Three-dimensional machining method

A three-dimensional machining apparatus for machining a workpiece, wherein machining of the workpiece is transferred from a first defined surface to a second defined surface continuously and smoothly, said three-dimensional machining apparatus comprising:

• means for calculating an intersection of a tool center Oath to machine the first defined surface and an offset surface of the second defined surface:
• means for calculating an intersection of a tool center path to machine the second defined surface and an offset surface of the first defined surface;
• means for generating a tool center path to create a connecting surface between the intersections;
• and
• means for machining the workpiece in accordance with the generated tool center path.

A three-dimensional machining apparatus for continuous machining of a first surface and a second surface of a workpiece, the three-dimensional machining apparatus comprising:

• (a) means for defining said first and second surfaces by
• defining two variations .lambda. and .mu., which are non-parametric with respect to a coordinate system, wherein .lambda. and .mu. fulfill the following condition:
• 0.ltoreq..lambda..ltoreq.1
• 0.ltoreq..mu..ltoreq.1,
• defining a first plurality of curves extending in direction of .lambda., c(.lambda.,.mu..sub.0), wherein .mu..sub.0 is a constant value of .mu.,
• defining a second plurality of curves extending in direction of .mu., c(.lambda..sub.0,.mu.), wherein .lambda..sub.0 is a constant value of .lambda., and
• forming said surfaces by said first and said second curves:
• (b) means for defining, for each of said surfaces, a plurality of offset points, each of said offset points being defined by
• defining a point on one of said surfaces to be machined, and
• defining a distance from said point in direction of the normal of said point, said distance being the distance between a working end of a machine tool and a center of said machine tool;
• (c) means for defining a first and a second offset surface by
• defining a first parallel surface that contains said offset points of said first surface, and
• defining a second parallel surfaces that contains said offset points of said second surface;
• and
• (d) means for defining a first tool center path for machining said first surface by connecting offset points of said first surface;
• (e) means for defining a second tool center path for machining said second surface by connecting offset points of said second surface:
• (f) means for calculating an intersection of said first tool center path and said offset surface of the second surface;
• (g) means for calculating an intersection of said second tool ,center path and said offset surface of the first surface;
• (h) means for generating a tool center path between said intersections for creating a connecting surface therebetween;
• and
• (i) means for machining the workpiece in accordance with the generated tool center path.