Apparatus and method for measuring surface shape

A surface shape measuring apparatus comprising:

• polar coordinate conversion means for converting surface shape data of a measurement object represented as three dimensional orthogonal coordinate data (x, y, z) into polar coordinate data (z, ρ, θ);
• approximate expression calculating means for calculating an approximate expression for the surface shape of the measurement object on the basis of said polar coordinate data, employing a polynomial for approximating a curved surface;
• angle calculating means for calculating an angle θ1 representing a generating line direction and an angle θ2 representing a principal line direction in the surface shape of the measurement object in accordance with said approximate expression;
• first approximate sectional shape calculating means for calculating first approximate sectional shapes both in the generating line and principal line directions on the surface shape of the measurement object on the basis of said angles θ1 and θ2 employing said approximate expression;
• second approximate sectional shapes calculating means for approximating said first approximate sectional shapes to quadratic curves with respect to the three dimensional orthogonal coordinates as second approximate sectional shapes, and calculating center coordinates and radiuses of curvature for said approximate quadratic curves representing said second approximate sectional shapes in the generating line and principal line directions;
• and
• sectional shape data calculating means for calculating numerical data of the second approximate sectional shapes both in the generating line and principal line directions and on the surface shape of the measurement object on the basis of the center coordinates and the radiuses of curvature for said approximate quadratic curves.