Shaving foil

A shaving foil for a shaving system comprises a foil support section and a hair-receiving section. The foil support section is provided for support of the foil over a cutting member of the shaving system. The hair-receiving section of the foil includes a plurality of hair-entrance apertures that define at least one amorphous arrangement of apertures and a plurality of foil surface members that form a network of surface area adjacent to the plurality of hair-entrance apertures.

FIELD OF THE INVENTION

The present invention relates in general to foils for shaving systems and in particular to foils having an amorphous arrangement of hair-entrance apertures. This invention further relates to methods of producing shaving system foils having an amorphous arrangement of hair-entrance apertures.

BACKGROUND OF THE INVENTION

The cutting head of an electric shaving system conventionally comprises a shear foil and an inner, movable cutter. The foil is a thin, flexible member that has a plurality of perforations or apertures therethrough for receiving hairs and stubble to be shaved. The corresponding cutter is positioned in contact with a rear surface of the foil and typically comprises a plurality of separate blades, but may also include a cutting foil or other suitable cutting device. Regardless of the specific configuration, the cutter vibrates or otherwise reciprocates back and forth over the apertures in the foil.

During a shaving operation, the foil is brought into intimate contact with the skin. As the shaving system is moved about an area to be shaved, hair and stubble pass through the apertures in the foil and are trimmed by the movable cutter, which repeatedly crosses the apertures in the foil. As such, the closeness, comfort and quality of the resulting shave are affected, at least in part, by the design of the foil.

In particular, the size, shape and orientation of the apertures in the foil affect the performance of the shaving operation. Thus, previous foils have been provided with repeating patterns of circular, rectangular, hexagonal and other geometric shaped apertures in an attempt to find a pattern that will provide a close and comfortable shave. However, hairs tend to grow in distinctly different directions. Moreover, hairs tend to exhibit differences in size.

SUMMARY OF THE INVENTION

An embodiment of the present invention provides a shaving foil for a shaving system comprising a foil support section and a hair-receiving section. The foil support section is provided for support of the foil over a cutting member of the shaving system. The hair-receiving section of the foil includes a plurality of hair-entrance apertures that define at least one amorphous arrangement of apertures and a plurality of foil surface members that form a network of surface area adjacent to the plurality of hair-entrance apertures.

Generally, the amorphous arrangement of apertures exhibits no readily discernable or perceptible pattern to the organization or regularity of the hair-entrance apertures within the bounds of one or more predetermined constraints, where the predetermined constraints may include limitations such as those imposed by the physical dimensions of the hair-receiving section of the foil, the desired number of hair-entrance apertures within the hair-receiving section of the foil, the desired minimum spacing between adjacent hair-entrance apertures, the minimum and maximum desired size of a given hair-entrance aperture and other considerations characteristic of performing the function of shaving.

According to another embodiment of the present invention, a shaving system comprises a housing and a cutting head. The cutting head is positioned at a first end of the housing and includes a cutting member extending from the housing, a foil frame mated with the housing and a foil supported by the foil frame so as to be oriented generally over the cutting member. The foil includes a hair-receiving section comprised of a plurality of foil surface members and a plurality of hair-entrance apertures that define at least one amorphous arrangement of apertures, wherein each hair-entrance aperture is at least partially surrounded by associated foil surface members that are interconnected in a network of surface area.

According to another embodiment of the present invention, a method of manufacturing a foil for a shaving system comprises providing a foil, defining a hair-receiving section of the foil and forming a plurality of apertures in the hair-receiving section of the foil to define at least one amorphous arrangement of apertures, wherein each hair-entrance aperture is at least partially surrounded by associated foil surface members that are interconnected in a network of surface area.

DETAILED DESCRIPTION OF THE INVENTION

Referring now to the drawings, and particularly toFIG. 1, a shaving system1comprises a housing2and a cutting head4. The cutting head4is positioned at one end of the housing2and includes one or more cutting members6that extend generally from the housing2, a detachable foil frame8that mates with the housing and one or more shaving foils10that are supported by the foil frame8so as to be oriented generally over the cutting member6when the foil frame8is attached to the housing2. The housing2also supports switches, motors, electronic circuitry and/or other components for selectively energizing the cutting members6of the cutting head4. Although the cutting members6are illustrated for purposes of clarity as a plurality of axially aligned, generally circular cutting disks, other cutting configurations including independent cutting blades and cutting foils may be used.

Referring toFIG. 2, the shaving foil, which is indicated generally by the reference numeral10, comprises a foil support section12and a hair-receiving section14. The foil support section12defines a securement arrangement that may be oriented, for example, adjacent to a perimeter16of the hair-receiving section14. The illustrated foil support section12includes mounting features18, such as holes, for attaching or otherwise mounting the foil10to the corresponding shaving system1, e.g., by attaching the foil10to the foil frame8on the shaving head4. The foil support section12may also be defined by the perimeter16or other portion of the hair-receiving section14of the foil10. Still further, other arrangements may alternatively be used to define the foil support section12including direct or indirect integration of the foil10with regard to the foil frame8.

The configuration of the shaving head4may vary considerably depending upon the particular shaving system1, thus the general size and shape of the particular foil10will correspond to the particular shaving system1. For example, as shown inFIG. 1, the shaving foil10conforms generally to the shape of the outer portion of the two axially extending cutting members6to form a generally arcuate, hair receiving sections14. The arcuate hair receiving sections14may be formed from a single foil10, or multiple foils10may be used, one foil10associated with each cutting member6.

The hair-receiving section14comprises a plurality of hair-entrance apertures20and foil surface members22. The plurality of hair-entrance apertures20define at least one amorphous arrangement of apertures and the plurality of foil surface members22form a network of surface area adjacent to the plurality of hair-entrance apertures20. As illustrated in the exemplary hair receiving section14, the foil surface members22are interconnected and surround each hair-entrance aperture20to form a continuous network of foil surface area about and/or within the hair-receiving section14in a manner that forms an amorphous arrangement of apertures24. As illustrated inFIG. 3, a foil surface width, which is designated by the dimension marking W, represents the width of a foil surface member22and corresponds to a distance between a point on one edge of a hair entrance aperture20and a proximal point on the edge of an adjacent hair-entrance aperture20.

As illustrated, the foil surface width W is configured to remain substantially uniform across a length L, which is a distance that corresponding edges of adjacent hair-entrance apertures remain substantially parallel to one another. However, the edges of adjacent hair entrance apertures20need not be parallel or substantially parallel and likewise, a chord between two points of adjacent hair entrance apertures20may not be perpendicular to either aperture edge. Moreover, the Width W may be substantially uniform for all foil surface members22, or alternatively, the width W may vary among the various foil surface members22. Still further, the foil surface members22may exhibit other arrangements of non-uniform width characteristics.

Characterization of an Amorphous Arrangement of Apertures

Generally, the amorphous arrangement of apertures24exhibits no readily discernable or perceptible organization or regularity of the hair-entrance apertures20within the bounds of one or more predetermined constraints, where the predetermined constraints may include limitations such as those imposed by the physical dimensions of the hair-receiving section14of the foil10, the desired number of hair-entrance apertures20within the hair-receiving section14of the foil10, the desired minimum spacing between adjacent hair-entrance apertures20, e.g., the width W of a corresponding foil surface member22, minimum and maximum desired size of a given hair-entrance aperture20, which will likely correspond to the minimum and maximum anticipated hair size, and other considerations characteristic of performing the function of shaving.

An amorphous arrangement of apertures24generally includes at least one feature that is random, pseudo-random, or apparently random, as will be described in greater detail herein. For example, an aperture size and/or shape feature may be implemented such that there is no readily discernable or perceptible pattern to the orientation, size and/or shape of the constituent hair-entrance apertures20within the amorphous arrangement of apertures24, again within the bounds of one or more of the predetermined constraints.

The hair-entrance apertures20are referred to generally as polygonal shaped apertures, or simply polygons, which may comprise geometric shapes having a finite number of straight sides, e.g., triangles, rectangles, parallelograms, etc. Also, a polygon, as used herein, may have an infinite number of straight sides, thus including within the general description of polygons, curvilinear and amoeba shapes and combinations thereof, including for example, circles, semi-circles, ellipsoids, wedges, truncated wedges, slots, wave and serpentine shaped apertures, etc.

In the amorphous arrangement illustrated inFIG. 3, the orientation and geometry of a first hair-entrance aperture20A with regard to a neighboring hair-entrance aperture20B appears to bear no predictable relationship to that of the next succeeding hair-entrance aperture20C. In one exemplary configuration, an amorphous arrangement of apertures24is characterized by a random center-to-center spacing feature in which aperture center-to-center spacing appears random or at least non-uniform within a designer specified range of values.

Here, the center of a hair-entrance aperture20may be defined in any reasonable manner and may include a point located either within or outside the bounds of a given hair-entrance aperture20. The particular choice of a defined center will likely depend upon whether the hair-entrance apertures20include odd or complex shapes such as amoebas, or curvilinear shapes such as slots or waves, or other non-simple geometric configurations. Some exemplary center points may include using a geometric center, center of mass, a point within an area that is approximately central within the aperture or some large region of the aperture or a principal or important point of concentration such as a nucleus of the aperture shape. The center may also comprise a point used in the generation of the aperture, such as a nucleation point center. The use of nucleation points as part of a process of generating the hair-entrance apertures20will be described in greater detail herein. However, there is a generally equal likelihood that the nearest aperture center to a given aperture center occurs at any given angular position within the plane of the foil10within reasonable tolerances and resolution.

As one example,FIG. 3illustrates that the nearest aperture center to hair-entrance aperture20D is aperture20E, as indicated by a loop surrounding their respective centers. The nearest aperture center to hair-entrance aperture20F is aperture20G, as indicated by a loop surrounding their respective centers. Similarly, the nearest aperture center to hair-entrance aperture20H is aperture201, as indicated by a loop surrounding their respective centers. As illustrated, there appears to be no order or pattern to the orientation of a closest aperture center to any given hair-entrance aperture20. The above three exemplary loops, by themselves, do not show that the total illustrated arrangement of apertures is amorphous, but rather illustrates one exemplary approach of how to determine if an arrangement of apertures is amorphous. As will be described in greater detail herein, the amorphous arrangement of apertures24may extend over the entire hair-receiving section14or only a portion thereof.

The size, shape and/or orientation features of the hair-entrance apertures20may be randomized, at least to a statistically significant degree, e.g., with or without constraints or other predetermined limitations. For example, the size range of the hair-entrance apertures20will likely depend upon the anticipated range of hair sizes that the shaving system1is designed to cut. The degree of randomness imposed in shape and/or orientation features of the hair-entrance apertures may also vary depending upon whether the amorphous arrangement of apertures24is manually generated or whether the amorphous arrangement of apertures24is generated by a computer. Other feature characteristics of the hair-entrance apertures20that may be randomized, at least to a statistically significant degree, includes the number of sides of the hair-entrance apertures20, minimum or maximum realizable angle between adjacent edges of the hair-entrance apertures20, and other shape affecting considerations.

There may be circumstances where it is undesirable or impractical to define a single amorphous arrangement of apertures24that is non-repeating across the entirety of the hair-receiving section14of the foil10. Also, there may be circumstances where it is desirable to use amorphous arrangements designed with different sets of constraints within different areas of the hair-receiving section14of the foil10. With reference toFIG. 4, a limited area of the hair-receiving section14of the foil10is shown in a partial view to illustrate a first amorphous arrangement of apertures24A adjacent to a second amorphous arrangement of apertures24B, where the first and second amorphous arrangement of apertures24A,24B were constructed using a different constraint that affects at least the variance in size of the corresponding hair-entrance apertures20. AsFIG. 4illustrates, the size variance of the hair-entrance apertures20in the first amorphous arrangement24A is greater than the variance in size of the hair-entrance apertures20in the second amorphous arrangement of apertures24B.

As an example, it may be desirable to have hair-entrance apertures20of a greater randomness generally near a first region, e.g., the central portion, of the hair-receiving section14of the foil10, and hair-entrance apertures20that have generally less deviation, e.g., in size, near a second region, e.g., the end regions of the hair-receiving section14of the foil10. Still further, it may be desirable to conceptually delineate the hair-receiving section14of the foil10into multiple regions of amorphous arrangements even to the point of replication of the same amorphous arrangement in two or more such regions, e.g., by replicating the amorphous arrangement of apertures24B on the opposite side of the amorphous arrangement of apertures24A. Still further, in a shaving system requiring more than one foil10, it may be desirable to have one or more foils10having hair-entrance apertures20defined by different amorphous characteristics or constraints.

Further, it may be desirable to include within the hair-receiving section14of the foil10, a combination of amorphous areas, and non-amorphous, patterned areas. Such may be required depending upon the capability of the manufacturing process or the needs of particular implementations of the present invention. For example, it may be desirable to limit or otherwise restrict the size, spacing or geometry of hair-entrance apertures20that align generally at a predetermined area of the hair-receiving section14of the foil10, to a pattern of defined shape or geometry, e.g., where that defined shape has been found to provide a useful feature during shaving. Also, non-amorphous patterns of apertures may be provided to add distinctive markings to the foil10. Additionally, an amorphous region may fully envelop or circumscribe one or more non-amorphous areas. With reference toFIG. 5, the amorphous arrangement of apertures24is illustrated as enclosing an exemplary repeating pattern of circular-shaped apertures26.

The term “random” as applied to describing one or more feature characteristics of the amorphous arrangement of apertures24may in practice be truly random, pseudorandom or apparently random. For example, a mathematically generated (e.g., computer generated) random number may be used to define a parameter that characterizes the hair-entrance apertures20as will be described in greater detail herein. However, the sophistication of the algorithm implementing the random function will affect how random the generated numbers truly are. Also, an amorphous arrangement of apertures24may be implemented or designed manually. Such a manually implemented design may result in an amorphous arrangement of apertures over predetermined constraints, but may also result in a pattern that is not random in a strict sense, but is apparently random or pseudorandom.

However, in either case, the hair-entrance apertures20may be arranged such that in the aggregate, there is at least an appearance of randomness to the apertures, at either a localized or global perspective, e.g., in the sense of a highly disordered or vaguely defined arrangement of apertures across the amorphous region of the hair-receiving section14of the foil10. For example, there may be more than one hair-entrance aperture20of a given size and/or shape within the amorphous arrangement of apertures24. However, the pattern of hair-entrance apertures20is non-uniform such that it is unlikely that a reasonably sized grouping of adjacent hair-entrance apertures20within the corresponding amorphous arrangement of apertures24will be the same as any other like grouping of hair-entrance apertures20.

The amorphous arrangement of apertures24may also be arranged so as to exhibit one or more isomorphic characteristics. An exemplary isomorphic characteristic comprises controlling the pattern formation so as to maintain generally uniform surface area of the foil surface members22associated with predefined regions of the hair-receiving section14. For example, if a prescribed area is defined within a subset of the corresponding amorphous arrangement of apertures24so as to encompass a statistically significant number of hair-entrance apertures20, the total foil area of the foil surface members22within that prescribed area would be substantially the same as a similarly prescribed foil area in a different location of the hair-receiving section14of the foil10. In this regard, the isomorphic characteristic may be defined in one dimension, e.g., across the width of the hair-receiving section14of the foil10, or in multiple directions.

With reference back toFIG. 2, as an example, the combined foil area of the foil surface members22within a first portion28A of the hair-receiving section14is generally similar to the combined foil area of the foil surface members22within a second portion28B of the hair-receiving section14. Expressed in a slightly different manner, an aperture ratio of the first portion28A is generally the same as an aperture ratio of the second portion28B, where the aperture ratio is defined as the ratio of the area of all of the hair-entrance apertures20within a given portion to the total area of that portion. Such an isomorphic characteristic may be beneficial, e.g., to prevent uneven or inconsistent deflection of the foil10in different areas of the hair-receiving section14to a degree that adversely affects the quality of a shaving operation. An example of how to control the foil area will be discussed in greater detail herein.

Other isomorphic characteristics that may be of interest may include the total surface area removed from the foil10due to the hair-entrance apertures20, number of hair-entrance apertures20, distributions of particular polygon geometries that define the shapes of the hair-entrance apertures20, etc.

Constraints

Depending upon the application, it may be desirable to constrain one or more parameters that define the hair-entrance apertures20in the hair-receiving section14of the foil10including their size, shape, orientation and/or spacing between adjacent aperture centers. Where the hair-entrance apertures20are polygonal in shape, aperture parameters including the number of sides, angles and area can each be controlled within predetermined designed-for ranges and still maintain an overall random characteristic.

The size of each hair-entrance aperture20will likely be bounded to some reasonable range of sizes. Hair-entrance apertures20that are too small to capture a hair are likely undesirable for shaving applications. Likewise, if the maximum size of a given hair-entrance aperture20is too large, then skin may press through that hair-entrance aperture20causing undesirable shaving performance. Also, a large distribution or improper weighting of sizes of the hair-entrance apertures20may undesirably impact the properties of a given shaving foil10. For example, smaller sized hair-entrance apertures20are less effective at capturing relatively long, coarse hairs.

Practical considerations such as strength, rigidity and flexibility of the foil substrate may limit the minimum realizable width W of the corresponding foil surface members22between adjacent hair-entrance apertures20so as to not compromise the foil structure. That is, the foil10must be flexible to accommodate the surface to be shaved. However, uneven deflection across the hair-receiving section14of the foil10may adversely affect the quality of shaving. One approach to address such uneven deflection is to maintain a generally consistent area of the foil surface members22within predetermined areas of the foil as noted in greater detail herein.

By limiting the number of sides of the polygons defining the hair-entrance apertures20to a practical finite number, it becomes easier to establish an interlocking relationship between adjacent hair-entrance apertures20. In this regard, the practical limit to the number of sides of each polygon can vary widely and may depend upon whether the amorphous arrangement of apertures24is to be defined manually, of through a computer implemented process.

An interlocking relationship between adjacent hair-entrance apertures20refers generally where a first hair-entrance aperture20includes a straight side edge that corresponds with, e.g., aligns substantially in parallel with, an associated straight side edge of an adjacent hair-entrance aperture20. Such an arrangement allows uniform spacing, e.g., via the width W of associated foil surface members22, between adjacent hair-entrance apertures20. An interlocking relationship between adjacent hair-entrance apertures20makes it easier for the designer to maintain a generally consistent foil surface area within predetermined portions of the hair-receiving section14of the foil10.

Likewise, too great a maximum realizable spacing between adjacent hair-entrance apertures may affect the overall performance of the shaving system, e.g., by requiring a relatively greater amount of time for an operator to navigate the hair-entrance apertures20in the foil10over the surface to be shaved. In this regard, the random characteristics of the amorphous hair-entrance apertures20may be statistically controlled by some predetermined measure. By limiting the aperture shape to polygons having a practical finite number of sides as noted in greater detail herein, e.g., so as to not be curvilinear, an interlocking pattern of hair-entrance apertures20can be arranged, at least theoretically, so that the foil area between adjacent hair-entrance apertures20can range from 0% to 100% of the area of the hair-receiving section14of the foil10.

Practical limits on the number of hair-entrance apertures20, the size range of the hair-entrance apertures20and the foil surface area between adjacent hair-entrance apertures20will set realistic constraints based for example, upon the size of the particular foil10, the strength and/or flexibility of the foil substrate and the thickness of the foil10. Moreover, from a practical standpoint, the ability to control the spacing between adjacent hair-entrance apertures20allows the foil area within the hair-receiving section14to be appropriately established as needed by a particular designed-for shaving application.

Methodology

Any suitable method, including manual approaches, may be utilized to design the hair-receiving section14of the foil10, e.g., in terms of desirable aperture size, shape, spacing, orientation, etc. However, where the number of imposed constraints, or other design parameters so warrant, a computer can be used to design the hair-receiving section14of the foil10.

One exemplary method of systematically generating an amorphous arrangement of apertures24utilizes a constrained Voronoi tessellation of 2-space. This method not only systematically generates the amorphous arrangement of apertures24, but it also permits the tailoring of desirable aperture size, shape, orientation and spacing with respect to the foil10. With reference toFIG. 6, the method30defines a bounded amorphous area at32. Such a bounded amorphous area may be defined by relative coordinates that characterize the size of the hair-receiving section14of the foil10or a subset thereof, e.g., where the hair-receiving section will further include one or more non-amorphous patterns or amorphous regions with different constraints. For sake of discussion herein, the coordinates will be discussed in Cartesian coordinate form that extend in a rectangular plane from 0,0 to XMAX, YMAX. However, different coordinate systems may be used.

A number of nucleation points N are determined at34A. The number of nucleation points corresponds to the number of polygonal hair-entrance apertures20desired in the amorphous area. The number of nucleation points N thus comprises an integer, and may be selected with regard to the average size and spacing of the polygonal hair-entrance apertures20desired in the amorphous area. One exemplary approach for determining an approximate number of nucleation points is to select a hypothetical polygon of arbitrary size and shape, e.g., an average size and average shape, and, to compute the number of uniform instances of the hypothetical polygon that is required to fill the amorphous area.

A larger value of N corresponds to relatively smaller polygonal shaped apertures, and a smaller value of N corresponds to relatively larger polygonal shaped apertures. As an alternative to selecting the number of nucleation points N, a desired average diameter D of the apertures may be selected at34B. If a choice is made to determine the number of nucleation points N at34A, then the average diameter D is computed at36A. Similarly, if a choice is made to determine the average diameter D at34B, then the number of nucleation points N is calculated at36B.

Based upon the number of nucleation points N, a series of coordinates are generated at38that map to the amorphous area to be filled with hair-entrance apertures. For example, when implementing constrained Voronoi tessellation of 2-space on a computer, a random number generator can be used to generate a series of random numbers that represent coordinates in the amorphous area. In the above example of mapping to a Cartesian coordinate system, two random numbers are generated for each nucleation point, one number corresponding to the X coordinate, and one number corresponding to the Y coordinate. The random number generator may generate normalized numbers or numbers in ranges that must be suitably scaled to map the coordinate space of the amorphous area. For example, many computer executed random number generators accept as an input, a seed value, which is converted into a random or pseudorandom number that is normalized between the values of 0 and 1. If such a value if provided, the normalized random number can be appropriately scaled within the range of 0,0 to XMAX, YMAX. Also, it may be desirable to store the generated pairs of (X,Y) coordinates for future reference.

In order to provide control over the degree of randomness associated with the generation of the nucleation point coordinates, a constraint may be imposed on the generation or selection of the random numbers that define the nucleation point coordinates in the amorphous area. One exemplary constraint, designated herein as β, limits the proximity of neighboring nucleation point locations through the introduction of an exclusion distance, E, which represents the minimum distance between any two adjacent nucleation points. The exclusion distance E is computed as follows:

In the above equation, λ defines the density of points, e.g., points per unit area and β is expressed as a value in the range from 0 to 1. If β=0, then the exclusion distance E is zero, and the nucleation point coordinates will be generally random, or at least pseudorandom. If β=1, the exclusion distance E is equal to the nearest neighbor distance for a hexagonally close-packed array. Thus, selecting β between 0 and 1 allows control over the “degree of randomness” between these two extremes. Once the constraint β is computed, each coordinate pair generated by the random number is compared against all previous other coordinate pairs based upon the computed exclusion distance. The currently considered coordinate pair is discarded if it falls within the exclusion distance of any one of the previously generated coordinate pairs.

By constraining the proximity of neighboring nucleation point locations through the introduction of an exclusion distance, the variation in center-to-center spacing of apertures is controlled, which will translate into a corresponding degree of variation in number of sides in the resulting polygons as well as polygon size. A less constrained set of nucleation point coordinates will exhibit a broader range of polygon sizes and shapes than a more constrained set of nucleation point addresses.

Additional constraints may also be imposed as the specific application dictates. Thus, the coordinates generated at38are checked against imposed constraints, if any, at40. If the generated coordinates fail to pass the requirements of the associated constraints, a new set of coordinates is generated at38. If the coordinates are accepted, a check is performed to determine whether N coordinate pairs have been generated, corresponding to a coordinate pair for each nucleation point at42. If less than N coordinate pairs have been generated, the process loops back to generate a new pair of coordinates at38.

Once the nucleation point coordinates have been computed, from at least a conceptual standpoint, a circle is grown for each nucleation point at44. Each circle grows radially outward from its associated nucleation point, e.g., simultaneously and at the same rate. As the perimeters of neighboring circles meet, growth for those circles stops, thus defining a boundary line. These boundary lines each form the edge of a polygon, with vertices formed by intersections of boundary lines.

Delaunay triangulation is one exemplary technique for conceptually growing the circles about the nucleation points. Using Delaunay triangulation, each nucleation point is assigned a unique identifier for identification purposes, and combinations of three nucleation points are assembled and tracked, e.g., by storing the combinations and their corresponding nucleation point identifiers.

The radius and center point coordinates are calculated for a circle passing through each set of three triangularly-arranged nucleation points. The coordinate locations of each remaining nucleation point, i.e., each nucleation point not used to define the particular triangle, are compared with the coordinates of the circle (radius and center point) to determine whether any of the other nucleation points fall within the circle of the three points of interest. If no other nucleation points fall within the circle, then the three nucleation point identifiers, their X and Y coordinates, the radius of the circle, and the X and Y coordinates of the circle center are stored. If a nucleation point not used to construct the triangle falls within the circle, no results are saved and the calculation progresses to the next set of three points.

Next, a polygon corresponding to each nucleation point is determined at46. For example, once the Delaunay triangulation has been completed, a Voronoi tessellation of 2-space is performed to generate the polygons. Each nucleation point saved as being a vertex of a Delaunay triangle defines the center of a polygon. The outline of the polygon is generated by sequentially connecting the center points of the circumscribed circles of each of the Delaunay triangles, which include that vertex, sequentially in clockwise fashion. In generating the polygons, a comparison is made such that any triangle vertices at the boundaries of the area may be omitted from the calculation since they will not define a complete polygon. Upon completion of the tessellation, each vertex of a polygonal shaped aperture can be saved as a coordinate in a data file.

Once an amorphous aperture arrangement is generated, the width of the foil surface members22between the polygons can be added at48. Foil surface member22can be added by thickening the boundary lines that form the edges of the polygonal shaped apertures. For example, to increase the width of foil surface members22between polygons, a computer program, routine or algorithm can be written to add one or more parallel lines to each side edge of adjacent polygons to increase the width W of the corresponding foil surface member width, and correspondingly decrease the area of the associated polygon.

The above technique for defining surface members22by thickening the boundary lines of the hair-entrance apertures20allows control over certain predetermined constraints if imposed, such as maintaining the minimum width W of the foil surface members22, or maintaining a generally consistent foil area across the amorphous arrangement of apertures, e.g., to prevent uneven or inconsistent deflection of the foil10in different areas of the hair-receiving section14to a degree that adversely affects the quality of a shaving operation. Additionally, the designer can customize any individual aperture or set of apertures for size, shape, orientation, or spacing. Other examples of implementing the generation of amorphous arrangements are defined in U.S. Pat. No. 5,965,235 to McGuire et al.

A photographic negative can be made from the generated amorphous arrangement or assembly of differing amorphous arrangements. This negative may be utilized as the input for a conventional etching process during manufacturing of the foil10. Any number of alternative techniques may also be used to manufacture the foil10based upon the generated amorphous arrangement(s).

Exemplary Approaches for Identifying Amorphous Arrangements

As noted in greater detail herein, the hair-receiving section14of the foil10may include at least one amorphous arrangement of apertures24, and optionally, a non-amorphous pattern of apertures. In this regard, the amorphous arrangement of apertures24appears disordered, whereas the non-amorphous pattern, if present will appear to exhibit some order.

The order of a non-amorphous pattern may be characterized in a number of different ways. For example, an ordered pattern may repeat in one or more directions. Moreover, the ordered pattern may be periodic, i.e., where the ordered pattern includes a subset that is repeated in a regular way throughout the ordered pattern.

The ordered pattern may also be quasi-periodic. An ordered pattern is quasi-periodic if a copy of a subset of that pattern can be moved about the pattern so as to align with a different subset of the pattern. However, if an exact copy of the entire ordered pattern were shifted over the original pattern, then various subsets can be matched up locally, but the original pattern and the copy pattern, as a whole, will not match up. A well-known example of a quasi-periodic pattern comprises a Penrose tiled patterns.

Still further, an ordered pattern may be symmetric. An ordered pattern is symmetric if a copy of a subset of the pattern can be moved to a different location within the pattern such that the copy exactly matches up with the pattern. In this regard, symmetry may be achieved via a rotation of the copy of the subset relative to the pattern, a translation or movement of the copy of the subset relative to the pattern, a reflection of the copy of the subset, e.g., a mirror image of the subset, relative to the pattern, or a combination of the above.

At least two exemplary functions can be analyzed to determine whether an arrangement of hair-entrance apertures20within the hair-receiving section14of the foil10is amorphous. The distribution of areas of the hair-entrance apertures20within the arrangement may be analyzed. Also, the point-to-point distances of the hair-entrance apertures20, e.g., as measured from a first aperture center to a second aperture center, may be analyzed.

Area Distributions

With reference toFIG. 7, an exemplary area distribution plot is illustrated. An amorphous arrangement will generally reveal a continuous distribution of areas within a reasonable sample area of the hair-receiving section14of the foil10. The size of the reasonable sample area will vary depending upon the size or size range of hair-entrance apertures20. With reference toFIG. 8, a graph depicts a similar comparison to that ofFIG. 7. However, the graph ofFIG. 8depicts the upper and lower limits (in percentage) of polygon area for an exemplary sample area.

For periodic patterns, e.g., patterns that repeat in a regular way, and for a periodic patterns, e.g., a Penrose tiling, the area distribution plot will consist of only a small number of distinct areas and will thus not represent a continuous distribution as illustrated inFIG. 9. For example, the apertures in the Penrose tiling are all fixed geometric shapes of limited number, e.g. two to four shapes. As such, the distribution illustrated inFIG. 9includes sharp discontinuities compared to the corresponding generally continuous arrangement ofFIG. 7. Thus, the exemplary arrangement of apertures graphed inFIG. 7is considered an amorphous arrangement of apertures and the exemplary arrangement of apertures graphed inFIG. 9is considered a non-amorphous pattern of apertures.

Distance Distributions

If each hair-entrance aperture20is assigned a center point, e.g., the center of mass of the hair-entrance aperture20, an analysis can determine whether such center points are substantially randomly distributed. The benchmark for complete randomness is the Poisson process. In a Poisson process, the center points are randomly distributed and the distance from any center point to any other center point can be expressed by Ripley's K function:
K(t)=λπt2

Ripley's K function states that the number of points (K) within a distance (t) from the point in question is proportional to the square of the distance. That is, if the density of points in an area of interest is known, which is the case for the present invention, then a circle of radius t and area πt2will contain K points. A separate function, L(t) can then be defined as:
L(t)=√{square root over (K(t)/λπ)}
wherein λ, as defined above, is the number of points per unit area.

For a Poisson (random) process, since K(t)∝t2, a plot of L against t would give a straight line with a slope of 1.

With reference toFIG. 10, to determine if the center points of the hair-entrance apertures20are randomly distributed within a predetermined sample area of interest, a method50comprises generating a plot of L against t. To create the plot, a point is chosen as the reference point at52. The number of points within a distance t of the reference point is determined at54. The above process may be repeated for all values of t (encompassing all of the other points). A K function is calculated at56. From the results, a slope is computed at58, e.g., by generating a plot, and randomness is determined at60.

Plots that are generally continuous and straight within reasonable tolerances indicate that the corresponding distribution of centers of the hair-entrance apertures20is random, thus the apertures are in an amorphous arrangement as illustrated by the plot inFIG. 11. That is, arbitrarily small changes in the X direction value on the plot produces arbitrarily small changes in the Y direction value on the plot, e.g., within predetermined confidence intervals.

Moreover, curve-fitted plots that have a line with discontinuities or abrupt undefined values indicates that the distribution of centers of the hair-entrance apertures20is not random and the apertures are considered in a non-amorphous pattern as illustrated by the plot inFIG. 12. For example, in a Penrose tiled pattern of apertures, or in a periodic pattern of apertures, the plot will have portions where an arbitrarily small change in the X direction of the plot will result in a relatively large or broken jump in the value on the Y direction of the plot, or the Y direction value may be undefined at points along the plot, and thus such patterns of apertures are not amorphous.

By way of example, a statistically significant selected subset of hair-entrance apertures20with regard to the entire amorphous arrangement should yield statistically substantially equivalent values for such properties as the number of apertures, the average area of the apertures, the average size of the apertures, the average spacing between apertures, etc. Such a correlation may be desirable with respect to physical foil properties because the uniform statistical properties should tend to also suggest uniform properties across the foil10. For example, the apertures may be provided such that a statistically equivalent number of apertures are realized per unit of measure by a line drawn in any given direction outwardly as a ray from a given point, so long as the unit of measure is selected so as to be at least big enough to derive a statistically significant number of apertures.

The shaver foils of the present invention can be used for a wide variety of shaving purposes including but not limited to men's and women's shaving (e.g., face, whiskers, underarms, other body hair including arms, legs, head, back of the neck, and bikini shaving, etc.), shaving of pets and animals, removal of frayed threads and pilling of fabrics and webs, and other purposes as may be known or apparent now or in the future.