Curved-surface generating method and program, and three-dimensional shape processing apparatus
View Patent ↗A plurality of representative points are selected from a group of points obtained as results of shape measurement of an object, respective principal curvatures are calculated at the representative points on the basis of positional relationships between the representative point and a plurality of points existing around the representative point, a line of curvature is created on the basis of the principal curvatures of the representative points and a curved surface is generated using this line of curvature.
1. A curved surface generating method, performed by a computer aided design system or a computer aided manufacturing system including a computer, for generating a curved surface from a group of points formed of a plurality of measurement points obtained as results of shape measurement of an object, comprising:
a representative-point selection step, performed by said computer, of selecting a plurality of representative points from the group of points;
a principal-curvature calculating step, performed by said computer, of calculating respective principal curvatures at each of the representative points on the basis of positional relationships between each representative point and a plurality of the measurement points existing around this representative point;
a line-of-curvature creating step, performed by said computer, of creating a line of curvature on the basis of the principal curvatures at each representative point; and
a curved-surface generating step, performed by said computer, of generating a curved surface by using the line of curvature,
wherein the principal-curvature calculating step includes,
a step of setting a normal at each representative point;
a tangential-vector setting step of setting a tangential vector that is orthogonal to the normal;
a step of generating element vectors by joining each representative point and each point existing around this representative point;
a step of calculating angles formed by the tangential vector and the element vectors around the normal;
a step of calculating angles formed by a tangential plane including the tangential vector and planes including the element vectors and defining the angles as curvatures;
a step of creating angle-curvature tables by plotting the calculation results on a horizontal axis in angle-curvature tables; and
a step of obtaining the principal curvatures on the basis of the curvature tables.
2. A curved-surface generating method according to claim 1 , wherein the principal-curvature calculating step includes
a step of setting a normal at each representative point;
a step of generating element vectors by joining each representative point and each points existing around this representative point; and
a step of determining the principal curvatures on the basis of relationships between the normal and the element vectors.
3. A curved-surface generating method according to claim 1 , wherein the principal-curvature calculating step includes
a step of setting a normal at each representative point;
a tangential-vector setting step of setting a tangential vector that is orthogonal to the normal;
a step of generating element vectors by joining each representative point and each point existing around this representative point;
a step of calculating angles formed by the tangential vector and the element vectors around the normal;
a step of calculating angles formed by a tangential plane including the tangential vector and planes including the element vectors and defining the angles as curvatures;
a step of creating angle-curvature tables by plotting the calculation results on a horizontal axis in angle-curvature tables;
an extraction step of extracting only a fundamental frequency from the curvature tables; and
a principal-curvature obtaining step of obtaining the principal curvatures from the angle-curvature table on the basis of the fundamental frequency.
4. A curved-surface generating method according to claim 1 , wherein the principal-curvature calculating step includes
a step of generating element vectors by joining each representative point and each point existing around this representative point;
a step of determining a group of normal vectors at each representative point by calculating vector products of the element vectors; and
a step of determining an average vector of the group of normal vectors and defining the average vector as a normal vector at each of the representative points.
5. A computer-readable storage medium storing a curved-surface generating program for executing, on a computer system, curved-surface generating processing for generating a curved surface from a group of points formed of a plurality of measurement points obtained as results of shape measurement of an object, the curved-surface generating program comprising:
a representative-point selection step of selecting a plurality of representative points from the group of points;
a principal-curvature calculation step of calculating respective principal curvatures at each representative point on the basis of positional relationships between each representative point a plurality of the measurement points existing around this representative point;
a line-of-curvature creating step of creating a line of curvature on the basis of the principal curvature at each representative point; and
a curved-surface generating step of generating a curved surface by using the line of curvature,
wherein the principal-curvature calculating step includes,
a step of setting a normal at each representative point;
a tangential-vector setting step of setting a tangential vector that is orthogonal to the normal;
a step of generating element vectors by joining each representative point and each point existing around this representative point;
a step of calculating angles formed by the tangential vector and the element vectors around the normal;
a step of calculating angles formed by a tangential plane including the tangential vector and planes including the element vectors and defining the angles as curvatures;
a step of creating angle-curvature tables by plotting the calculation results on a horizontal axis in angle-curvature tables; and
a step of obtaining the principal curvatures on the basis of the curvature tables.
6. A three-dimensional shape processing apparatus, comprising:
a computer-readable storage medium storing a curved-surface generating program and which generates a curved surface from a group of points formed of a plurality of measurement points obtained as results of shape measurement of an object by executing the curved-surface generating program, wherein the curved-surface generating program includes
a representative-point selection step of selecting a plurality of representative points from the group of points;
a principal-curvature calculating step of calculating respective principal curvatures at each representative point on the basis of positional relationships between each representative point and a plurality of the measurement points existing around this representative point;
a line-of-curvature creating step of creating a line of curvature on the basis of the principal curvature at each representative point; and
a curved-surface generating step of generating a curved surface by using the line of curvature,
wherein the principal-curvature calculating step includes,
a step of setting a normal at each representative point;
a tangential-vector setting step of setting a tangential vector that is orthogonal to the normal;
a step of generating element vectors by joining each representative point and each point existing around this representative point;
a step of calculating angles formed by the tangential vector and the element vectors around the normal;
a step of calculating angles formed by a tangential plane including the tangential vector and planes including the element vectors and defining the angles as curvatures;
a step of creating angle-curvature tables by plotting the calculation results on a horizontal axis in angle-curvature tables; and
a step of obtaining the principal curvatures on the basis of the curvature tables.