Methods for generating free curves and sculptured surfaces

Claim 1

A method for producing a sculpted surface by electronically generating data representing a free curve in a vector coordinate system, using a predetermined parameter based upon two nodes having control points interposed therebetween in a cubic space, the method comprising the steps of: inputting data representative of a point sequence, the point sequence defininga free curve; establishing one of the two nodes as a starting point and the other of the two nodes as an end point of the point sequence; temporarily establishing the control point based upon points in the points sequence, the points in the point sequence being adjacent to the starting point and the end point; generating data representative of perpendiculars from the points in the point sequence to a free curve vector determined by the nodes and by the control points; generating data representative of an intersection point of each perpendicular and the free curve; re-establishing the control points by determining the solution to simultaneous linear equations having two unknowns and a square-sum as variables, the square-sum equal to the total of the square of each distance between the points in the point sequence and the intersection point of each perpendicular and the free curve; generating data representative of the free curve, the point sequence based upon the two nodes and the re-established control points; transferring the data representative of the free curve to milling means; and driving the milling means according to the transferred data to cut at least a portion of a workpiece to correspond to at least a portion of the free curve.

Claim 2

A method for producing a sculpted surface by electronically generating data representing a free curve in a vector coordinate system, using a predetermined parameter based upon two nodes having control points interposed therebetween in a cubic space, the method comprising the steps of: inputting data representative of a point sequence, the point sequence defininga free curve; establishing one of the two nodes as a starting point and the other of the two nodes as an end point of the point sequence; temporarily establishing the control point based upon points in the points sequence, the points in the point sequence being adjacent to the starting point and the end point; generating data representative of perpendiculars from the points in the point sequence to a free curve vector determined by the nodes and by the control points; generating data representative of an intersection point of each perpendicular and the free curve; re-establishing the control points by determining the solution to simultaneous linear equations having two unknowns and a square-sum as variables, the square-sum equal to the total of the square of each distance between the points in the point sequence and the intersection point of each perpendicular and the free curve; generating data representative of the free curve, the point sequence based upon the two nodes and the re-established control points; transferring the data representative of the free curve to milling means; and driving the milling means according to the transferred data to cut at least a portion of a workpiece to correspond to at least a portion of the free curve.

Claim 3

A method for generating a sculptured surface by locating in a frame space a patch expressed by a predetermined vector function based upon internal control points established in said frame space enclosed by boundary curves in a cubic space, said method comprising the steps of: inputting data representative of coordinate data of a plurality of points defining the sculpted surface; detecting a shortest distance based upon the coordinate data, between each of the plurality of points and the patch; generating a new patch by re-establishing the internal control points, the internal control points re-established by determining the solution to simultaneous linear equations having two unknowns and a square-sum as variables, the square sum equal to the total sum of the square of each distance between each of the plurality of points and sculpted surface; transferring data representative of the new patch to milling means; and driving the milling means according to the transferred data to shape at least a portion of a workpiece to correspond to the sculpted surface.

Claim 4

A method for generating a sculptured surface by locating in a frame space a patch expressed by a predetermined vector function based upon internal control points established in said frame space enclosed by boundary curves in a cubic space, said method comprising the steps of: inputting data representative of coordinate data of a plurality of points defining the sculpted surface; detecting a shortest distance based upon the coordinate data, between each of the plurality of points and the patch; generating a new patch by re-establishing the internal control points, the internal control points re-established by determining the solution to simultaneous linear equations having two unknowns and a square-sum as variables, the square sum equal to the total sum of the square of each distance between each of the plurality of points and sculpted surface; transferring data representative of the new patch to milling means; and driving the milling means according to the transferred data to shape at least a portion of a workpiece to correspond to the sculpted surface.

Claim 5

A method for generating a sculptured surface by locating in a frame space a patch expressed by a predetermined vector function based upon internal control points established in said frame space enclosed by boundary curves in a cubic space, said method comprising the steps of: inputting data representative of coordinate data of a plurality of points defining the sculpted surface; detecting a shortest distance, based upon the coordinate data between each of the plurality of points and the patch; establishing the internal control points in the frame space containing the patch to minimize the total sum of the shortest distances; generating a new patch by having an external shape defined by the plurality of points; transferring data representative of the new patch to milling means; and driving the milling means according to the transferred data to shape at least a portion of a workpiece to correspond to the sculpted surface.

Claim 6

A method for generating a sculptured surface by locating in a frame space a patch expressed by a predetermined vector function based upon internal control points established in said frame space enclosed by boundary curves in a cubic space, said method comprising the steps of: inputting data representative of coordinate data of a plurality of points defining the sculpted surface; detecting a shortest distance, based upon the coordinate data between each of the plurality of points and the patch; establishing the internal control points in the frame space containing the patch to minimize the total sum of the shortest distances; generating a new patch by having an external shape defined by the plurality of points; transferring data representative of the new patch to milling means; and driving the milling means according to the transferred data to shape at least a portion of a workpiece to correspond to the sculpted surface.

Claim 7

A method for generating a sculptured surface by locating in a frame space a patch expressed by a predetermined vector function based upon internal control points established in said frame space enclosed by boundary curves in a cubic space, said method comprising the steps of: inputting data representative of coordinate data of a plurality of points defining a patch; establishing a plurality of points on the patch to be modified; detecting a shortest distance between each of said plurality of points on the one hand, and a reference patch for modification on the other; establishing said internal control points within said frame space of said patch to be modified, the establishing of said internal control points being performed in such a manner as to minimize a total sum of said shortest distances; generating data representative of a patch approximating a surface shape of said reference patch for modification, said patch being generated within said frame space of said patch to be modified; transferring the data representative of the patch to milling means; and driving the milling means according to the transferred data to shape at least a portion of a workpiece into the sculpted surface.

Claim 8

A method for generating a sculptured surface by locating in a frame space a patch expressed by a predetermined vector function based upon internal control points established in said frame space enclosed by boundary curves in a cubic space, said method comprising the steps of: inputting data representative of coordinate data of a plurality of points defining a patch; establishing a plurality of points on the patch to be modified; detecting a shortest distance between each of said plurality of points on the one hand, and a reference patch for modification on the other; establishing said internal control points within said frame space of said patch to be modified, the establishing of said internal control points being performed in such a manner as to minimize a total sum of said shortest distances; generating data representative of a patch approximating a surface shape of said reference patch for modification, said patch being generated within said frame space of said patch to be modified; transferring the data representative of the patch to milling means; and driving the milling means according to the transferred data to shape at least a portion of a workpiece into the sculpted surface.