Method of creating a curved surface

Claim 3

A method according to claim 1, wherein step (f) comprises the step of punching a numerical control tape in accordance with said created machining data relating to said curved surface.

Claim 4

A method according to claim 1, wherein step (b) further comprises the step of generating said intermediate sections that lie in parallel with said given sections.

Claim 5

A method according to claim 1, wherein step (b) further comprises the step of generating each of said intermediate sections where each lies perpendicular to said reference sectin and to the reference curve which lies in said reference section.

Claim 6

A method according to claim 1, wherein step (b) further comprises the step of generating each of said intermediate sections where each lies perpendicular to said reference section and passes through a straight line which is perpendicular to said reference section, said straight line serving as an axis from which said intermediate sections radiate.

Claim 7

A method according to claim 1, wherein step (a) further comprises the step of inputting first and second reference sections containing respective first and second reference curves which specify the external form of the body, as said given sections.

Claim 8

A method according to claim 1, wherein step (b) further comprises the step of generating each of said intermediate sections where each lies perpendicular to one of said reference sections.

Claim 11

A method according to claim 8, wherein step (b) comprises the steps of: (i) dividing said reference curve internally into a ratio of m:n; and (ii) generating said dividing points by changing the ratio m:n.

Claim 12

A method according to claim 9, wherein step (d) comprises the steps of: (i) transforming each section curve into a corresponding curve in a predetermined planar coordinate system to bring into coincidence the first and second points and to bring into coincidence lines of intersection of the reference section and said two parallel sections; (ii) computing an intermediate point by dividing internally into a ratio of a:b each section curve transformed into said predetermined planar coordinate system, the dividing at the ratio a:b designating third and fourth points, and dividing internally into the ratio of m:n a straight line connecting the third and fourth points at which said section curves are internally divided into the ratio a:b, the straight line dividing designating the intermediate point; (iii) computing an untransformed intermediate section curve in said predetermined planar coordinate system by computing a number of intermediate points by varying the ratio a:b; and (iv) transforming said untransformed intermediate section curve in said predetermined planar coordinate system into the corresponding intermediate section curve in said intermediate section.

Claim 15

A method according to claim 11, wherein step (d) comprises the steps of: (i) dividing said reference curve internally into a ratio m:n; and (ii) generating said dividing points by changing the ratio m:n.

Claim 16

A method according to claim 12, wherein step (d) includes the steps of: (i) transforming each said section curve into a corresponding section curve in a predetermined planar coordinate system to bring into coincidence said two points whch are points of intersection of the reference curve and each of said two sections and to bring into coincidence lines of intersection of the reference section and each of said two sections; (ii) computing an intermediate point by dividing internally into a ratio a:b each said corresponding section curve transformed into said predetermined planar coordinate system, the dividing at the ratio a:b designating third and fourth points, and dividing internally into the ratio m:n a straight line connecting the third and fourth points at which said section curves are internally divided into the ratio a:b, the straight line dividing designating the intermediate point; (iii) computing an untransformed intermediate section curve in said predetermined planar coordinate system by computing a number of intermediate points by changing the ratio a:b, and (iv) transforming the untransformed intermediate section curve in said predetermined planar coordinate system into the intermediate section curve in said intermediate section.

Claim 19

A method according to claim 14, wherein step (b) further comprises the steps of: (i) dividing said reference curve internally into a ratio m:n; and (ii) generating said dividing points by changing the ratio m:n.

Claim 20

A method according to claim 15, wherein step (d) comprises the steps of: (i) transforming each said section curve into a corresponding section curve in a predetermined planar coordinate system to bring into coincidence the first and second points and to bring into coincidence lines of intersection of said reference section and each of said two sections; (ii) computing an intermediate point by dividing internally into a ratio a:b each said corresponding section curves transformed into said predetermined planar coordinate system, the dividing at the ratio a:b designating third and fourth points, and dividing internally into a ratio m:n a straight line connecting the third and fourth points at which said section curves are internally divided into the ratio a:b, the straight line dividing designating the intermediate point; (iii) computing an untransformed intermediate section curve in said predetermined planar coordinate system by computing a number of intermediate points by changing the ratio a:b; and (iv) transforming the untransformed intermediate section curve in said predetermined planar coordinate system into the intermediate section curve in said intermediate section.

Claim 23

A method according to claim 17, wherein said step (b) comprises the steps of: (i) dividing said first reference curve internally into a ratio of m:n; and (ii) generating said dividing points by changing the ratio m:n.

Claim 24

A method according to claim 18, wherein step (e) comprises the steps of: (i) transforming said section curve, said point of intersection and the one of said dividing points into a corresponding section curve and corresponding points in a predetermined coordinate system to bring into coincidence the first point and the one of the dividing points of said intermediate section and said first reference curve, and to bring into coincidence the line of intersection of said section and said first reference section and the line of intersection of said intermediate section and said first reference section; (ii) computing a ratio L1:L2, where L1 is the length of a line segment connecting the first point and the second point of the section curve transformed into the corresponding section curve in said predetermined planar coordinate system, and where L2 is the length of a line segment connecting the one of said dividing points and the point of intersection transformed into points in said predetermined planar coordinate system; (iii) finding a first curve point which divides said transformed corresponding section curve internally into a ratio a:b; (iv) computing an angle defined by the second point, the first point and the point of intersection; (v) computing a second curve point obtained by rotating by the angle a third curve point which divides a line segment defined by the first point and the first curve point externally into the ratio L1:L1; (vi) generating an untransformed intermediate section curve in said predetermined planar coordinate system by finding a plurality of second curve points by changing the ratio a:b; and (vii) transforming the untransformed intermediate section curve in said predetermined planar coordinate system into the intermediate section curve in said intermediate section.

Claim 27

A method according to claim 20,, wherein step (b) comprises the steps of: (i) dividing said first reference curve internally into a ratio m:n; and (ii) generating said dividing points by changing the ratio m:n.

Claim 28

A method according to claim 21, wherein step (e) comprises the steps of: (i) transforming said section curve, said point of intersection and the one of said dividing points into a corresponding curve and corresponding points in a predetermined coordinate system to bring into coincidence the first point and the one of the dividing points of said intermediate section and said first reference curve, and to bring into coincidence the line of intersection of said section and said first reference section and the line of intersection of said intermediate section and said first reference section; (ii) computing a ratio L1:L2, where L1 is the length of a line segment connecting the first point and the second point of the section curve transformed into the corresponding curve in said predetermined planar coordinate sytem, and where L2 is the length of a line segment connecting the one of said dividing points and the point of intersection transformed into points in said predetermined planar coordinate system; (iii) finding a first curve point which divides said transformed corresponding section curve internally into a ratio a:b; (iv) computing an angle defined by the second pont, the first point and the point of intersection; (v) computing a second curve point obtained by rotating by the angle a third curve point which divides a line segment defined by the first point and the first curve point externally into the ratio L1:L2; (vi) generating the untransformed intermediate section curve in said predetermined planar coordinate system by finding a plurality of second curve points by changing the ratio a:b; and (vii) transforming said untransformed intermediate section curve in said predetermined planar coordinate system into the intermediate section curve in said intermediate section.

Claim 31

A method according to claim 23, wherein step (b) comprises the steps of: (i) dividing said first reference curve internally into a ratio m:n; and (ii) generating said dividing points by changing the ratio m:n.

Claim 32

A method according to claim 24, wherein step (b) comprises the steps of: (i) transforming said section curve, said point of intersection and the one of said dividing points into a corresponding section curve and corresponding points in a predetermined planar coordinate system to bring into coincidence the first point and the one of said dividing points of said intermediate section and said first reference curve, and to bring into coincidence the line of intersection of said section and a reference section and the line of intersection of said intermediate section and said reference section; (ii) computing a ratio L1:L2, where L1 is the length of a line segment connecting the first point and the second point of the section curve transformed into the corresponding section curve in said predetermined planar coordinate system, and where L2 is the length of a line segment connecting the one of said dividing points and said point of intersection transformed into points in said predetermined planar coordinate system; (iii) finding a first curve point which divides said transformed corresponding section curve internally into a ratio a:b; (iv) computing an angle defined by the second points, the first point and the point of intersection; (v) computing a second curve point obtained by rotating by the angle a third curve point which divides a line segment defined by the first point and the first curve point externally into the ratio L1:L2; (vi) generating an untransformed intermediate section curve in said predetermined planar coordinate system by finding a plurality of second curve points by changing the ratio a:b; and (vii) transforming said untransformed intermediate section curve in said predetermined planar coordinate system into the intermediate section curve in said intermediate section.

Claim 35

A method according to claim 26, wherein step (d) comprises the steps of: (i) transforming said section curve, the one of the dividing points and said corresponding dividing point into a corresponding section curve and corresponding points in a predetermined coordinate system to bring into coincidence the first point and the one of the dividing points of said intermediate section and said first reference curve, and to bring into coincidence the line of intersection of said section and a reference section and the line of intersection of said intermediate section and said reference section; (ii) computing a ratio L1:L2, where L1 is the length of a line segment connecting the first point and second point of the corresponding section curve transformed into the curve in said predetermined planar coordinate system, and where L2 is the length of a line segment connecting the one of said dividing points and the corresponding dividing point transformed into points in said predetermined planar coordinate system; (iii) finding a first curve point which divides said transformed corresponding section curve internally into a ratio a:b; (iv) computing an angle defined by the second point, the first point and the corresponding dividing point; (v) computing a second curve point obtained by rotating by the angle a third curve point which divides a line segment defined by the first point and the first curve point externally into the ratio L1:L2; (vi) generating an untransformed section curve in said predetermined planar coordinate system by finding a plurality of second curve points by changing the ratio a:b; and (vii) transforming said untransformed intermediate section curve in said predetermined planar coordinate system into the intermediate section curve in said intermediate section.

Claim 38

A method according to claim 28, wherein step (e) comprises the steps of: (i) transforming each of said section curves, said dividing point and said point of intersection of the intermediate section and said first and second reference curves into a corresponding section curve, and corresponding points in a predetermined planar coordinate system, to bring into coincidence the first and second points of said first reference curve and each of said sections and said dividing point, and to bring into coincidence lines of intersection of said first reference section and each of said sections and a line of intersection of said intermediate section and said first reference section; (ii) computing an intermediate point by internally dividing into a ratio a:b each of said corresponding section curves transformed into said predetermined planar coordinate system, the dividing by the ratio a:b designating fifth and sixth points, and dividing internally into the ratio m:n a straight line connecting the fifth and sixth points at which said section curves are internally divided into the ratio a:b, the straight line dividing designating the intermediate point; (iii) generating a temporary intermediate section curve comprising intermediate points by finding a number of intermediate points by changing the ratio a:b and containing a temporary intermediate section curve end point; (iv) computing a ratio L1:L2, where L1 is the length of a line segment connecting the first point and the third point and where L2 is the length of a line segment connecting said dividing point and the point of intersection transformed into points in said predetermined planar coordinate system; (v) finding a first curve point which divides said temporary intermediate section curve into a ratio c:d; (vi) computing an angle defined by the temporary intermediate section curve end point, the first point and the point of intersection; (vii) computing a second curve point obtained by rotating by the angle a third curve point which divides a line segment defined by the first point and the first curve point externally into the ratio L1:L2; (viii) generating an untransformed intermediate section curve in said predetermined planar coordinate system by finding a number of second curve points by changing the dividing ratio c:d; and (ix) transforming said untransformed intermediate section curve in said predetermined planar coordinate system into the intermediate section curve in said intermediate section.

Claim 41

A method according to claim 30, wherein step (e) comprises the steps of: (i) transforming each of said section curves, said dividing point and said point of intersection into a corresponding section curve and corresponding points in a predetermined planar coordinate system to bring into coincidence the first and third points, and said dividing point of said first reference curve, and to bring into coincidence lines of intersection of said first reference section and each of said sections and a line of intersection of said intermediate section and said first reference section; (ii) computing an intermediate point by internally dividing into a ratio a:b each of said corresponding section curves transformed into said predetermined planar coordinate system, the dividing at the ratio a:b designating fifth and sixth points, and dividing internally into a ratio m:n a straight line connecting the fifth and sixth points at which said section curves are internally divided into the ratio a:b, the straight line dividing designating the intermediate point; (iii) generating a temporary intermediate section curve comprising intermediate points by finding a number of intermediate points by changing said internal dividing ratio a:b and containing a temporary intermediate section curve end point; (iv) computing a ratio L1:L2, where L1 is the length of a line segment connecting the first point and the third point and where L2 is the length of a line segment connecting the one of said dividing points and said point of intersection transformed into points in said predetermined planar coordinate system; (v) finding a first curve point which divides said temporary intermediate section curve into a ratio c:d; (vi) computing an angle defined by the temporary intermediate section curve end point, the first point and said point of intersection; (vii) computing a second curve point obtained by rotating by the angle a third curve which divides a line segment defined by the first point and the first curve point externally into the ratio L1:L2; (viii) generating an untransformed intermediate section curve in said predetermined planar coordinate system by finding a number of second curve points by changing the ratio c:d; and (ix) transforming said untransformed intermediate section curve in said predetermined planar coordinate system into the intermediate section curve in said intermediate section.

Claim 44

A method according to claim 32, wherein step (e) comprises the steps of: (i) transforming each of said section curves, said dividing point and said point of intersection into a corresponding section curve, and corresponding points in a predetermined planar coordinate system to bring into coincidence the first and third points, and said dividing point of said first reference curve, and to bring into coincidence lines of intersection of said first reference section and each of said sections and a line of intersection of said intermediate section and said first reference section; (ii) computing an intermediate point by internally dividing into a ratio a:b each of said corresponding section curves transformed into said predetermined planar coordinate system, the dividing at the ratio a:b designating fifth and sixth points, and dividing internally into a ratio of m:n a straight line connecting the fifth and sixth points at which said section curves are internally divided into the ratio a:b, the straight line dividing designating the intermediate point; (iii) generating a temporary intermediate section curve comprising intermediate points by finding a number of intermediate points by changing the ratio a:b and containing a temporary intermediate section curve end point; (iv) computing a ratio L1:L2, where L1 is the length of a line segment connecting the first point and the third point and where L2 is the length of a line segment connecting said dividing point and said point of intersection transformed into points in said predetermined planar coordinate system; (v) finding a first curve point which divides said temporary intermediate section curve into a ratio c:d; (vi) computing an angle defined by said temporary intermediate section curve end point, the first point and said point of intersection; (vii) computing a second curve point obtained by rotating by the angle a third curve point which divides a line segment defined by the first point and the first curve point externally into the ratio L1:L2; (viii) generating an untransformed intermediate section curve in said predetermined planar coordinate system by finding a number of second curve points by changing the ratio c:d; and (ix) transforming said untransformed intermediate section curve in said predetermined planar coordinate system into the intermediate section curve in said intermediate section.

Claim 47

A method according to claim 34, wherein step (e) comprises the steps of: (i) transforming each of said section curves and the first and second dividing points of said first and second reference curves into corresponding section curves and corresponding points in a predetermined planar coordinate system to bring into coincidence the first and second points of said first reference curve and each of said sections and said first dividing point of said first reference curve, and to bring into coincidence lines of intersection of said first reference section and each of said sections and a line of intersection of said intermediate section and said first reference section; (ii) computing intermediate points by internally dividing into a ratio a:b each of said corresponding section curves transformed into said predetermined planar coordinate system, the dividing at the ratio a:b designating fifth and sixth points for each of said section curves, and dividing internally into a ratio of m:n the straight line connecting the fifth and sixth points at which said section curves are internally divided into a ratio a:b, said straight line dividing designating an intermediate point for each said curve; (iii) generating a temporary intermediate section curve for each section comprising respective intermediate points by finding a number of respective intermediate points by changing the ratio a:b and each section curve having a temporary intermediate section curve end point; (iv) computing ratio L1:L2 for each intermediate section, where L1 is the length of a line segment connecting the first point and the third point, and where L2 is the length of a line segment connecting said first and second dividing points transformed into points in said predetermined planar coordinate system; (v) finding first a curve point for each intermediate section which divides said temporary intermediate section curve into a ratio c:d; (vi) computing an angle for each intermediate section defined by said temporary intermediate section curve end point, the first point and said second dividing point; (vii) computing a second curve point for each intermediate section obtained by rotating by the angle a third curve point which divides a line segment defined by the first point and the first curve point externally into the ratio L1:L2; (viii) generating untransformed intermediate section curves for each intermediate section in said predetermined planar coordinate system by finding a number of respective second curve points by changing the ratio c:d; and (ix) transforming said untransformed intermediate section curves in said predetermined planar coordinate system into the intermediate section curves in said intermediate sections.

Claim 50

A method according to claim 36, wherein step (e) comprises the steps of creating a numerical control tape based on the intermediate section curve data.

Claim 51

A method according to claim 36, wherein step (b) comprises the step of: (i) defining intermediate sections parallel with the given sections.

Claim 52

A method according to claim 38, wherein the given section data includes data defining the plane of the given section, and wherein step (i) comprises the steps of: (1) inputting reference section data for a reference section which passes through the two given sections and reference curve data for a reference curve defining the external shape of the body having end points corresponding to one of the end points of each of the given curves; (2) dividing the reference curve by a ratio m:n to define a dividing point, the dividing point lying in the intermediate section; (3) transforming the section data for one of the given sections into intermediate section data by translating the data defining the plane, where the translated plane passes through the dividing point; and (4) repeating steps (2) and (3) a plurality of times by varying the ratio m:n by an increment which insures the machined surface between the given sections.

Claim 53

A method according to claim 36, wherein step (b) comprises the steps of: (i) inputting reference section data for a reference section which passes through the given sections and reference curve data for a reference curve, where the reference curve data defines the external shape of the body; and (ii) defining intermediate sections perpendicular to the reference curve and contacting the reference curve.

Claim 54

A method according to claim 40, wherein the given section data includes data defining the plane of the given section, and wherein said step (ii) comprises the steps of: (1) dividing the reference curve by a ratio m:n to define a dividing point, the dividing point lying in one of the intermediate sections; (2) defining a normal line passing through the reference curve and the dividing point; (3) transforming the section data for one of the given sections into intermediate section data by translating the data defining the plane, where the translated plane passes through the normal and the reference section; and (4) repeating steps 1-3 a plurality of times by varying the ratio m:n by an increment which insures the machined surface between the given sections.

Claim 55

A method according to claim 36, wherein step (b) comprises the steps of: (i) inputting reference section data for a reference section which passes through the given sections and reference curve data for a reference curve having end points corresponding to one of the end points of each of the given curves; (ii) defining an axis perpendicular to the reference section; and (iii) defining intermediate sections radiating from the axis.

Claim 56

A method according to claim 42, wherein the given section data includes data defining the plane of the given section, and wherein step (iii) comprises the steps of: (1) dividing the reference curve by a ratio m:n to define a dividing point, the dividing point lying in the reference section; (2) transforming the section data for one of the given sections into intermediate section data by translating the data defining the plane, where the translated plane passes through the dividing point and the axis; and (3) repeating steps (1) and (2) a plurality of times by varying the ratio m:n by an increment which insures the machined surface between given sections.

Claim 57

A method according to claim 36, wherein step (b) comprises the steps of: (i) inputting reference section data for two reference sections and reference curve data for two reference curves in the reference sections having end points corresponding to one of the end points of each of the given curves; and (ii) defining intermediate sections perpendicular to one of the two reference sections and contacting the corresponding section curve.

Claim 58

A method according to claim 44, wherein the given section data includes data defining the plane of the given section, and wherein step (ii) comprises the steps of: (1) dividing the two reference curves by a ratio m:n to define respective reference curve dividing points, the reference curve dividing points lying in the intermediate section; (2) defining a perpendicular line from one of the reference sections which passes through the dividing point of the other of the reference sections; (3) transforming the section data for one of the given sections into intermediate section data by translating the data defining the plane where the translated plane passes through the perpendicular line and the two dividing points; and (4) repeating steps 1-3 a plurality of times by varying the ratio by an increment which insures the machined surface between the given sections.

Claim 59

A method according to claim 39, 41, 43 or 45, wherein step (c) comprises the steps of: (I) transforming the given sections and given section curves onto the same plane where the end points coincide; (II) dividing the two given curves by a ratio a:b to define respective given curve dividing points; (III) dividing a straight line connecting the given curve dividing points by the ratio m:n; (IV) repeating steps (II) and (III) a plurality of times by changing the ratio a:b by a curve increment to create an intermediate section curve; and (V) transforming the intermediate section curve into intermediate section curve data.

Claim 61

A method according to claim 45, wherein step (c) comprises the steps of: (I) transforming the given section curves and the reference curve dividing points into the same plane where the corresponding end points of the given curves and the corresponding reference curve dividing point coincide; (II) dividing the given curves by a ratio a:b to define respective given curve dividing points; (III) dividing a straight line connecting the given curve dividing points by the ratio m:n; (IV) repeating steps (II) and (III) a plurality of times by changing the ratio a:b by a curve increment to create a temporary intermediate curve having an end point; (V) determining a ratio L1:L2 where L1 is the length of a first straight line connecting the end points of the temporary intermediate curve and L2 is the length of a second straight line connecting the reference curve dividing points; (VI) determining an angle between the first and second straight lines; (VII) dividing the temporary intermediate curve by a ratio c:d to define a temporary curve dividing point; (VIII) determining a translated and rotated point by rotating the temporary curve dividing point by the angle and translating the temporary curve dividing point based on the ratio L1:L2; (IX) repeating steps (VII) and (VIII) a plurality of times by changing the ratio c:d by a final curve increment to create the intermediate section curve; and (X) transforming the intermediate section curve into intermediate section curve data.