Method and apparatus for determining shapes of countersunk holes

A method of determining an orientation of a countersunk hole relative to a surrounding surface, the method comprising the steps of:

• a) using a camera to measure coordinates of a plurality of points on a countersunk hole, the countersunk hole having an axis and an apex, and storing said coordinates in a memory of a computer, said coordinates of each of said plurality of points being designated by (x.sub.i, y.sub.i, z.sub.i),
• b) deriving two distinct expressions for a radius of the countersunk hole corresponding to each of said points, wherein said expressions are functions of x.sub.0, y.sub.0, z.sub.0, x.sub.1, y.sub.1, and .phi., where (x.sub.0, y.sub.0, z.sub.0) is the apex of the countersunk hole, (x.sub.1, y.sub.1, z.sub.1) is a point at which the axis of the countersunk hole intersects a reference plane z=z.sub.1 =0, and .phi. is an angle between the axis of the countersunk hole and a line connecting the apex of the countersunk hole and one of the points (x.sub.i, y.sub.i, z.sub.i),
• c) selecting values of parameters x.sub.0, y.sub.0, z.sub.0, x.sub.1, y.sub.1, and .phi. so as to minimize an error function comprising a comparison of said two distinct expressions,
• d) determining an orientation of vector V defined by
• V=(x.sub.1 -x.sub.0)i+(y.sub.1 -y.sub.0)j+(z.sub.1 -z.sub.0)k
• wherein the orientation of V corresponds to an orientation of the camera with respect to the countersunk hole,
• e) repeating step (a) to determine a second plurality of points on a surrounding surface of the countersunk hole, and using said second plurality of points to determine a surface normal vector V', and
• f) using a difference between V and V' to calculate an angle at which the countersunk hole was drilled relative to the surrounding surface.

An apparatus for determining an orientation of a camera used to observe a countersunk hole, comprising:

• a) means for electronically measuring coordinates of a plurality of points on a countersunk hole, the countersunk hole having an axis and an apex, and for storing said coordinates in a memory of a computer, said coordinates of each of said plurality of points being designated by (x.sub.i, y.sub.i, z.sub.i),
• b) means for deriving two distinct expressions for a radius of the countersunk hole corresponding to each of said points, wherein said expressions are functions of x.sub.0, y.sub.0, z.sub.0, x.sub.1, y.sub.1, and .phi., where (x.sub.0, y.sub.0, z.sub.0) is the apex of the countersunk hole, (x.sub.1, y.sub.1, z.sub.1) is a point at which the axis of the countersunk hole intersects a reference plane z=z.sub.1 =0, and .phi. is an angle between the axis of the countersunk hole and a line connecting the apex of the countersunk hole and one of the points (x.sub.i, y.sub.i, z.sub.i),
• c) means for selecting values of parameters x.sub.0, y.sub.0, z.sub.0, x.sub.1, y.sub.1, and so as to minimize an error function comprising a comparison of said two distinct expressions,
• d) means for determining an orientation of vector V defined by
• V=(x.sub.1 -x.sub.0)i+(y.sub.1 -y.sub.0)j+(z.sub.1 -z.sub.0)k
• wherein the orientation of V corresponds to an orientation of the camera with respect to the countersunk hole.

An apparatus for determining an orientation of a countersunk hole relative to a surrounding surface, comprising:

• a) means for manipulating a camera so as to measure coordinates of a plurality of points on a countersunk hole, the countersunk hole having an axis and an apex, and means for storing said coordinates in a memory of a computer, said coordinates of each of said plurality of points being designated by (x.sub.i, y.sub.i, z.sub.i),
• b) means for deriving two distinct expressions for a radius of the countersunk hole corresponding to each of said points, wherein said expressions are functions of x.sub.0, y.sub.0, z.sub.0, x.sub.1, y.sub.1, and .phi., where (x.sub.0, y.sub.0, z.sub.0) is the apex of the countersunk hole, (x.sub.1, y.sub.1, z.sub.1) is a point at which the axis of the countersunk hole intersects a reference plane z=z.sub.1 =0, and .phi. is an angle between the axis of the countersunk hole and a line connecting the apex of the countersunk hole and one of the points (x.sub.i, y.sub.i, z.sub.i),
• c) means for selecting values of parameters x.sub.0, y.sub.0, z.sub.0, x.sub.1, y.sub.1, and so as to minimize an error function comprising a comparison of said two distinct expressions,
• d) means for determining an orientation of vector V defined by
• V=(x.sub.1 -x.sub.0)i+(y.sub.1 -y.sub.0)j+(z.sub.1 -z.sub.0)k
• wherein the orientation of V corresponds to an orientation of the camera with respect to the countersunk hole,
• e) means for determining a vector V' representing an orientation of a surrounding surface of the countersunk hole, and
• f) means for calculating a difference between V and V' and for using said difference to determine an angle at which the countersunk hole was drilled relative to the surrounding surface.