Numerically controlled system and numerical control method

A numerically controlled system comprising:

• an evaluating section forming evaluation data by arranging, virtually, a process applying portion of a system to be numerically controlled on a given scheduled path locus not interfering with a processed surface of a processing object and by setting a plurality of evaluation points to evaluate the processed surface;
• a command speed deciding section deciding a command speed, at which the process applying portion is moved, based on the evaluation data;
• and
• a process applying portion position data forming section having a process applying portion position deciding section for deciding a process applying portion position to be given to the numerically controlled system based on the command speed and shape of the processed surface such that the process applying portion does not interfere with the processed surface wherein operation of said evaluating section and operation of said process applying portion position data forming section are executed in real time.