Method and device for determining geometric data of a conical measurement object

A computer program product comprising a storage medium and program code stored on the storage medium, wherein the program code is designed to carry out a method according to the following steps, when the program code is executed on a computer:

• a) determining at least six spatial coordinates at least six different measurement points on the conical measurement object,
• b) determining a tangential conical substitute element for the measurement object using the at least six spatial coordinates, and
• c) determining the geometric data of the measurement object by means of the tangential conical substitute element,
• wherein step b) comprises the substeps of
• b1) defining at least six element parameters that represent a cone axis of the tangential conical substitute element, a cone angle of the tangential conical substitute element, and a suspension point of the tangential conical substitute element on the cone axis, and
• b2) calculating the at least six element parameters using the at least six spatial coordinates and using a system of equations,
• wherein the system of equations describes difference values between the spatial coordinates and the tangential conical substitute element,
• wherein each difference value is modeled by means of at least two difference parameters whose sum represents a perpendicular spacing between the tangential conical substitute element and a spatial coordinate, and
• wherein a first one of the at least two difference parameters defines a solution condition in the form of a limit value, and a second one of the at least two difference parameters defines a solution condition in the form of an extreme value.

A device for determining geometric data of a conical measurement object, comprising:

• a moveable measuring head and position-measuring devices in order to determine a spatial position of the measuring head,
• a memory for storing a plurality of spatial coordinates of a plurality of measurement points on the measurement object, and
• an evaluation unit for determining a tangential conical substitute element for the measurement object by using the spatial coordinates, and for determining the geometric data of the measurement object by means of the substitute element,
• wherein the memory is designed to store at least six spatial coordinates of at least six different measurement points of the measurement object,
• wherein the evaluation unit is designed to calculate at least six element parameters by using the at least six spatial coordinates and by using a system of equations,
• wherein the at least six element parameters represent a cone axis of the tangential conical substitute element, a cone angle of the tangential conical substitute element, and a suspension point of the tangential conical substitute element on the cone axis,
• wherein the system of equations describes difference values between the spatial coordinates and the tangential conical substitute element,
• wherein each difference value is modeled by means of at least two difference parameters whose sum represents a perpendicular spacing between the tangential conical substitute element and a spatial coordinate, and
• wherein a first one of the at least two difference parameters defines a solution condition in the form of a limit value, and a second one of the at least two difference parameters defines a solution condition in the form of an extreme value.