Numerically controlled system and numerical control method

A numerically controlled system comprising:

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