonstrated on the S61 ops at Penzance.
Due to having to operate genuine Class 1 out of a 380 metre strip (2 pilots, 1 cabin attendent and typically 28-32 pax) a specific take-off technique was devised (in the 70's) which has a 'variable' TDP dependent on aircraft weight and wind velocity. It varies from 50ft/20 kts IAS to 170ft/20kts IAS (or positive groundspeed if w/v >20kts) - all heights are Bar Alt heights (no Rad Alt fitted when they were devised!). It is a complicated calculation involving accountable wind/temp/press etc.
As we always attempt to depart at max RTOW believe me when I say that TDP is DEFINITELY TDP in that there is simply no space left to reject after it ( as any available 'space' would be converted back into payload)!
I think much of the confusion above concerning TDP may come from operators not used to Class 1 operations?