Patent US5636338A successfully refreshed from Google Patents.
US5636338A
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Method for designing curved shapes for use by a computer
Assignee: Microsoft Technology Licensing LLC
•
Filing: 1993-01-29
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Granted: 1997-06-03
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Expires: 2013-01-29
Abstract
Abstract Methods for forming computer models of curves, networks, or surfaces from user defined specifications of the shape to be modeled. Each specification includes a set of geometric constraints, such as positions, tangents curvatures, and torsions, and may also include discontinuity specifications. In the preferred embodiment, curves are computed so as to locally minimize a scale invariant functional of the geometry of the curve, such as a magnitude of variation in curvature of the curve (MVC) or a magnitude of curvature of the curve (MEC), while satisfying a user defined specification. An improvement on the MVC functional is to add a magnitude of variation in torsion of the curve. An improvement on the MEC functional is to add a magnitude of torsion of the curve. Networks of curves are produced using similar techniques of computing a local minimum of a functional of the geometry of the curves comprising the network, such as a magnitude of variation in curvature of the curves (MVN) or a magnitude of curvature of the curves (MEN), while satisfying a user defined specification. An improvement on these methods is to make the MVN and MEN functionals scale invariant. Another improvement is to make the MVN and MEN functionals torsion dependent. Surfaces are produced using a technique of computing a locally minimized functional of a magnitude of variation in curvature of the surface (MVS), while satisfying a set of surface constraints. An improvement on this method is to make the MVS functional scale invariant.
Inventors
- 👤 Henry P. Moreton
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-09 22:58
CPC Classifications
G; G06; G06T; G06T17/00; G06T17/30
Claims Analysis
Total Claims: 110
Claim 1
Independent Claim
94 words
A method for producing a representation of a curve for display by a computer system, comprising: specifying a desired shaped of the curve utilizing a set of geometric constraints; specifying a scale invariant functional of the desired shape that is locally minimized and operative to measure a magnitude of variation in a curvature of the desired shape; producing a representation of the curve based on the functional and the set of geometric constraints; and displaying the representation of the curve via an output device to create a visual or physical embodiment of the curve.
Claim 2
Independent Claim
94 words
A method for producing a representation of a curve for display by a computer system, comprising: specifying a desired shaped of the curve utilizing a set of geometric constraints; specifying a scale invariant functional of the desired shape that is locally minimized and operative to measure a magnitude of variation in a curvature of the desired shape; producing a representation of the curve based on the functional and the set of geometric constraints; and displaying the representation of the curve via an output device to create a visual or physical embodiment of the curve.
Claim 3
Dependent Claim
23 words
The method as recited in claim 1, wherein the functional is further operative to measure variations in a torsion of the desired shape.
Claim 4
Dependent Claim
56 words
The method as recited in claim 2, wherein the functional is a sum of an arc length integral of a square of a magnitude of an arc length derivative of the curvature of the desired shape and an arc length integral of a square of an arc length derivative of the torsion of the desired shape.
Claim 5
Dependent Claim
29 words
The method as recited in claim 3, wherein said functional is made scale invariant by multiplying the sum by a cube of an arc length of the desired shape.
Claim 6
Dependent Claim
27 words
The method as recited in claim 1 wherein the set of geometric constraints includes at least one point that the desired shape of the curve must interpolate.
Claim 7
Dependent Claim
27 words
The method as recited in claim 1 wherein the set of geometric constraints includes at least one tangent that the desired shape of the curve must interpolate.
Claim 8
Dependent Claim
27 words
The method as recited in claim 1 wherein the set of geometric constraints includes at least one curvature that the desired shape of the curve must interpolate.
Claim 9
Dependent Claim
27 words
The method as recited in claim 1, wherein the set of geometric constraints includes at least one torsion that the desired shape of the curve must interpolate.
Claim 10
Dependent Claim
28 words
The method as recited in claim 1 wherein the set of geometric constraints includes at least one G 2 discontinuity specification for the desired shape of the curve.
Claim 11
Dependent Claim
28 words
The method as recited in claim 1, wherein the set of geometric constraints includes at least one G 1 discontinuity specification for the desired shape of the curve.
Claim 12
Dependent Claim
35 words
The method as recited in claim 1, wherein the magnitude of variation is an arc length integral of a square of a magnitude of an arc length derivative of the curvature of the desired shape.
Claim 13
Dependent Claim
31 words
The method as recited in claim 1, wherein the functional is made scale invariant by multiplying the magnitude of variation by a cube of an arc length of the desired shape.
Claim 14
Dependent Claim
28 words
The method as recited in claim 1, wherein the functional is made scale invariant by multiplying the magnitude of curvature by an arc length of the desired shape.
Claim 15
Independent Claim
108 words
A method for producing a representation of a curve for display by a computer system, comprising: specifying a desired shape of the curve utilizing a set of geometric constraints; specifying a functional of the desired shape that is locally minimized, operative to measure a magnitude of variation in a curvature of the desired shape, and operative to measure a magnitude of variation in a torsion of the desired shape; producing a representation of the curve based on the specified functional and the specified set of geometric constraints; and displaying the representation of the curve via an output device to create a visual or physical embodiment of the curve.
Claim 16
Independent Claim
108 words
A method for producing a representation of a curve for display by a computer system, comprising: specifying a desired shape of the curve utilizing a set of geometric constraints; specifying a functional of the desired shape that is locally minimized, operative to measure a magnitude of variation in a curvature of the desired shape, and operative to measure a magnitude of variation in a torsion of the desired shape; producing a representation of the curve based on the specified functional and the specified set of geometric constraints; and displaying the representation of the curve via an output device to create a visual or physical embodiment of the curve.
Claim 17
Dependent Claim
56 words
The method as recited in claim 14, wherein the functional is a sum of an arc length integral of a square of a magnitude of an arc length derivative of the curvature of the desired shape and an arc length integral of a square of an arc length derivative of the torsion of the desired shape.
Claim 18
Dependent Claim
27 words
The method as recited in claim 14, wherein the set of geometric constraints includes at least one point that the desired shape of the curve must interpolate.
Claim 19
Dependent Claim
27 words
The method as recited in claim 14, wherein the set of geometric constraints includes at least one tangent that the desired shape of the curve must interpolate.
Claim 20
Dependent Claim
27 words
The method as recited in claim 14, wherein the set of geometric constraints includes at least one curvature that the desired shape of the curve must interpolate.
Claim 21
Dependent Claim
27 words
The method as recited in claim 14, wherein the set of geometric constraints includes at least one torsion that the desired shape of the curve must interpolate.
Claim 22
Dependent Claim
28 words
The method as recited in claim 14, wherein the set of geometric constraints includes at least one G 2 discontinuity specification for the desired shape of the curve.
Claim 23
Dependent Claim
28 words
The method as recited in claim 14, wherein the set of geometric constraints includes at least one G 1 discontinuity specification for the desired shape of the curve.
Claim 24
Dependent Claim
35 words
The method as recited in claim 14, wherein the magnitude of variation is an arc length integral of a square of a magnitude of an arc length derivative of the curvature of the desired shape.
Claim 25
Independent Claim
88 words
A method for producing a representation of a curve for use by a computer system, comprising: specifying a desired shape of the curve utilizing a set of geometric constraints; specifying a scale invariant functional of the desired shape that is locally minimized and operative to measure a magnitude of curvature of the desired shape; producing a representation of the curve based on the functional and the set of geometric constraints; and displaying the representation via an output device to create a visual or physical embodiment of the curve.
Claim 26
Independent Claim
88 words
A method for producing a representation of a curve for use by a computer system, comprising: specifying a desired shape of the curve utilizing a set of geometric constraints; specifying a scale invariant functional of the desired shape that is locally minimized and operative to measure a magnitude of curvature of the desired shape; producing a representation of the curve based on the functional and the set of geometric constraints; and displaying the representation via an output device to create a visual or physical embodiment of the curve.
Claim 27
Dependent Claim
21 words
The method as recited in claim 23, wherein the functional is further operative to measure a torsion of the desired shape.
Claim 28
Dependent Claim
45 words
The method as recited in claim 24, wherein the functional is a sum of an arc length integral of a square of the magnitude of curvature of the desired shape and an arc length integral of a square of the torsion of the desired shape.
Claim 29
Dependent Claim
29 words
The method as recited in claim 25, wherein the functional is made scale invariant by multiplying the sum by a cube of an arc length of the desired shape.
Claim 30
Dependent Claim
27 words
The method as recited in claim 23, wherein the set of geometric constraints includes at least one point that the desired shape of the curve must interpolate.
Claim 31
Dependent Claim
27 words
The method as recited in claim 23, wherein the set of geometric constraints includes at least one tangent that the desired shape of the curve must interpolate.
Claim 32
Dependent Claim
27 words
The method as recited in claim 23, wherein the set of geometric constraints includes at least one curvature that the desired shape of the curve must interpolate.
Claim 33
Dependent Claim
27 words
The method as recited in claim 23, wherein the set of geometric constraints includes at least one torsion that the desired shape of the curve must interpolate.
Claim 34
Dependent Claim
28 words
The method as recited in claim 23, wherein the set of geometric constraints includes at least one G 1 discontinuity specification for the desired shape of the curve.
Claim 35
Dependent Claim
28 words
The method as recited in claim 23, wherein the set of geometric constraints includes at least one G 2 discontinuity specification for the desired shape of the curve.
Claim 36
Dependent Claim
27 words
The method as recited in claim 23, wherein the functional is an arc length integral of a square of the magnitude of curvature of the desired shape.
Claim 37
Independent Claim
98 words
A method for producing a representation of a curve for display by a computer system, comprising: specifying a desired shape of the curve utilizing a set of geometric constraints; specifying a functional of the desired shape that is locally minimized, operative to measure a magnitude of curvature of the desired shape, and operative to measure a torsion of the desired shape; producing a representation of the curve based on the functional and the set of geometric constraints; and displaying the representation of the curve via an output device to create a visual or physical embodiment of the curve.
Claim 38
Independent Claim
98 words
A method for producing a representation of a curve for display by a computer system, comprising: specifying a desired shape of the curve utilizing a set of geometric constraints; specifying a functional of the desired shape that is locally minimized, operative to measure a magnitude of curvature of the desired shape, and operative to measure a torsion of the desired shape; producing a representation of the curve based on the functional and the set of geometric constraints; and displaying the representation of the curve via an output device to create a visual or physical embodiment of the curve.
Claim 39
Dependent Claim
45 words
The method as recited in claim 34, wherein the functional is a sum of an arc length integral of a square of the magnitude of curvature of the desired shape and an arc length integral of a square of the torsion of the desired shape.
Claim 40
Dependent Claim
27 words
The method as recited in claim 34, wherein the set of geometric constraints includes at least one point that the desired shape of the curve must interpolate.
Claim 41
Dependent Claim
27 words
The method as recited in claim 34, wherein the set of geometric constraints includes at least one tangent that the desired shape of the curve must interpolate.
Claim 42
Dependent Claim
27 words
The method as recited in claim 34, wherein the set of geometric constraints includes at least one curvature that the desired shape of the curve must interpolate.
Claim 43
Dependent Claim
27 words
The method as recited in claim 34, wherein the set of geometric constraints includes at least one torsion that the desired shape of the curve must interpolate.
Claim 44
Dependent Claim
28 words
The method as recited in claim 34, wherein the set of geometric constraints includes at least one G 1 discontinuity specification for the desired shape of the curve.
Claim 45
Dependent Claim
28 words
The method as recited in claim 34, wherein the set of geometric constraints includes at least one G 2 discontinuity specification for the desired shape of the curve.
Claim 46
Dependent Claim
27 words
The method as recited in claim 34, wherein the functional is an arc length integral of a square of the magnitude of curvature of the desired shape.
Claim 47
Independent Claim
104 words
A method for producing a representation of a network of curves for display by a computer system, comprising: specifying a desired shape of the network of curves utilizing a set of geometric constraints; specifying a scale invariant functional of the desired shape that is locally minimized and operative to measure a magnitude of variation in a curvature of the desired shape; producing a representation of the network of curves based on the functional and the set of geometric constraints; and displaying the representation of the network of curves via an output device to create a visual or physical embodiment of the network of curves.
Claim 48
Independent Claim
104 words
A method for producing a representation of a network of curves for display by a computer system, comprising: specifying a desired shape of the network of curves utilizing a set of geometric constraints; specifying a scale invariant functional of the desired shape that is locally minimized and operative to measure a magnitude of variation in a curvature of the desired shape; producing a representation of the network of curves based on the functional and the set of geometric constraints; and displaying the representation of the network of curves via an output device to create a visual or physical embodiment of the network of curves.
Claim 49
Dependent Claim
33 words
The method as recited in claim 43, wherein the functional is an arc length integral of a square of a magnitude of an arc length derivative of the curvature of the desired shape.
Claim 50
Dependent Claim
23 words
The method as recited in claim 43, wherein the functional is further operative to measure variations in a torsion of the desired shape.
Claim 51
Dependent Claim
56 words
The method as recited in claim 45, wherein the functional is a sum of an arc length integral of a square of a magnitude of an arc length derivative of the curvature of the desired shape and an arc length integral of a square of an arc length derivative of the torsion of the desired shape.
Claim 52
Dependent Claim
29 words
The method as recited in claim 46, wherein the functional is made scale invariant by multiplying the functional by a cube of an arc length of the desired shape.
Claim 53
Dependent Claim
29 words
The method as recited in claim 43, wherein the functional is made scale invariant by multiplying the functional by a cube of an arc length of the desired shape.
Claim 54
Dependent Claim
29 words
The method as recited in claim 43, wherein the set of geometric constraints includes at least one point that the desired shape of the network of curves must interpolate.
Claim 55
Dependent Claim
30 words
The method as recited in claim 43, wherein the set of geometric constraints includes at least one tangent plane that the desired shape of the network of curves must interpolate.
Claim 56
Dependent Claim
36 words
The method as recited in claim 43, wherein the set of geometric constraints includes at least one direction of principle curvature of the desired shape that the desired shape of the network of curves must interpolate.
Claim 57
Dependent Claim
35 words
The method as recited in claim 43, wherein the set of geometric constraints includes at least one maximum principle curvature of the desired shape that the desired shape of the network of curves must interpolate.
Claim 58
Dependent Claim
35 words
The method as recited in claim 43, wherein the set of geometric constraints includes at least one minimum principle curvature of the desired shape that the desired shape of the network of curves must interpolate.
Claim 59
Dependent Claim
30 words
The method as recited in claim 43, wherein the set of geometric constraints includes at least one tangent direction that the desired shape of the network of curves must interpolate.
Claim 60
Dependent Claim
34 words
The method as recited in claim 43, wherein the set of geometric constraints includes at least one pair of curves that meet with G 1 continuity at a node of the network of curves.
Claim 61
Dependent Claim
34 words
The method as recited in claim 43, wherein the set of geometric constraints includes at least one pair of curves that meet with G 2 continuity at a node of the network of curves.
Claim 62
Independent Claim
113 words
A method for producing a representation of a network of curves for display by a computer system, comprising: specifying a desired shape of the network of curves utilizing a set of geometric constraints; specifying a functional of the desired shape that is locally minimized, operative to measure a magnitude of variation in a curvature of the desired shape, and operative to measure variations in a torsion of the desired shape; producing a representation of the network of curves based on the functional and the set of geometric constraints; and displaying the representation of the network of curves via an output device to create a visual or physical embodiment of the network of curves.
Claim 63
Independent Claim
113 words
A method for producing a representation of a network of curves for display by a computer system, comprising: specifying a desired shape of the network of curves utilizing a set of geometric constraints; specifying a functional of the desired shape that is locally minimized, operative to measure a magnitude of variation in a curvature of the desired shape, and operative to measure variations in a torsion of the desired shape; producing a representation of the network of curves based on the functional and the set of geometric constraints; and displaying the representation of the network of curves via an output device to create a visual or physical embodiment of the network of curves.
Claim 64
Dependent Claim
56 words
The method as recited in claim 57, wherein the functional is a sum of an arc length integral of a square of a magnitude of an arc length derivative of the curvature of the desired shape and an arc length integral of a square of an arc length derivative of the torsion of the desired shape.
Claim 65
Dependent Claim
29 words
The method as recited in claim 57, wherein the set of geometric constraints includes at least one point that the desired shape of the network of curves must interpolate.
Claim 66
Dependent Claim
30 words
The method as recited in claim 57, wherein the set of geometric constraints includes at least one tangent plane that the desired shape of the network of curves must interpolate.
Claim 67
Dependent Claim
36 words
The method as recited in claim 57, wherein the set of geometric constraints includes at least one direction of principle curvature of the desired shape that the desired shape of the network of curves must interpolate.
Claim 68
Dependent Claim
35 words
The method as recited in claim 57, wherein the set of geometric constraints includes at least one maximum principle curvature of the desired shape that the desired shape of the network of curves must interpolate.
Claim 69
Dependent Claim
35 words
The method as recited in claim 57, wherein the set of geometric constraints includes at least one minimum principle curvature of the desired shape that the desired shape of the network of curves must interpolate.
Claim 70
Dependent Claim
30 words
The method as recited in claim 57, wherein the set of geometric constraints includes at least one tangent direction that the desired shape of the network of curves must interpolate.
Claim 71
Dependent Claim
34 words
The method as recited in claim 57, wherein the set of geometric constraints includes at least one pair of curves that meet with G 1 continuity at a node of the network of curves.
Claim 72
Dependent Claim
34 words
The method as recited in claim 57, wherein the set of geometric constraints includes at least one pair of curves that meet with G 2 continuity at a node of the network of curves.
Claim 73
Independent Claim
108 words
A method for producing a representation of a network of curves for display by a computer system, comprising: specifying a desired shape of the network of curves utilizing a set of geometric constraints; specifying a functional of the desired shape that is locally minimized, operative to measure a magnitude of curvature of the desired shape, and operative to measure a torsion of the desired shape; producing a representation of the network of curves based on the functional and the set of geometric constraints; and displaying the representation of the network of curves via an output device to create a visual or physical embodiment of the network of curves.
Claim 74
Independent Claim
108 words
A method for producing a representation of a network of curves for display by a computer system, comprising: specifying a desired shape of the network of curves utilizing a set of geometric constraints; specifying a functional of the desired shape that is locally minimized, operative to measure a magnitude of curvature of the desired shape, and operative to measure a torsion of the desired shape; producing a representation of the network of curves based on the functional and the set of geometric constraints; and displaying the representation of the network of curves via an output device to create a visual or physical embodiment of the network of curves.
Claim 75
Dependent Claim
46 words
The method as recited in claim 67, wherein the functional is a sum of an arc length integral of a square of a magnitude of the curvature of the desired shape and an arc length integral of a square of the torsion of the desired shape.
Claim 76
Dependent Claim
29 words
The method as recited in claim 67, wherein the set of geometric constraints includes at least one point that the desired shape of the network of curves must interpolate.
Claim 77
Dependent Claim
30 words
The method as recited in claim 67, wherein the set of geometric constraints includes at least one tangent plane that the desired shape of the network of curves must interpolate.
Claim 78
Dependent Claim
32 words
The method as recited in claim 67, wherein the set of geometric constraints includes at least one direction of principle curvature that the desired shape of the network of curves must interpolate.
Claim 79
Dependent Claim
31 words
The method as recited in claim 67, wherein the set of geometric constraints includes at least one maximum principle curvature that the desired shape of the network of curves must interpolate.
Claim 80
Dependent Claim
31 words
The method as recited in claim 67, wherein the set of geometric constraints includes at least one minimum principle curvature that the desired shape of the network of curves must interpolate.
Claim 81
Dependent Claim
34 words
The method as recited in claim 67, wherein the set of geometric constraints includes at least one pair of curves that meet with G 1 continuity at a node of the network of curves.
Claim 82
Dependent Claim
30 words
The method as recited in claim 67, wherein the set of geometric constraints includes at least one tangent direction that the desired shape of the network of curves must interpolate.
Claim 83
Independent Claim
101 words
A method for producing a representation of a network of curves for display by a computer system, comprising: specifying a desired shape of the network of curves utilizing a set of geometric constraints; specifying a scale invariant functional of the desired shape that is locally minimized and operative to measure a magnitude of curvature of the desired shape; producing a representation of the network of curves based on the functional and the set of geometric constraints; and displaying the representation of the network of curves via an output device to create a visual or physical embodiment of the network of curves.
Claim 84
Independent Claim
101 words
A method for producing a representation of a network of curves for display by a computer system, comprising: specifying a desired shape of the network of curves utilizing a set of geometric constraints; specifying a scale invariant functional of the desired shape that is locally minimized and operative to measure a magnitude of curvature of the desired shape; producing a representation of the network of curves based on the functional and the set of geometric constraints; and displaying the representation of the network of curves via an output device to create a visual or physical embodiment of the network of curves.
Claim 85
Dependent Claim
33 words
The method as recited in claim 76, wherein the functional is an arc length integral of a square of a magnitude of an arc length derivative of the curvature of the desired shape.
Claim 86
Dependent Claim
23 words
The method as recited in claim 76, wherein the functional is further operative to measure variations in a torsion of the desired shape.
Claim 87
Dependent Claim
46 words
The method as recited in claim 78, wherein the functional is a sum of an arc length integral of a square of a magnitude of the curvature of the desired shape and an arc length integral of a square of the torsion of the desired shape.
Claim 88
Dependent Claim
29 words
The method as recited in claim 79, wherein the functional is made scale invariant by multiplying the functional by a cube of an arc length of the desired shape.
Claim 89
Dependent Claim
29 words
The method as recited in claim 76, wherein the functional is made scale invariant by multiplying the functional by a cube of an arc length of the desired shape.
Claim 90
Dependent Claim
29 words
The method as recited in claim 76, wherein the set of geometric constraints includes at least one point that the desired shape of the network of curves must interpolate.
Claim 91
Dependent Claim
30 words
The method as recited in claim 76, wherein the set of geometric constraints includes at least one tangent plane that the desired shape of the network of curves must interpolate.
Claim 92
Dependent Claim
32 words
The method as recited in claim 76, wherein the set of geometric constraints includes at least one direction of principle curvature that the desired shape of the network of curves must interpolate.
Claim 93
Dependent Claim
31 words
The method as recited in claim 76, wherein the set of geometric constraints includes at least one maximum principle curvature that the desired shape of the network of curves must interpolate.
Claim 94
Dependent Claim
31 words
The method as recited in claim 76, wherein the set of geometric constraints includes at least one minimum principle curvature that the desired shape of the network of curves must interpolate.
Claim 95
Dependent Claim
34 words
The method as recited in claim 76, wherein the set of geometric constraints includes at least one pair of curves that meet with G 1 continuity at a node of the network of curves.
Claim 96
Dependent Claim
30 words
The method as recited in claim 76, wherein the set of geometric constraints includes at least one tangent direction that the desired shape of the network of curves must interpolate.
Claim 97
Independent Claim
97 words
A method for producing a representation of a curved surface for display by a computer system, comprising: specifying a desired shape of the curved surface utilizing a set of geometric constraints; specifying a functional of the desired shape that is locally minimized and operative to measure a magnitude of variation in a curvature of the desired shape; producing a representation of the curved surface based on the functional and the set of geometric constraints; and displaying the representation of the curved surface via an output device to create a visual or physical embodiment of the curved surface.
Claim 98
Independent Claim
97 words
A method for producing a representation of a curved surface for display by a computer system, comprising: specifying a desired shape of the curved surface utilizing a set of geometric constraints; specifying a functional of the desired shape that is locally minimized and operative to measure a magnitude of variation in a curvature of the desired shape; producing a representation of the curved surface based on the functional and the set of geometric constraints; and displaying the representation of the curved surface via an output device to create a visual or physical embodiment of the curved surface.
Claim 99
Dependent Claim
71 words
The method as recited in claim 89, wherein the functional is an area integral of a sum of a square of an arc length derivative of a maximum principle curvature of the desired shape taken in a maximum principle direction of the desired shape and a square of an arc length derivative of a minimum principle curvature of the desired shape taken in a minimum principle direction of the desired shape.
Claim 100
Dependent Claim
25 words
The method as recited in claim 89, wherein the functional is made scale invariant by multiplying the functional by an area of the desired shape.
Claim 101
Dependent Claim
28 words
The method as recited in claim 89, wherein the set of geometric constraints includes at least one point that the desired shape of the curved surface must interpolate.
Claim 102
Dependent Claim
29 words
The method as recited in claim 89, wherein the set of geometric constraints includes at least one tangent plane that the desired shape of the curved surface must interpolate.
Claim 103
Dependent Claim
35 words
The method as recited in claim 89, wherein the set of geometric constraints includes at least one direction of principle curvature of the desired shape that the desired shape of the curved surface must interpolate.
Claim 104
Dependent Claim
34 words
The method as recited in claim 89, wherein the set of geometric constraints includes at least one maximum principle curvature of the desired shape that the desired shape of the curved surface must interpolate.
Claim 105
Dependent Claim
34 words
The method as recited in claim 89, wherein the set of geometric constraints includes at least one minimum principle curvature of the desired shape that the desired shape of the curved surface must interpolate.
Claim 106
Dependent Claim
33 words
The method as recited in claim 89, wherein the set of geometric constraints includes at least one continuous curve of tangent plane specification that the desired shape of the curved surface must interpolate.
Claim 107
Dependent Claim
43 words
The method as recited in claim 97, wherein the continuous curve of tangent plane specification further specifies a continuous surface normal curvature in a direction perpendicular to the curve of tangent plane specification that the desired shape of the curved surface must interpolate.
Claim 108
Dependent Claim
31 words
The method as recited in claim 89, wherein the set of geometric constraints includes at least one curve of G 2 discontinuity specification for the desired shape of the curved surface.
Claim 109
Independent Claim
30 words
The method as recited in claims 89, wherein the set of geometric constraints includes at least one curve G 1 discontinuity specification for the desired shape of the curved surface.
Claim 110
Dependent Claim
25 words
The method as recited in claim 89, wherein the functional is made scale invariant by multiplying the functional by an area of the desired shape.
References Cited (Backward Citations)
US4864520A
Cited
US5251160A
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