CN103801059B - The patterns of indentations of golf - Google Patents

Abstract

The present invention provides a kind of method for arranging dent on golf ball surface, and wherein dent is with the pattern arrangement derived from least one irregular domain generated by rule or irregular polyhedrons, particularly dipyramid.This method includes selecting polyhedral control point, irregular domain is generated based on these control points, and fill irregular domain with dent, and inlay irregular domain, to cover golf ball surface.Control point includes center, polyhedral vertex, the midpoint on polyhedral edge or other points of face of a polyhedron etc..This method ensures be reduced or eliminated due to that can keep following polyhedral symmetry while big circle caused by parting line.

Description

The patterns of indentations of golf

The cross reference of related application

The application is that the part of the U.S. Patent application No.13/667175 submitted on November 2nd, 2012 is continued, this application It is the U.S. Patent application No.13/252260 submitted on October 4th, 2011 and the United States Patent (USP) submitted on March 14th, 2011 Apply for that the part of No.13/046823 is continued, is the U.S. Patent application No.12/262464 submitted on October 31st, 2008, existing In the part continuation for United States Patent (USP) No.8029388, whole disclosure is incorporated herein by reference.

Technical field

The present invention relates to golf, having unique filling more particularly to one kind（packed）The golf of patterns of indentations Ball.More particularly, the present invention relates to one kind by generating irregular domain according to polyhedron, particularly dipyramid, using dent It fills irregular domain and the domain is embedded in the method for arranging dent on golf surface on golf.

Background technology

In history, the patterns of indentations for being used for golf has had a variety of geometries, pattern and construction.Mainly, Pattern is arranged to according to specific ball construction, material properties and the initial sportsman for firing angle and rotation status for influencing ball Characteristic provides desired manipulation characteristic.Therefore, the exploitation of pattern is for realizing aerodynamic quality appropriate, thus controlling The flight characteristics of ball and the secondary design procedure of performance.

The air force educational level awing generated by ball is caused by its speed and rotation.These power can be expressed For lifting force and drag.Lifting force perpendicular to the direction of flight, and be rotation ball above and below air velocity it is poor It is caused.This phenomenon is summarized as Magnus Effect, and Magnus is in 1853 on research spinning ball and cylinder So description after air force educational level, and pass through Bernoulli equation（The simplification of first law of thermodynamics）Description.Bernoulli Jacob Equation makes pressure and velocity correlation, and wherein pressure and speed square is inversely proportional.Due to top very fast motive air and Speed difference caused by the slower motive air of bottom causes the relatively low air pressure at top and acts on being directed upwards towards on ball Power.

The direction of towing is opposite with heading and perpendicular to lifting force.Drag on ball is summarized as parasitic drag, It includes pressure towing and viscosity or friction subsurface towing.Ball is bluff body, with non-effective aerodynamic shape.Cause This, prodigious pressure difference is caused in the acceleration flow field around ball, and mesohigh is before ball, and low pressure is behind ball.Behind ball Area of low pressure also be known as tail (wake).In order to keep pressure towing minimum, dent, which provides, to energize for flow field and postpones to flow Separation or reduce the measure in ball subsequent tail region.Friction subsurface is proximate to the viscosity effect of the ball surface in boundary layer It answers.

Many effort are sought come so that the air of golf is dynamic in this field by dent interference and other methods Force efficiency is maximum, although they pass through governing body of golf country（United States Golf Association（USGA））Stringent control.USGA A requirement be that golf club has air force symmetry.Air force symmetry allows ball with very small variable quantity How flight, be placed on but regardless of golf on ball seat or ground.Preferably, the maximum surface face of dent covering golf Product, the air force symmetry without negatively affecting golf.

In the trial for improving air force symmetry, many patterns of indentations are based on geometry.These shapes include circle Shape, hexagon, triangle etc..Other patterns of indentations are generally basede on five kinds of Platonic solids comprising icosahedron, 12 faces Body, octahedron, cube or tetrahedron.Other patterns of indentations are based on 13 kinds of Archimedes's entities, such as small 32 face Body, oblique icosidodecahedron, small tiltedly double cuboctahedrons, short cube, short dodecahedron cut icosahedron.In addition, other recessed Trace pattern is based on hexagon dipyramid.Since the quantity of symmetrical physical plane system is restricted, it is difficult to design new symmetrical Pattern.In addition, the patterns of indentations of some shapes based on these geometries cause not best surface cover and it is other not The dent arrangement of profit.Therefore, the dent performance of manipulation such as quantity, shape, size, volume and arrangement is generally attempted to form tool There is the golf of improved aerodynamic quality.

The United States Patent (USP) No.5562552 of Thurman discloses a kind of golf, with icosahedron patterns of indentations, In icosahedral each gore by three straight lines separate, which divides the corner in the face equally respectively, with formed be used for Three gores in each icosahedron face, wherein dent are consistently arranged on icosahedron face.

The United States Patent (USP) No.5046742 of Mackey discloses a kind of golf, has and is filled into including hexagon and five Dent in the polyhedron in 32 faces of side shape, wherein the dent filling in each hexagon and pentagon is identical.

The United States Patent (USP) No.4998733 of Lee discloses a kind of formation golf by ten " spherical shape " hexagons, six sides Shape is respectively classified into six equilateral triangles, wherein each triangle passes through in vertex of a triangle and the side opposite with the vertex Midpoint between the bisector segmentation that extends, and bisector is directed, to realize improved symmetry.

The United States Patent (USP) No.6682442 of Winfield discloses making for the polygon as the packing elements for dent With so that predictable variation is introduced patterns of indentations.Polygon extends to parting line from the pole of ball.It is any not from polygon Fill the other dents of space filling of dent.

Invention content

In one embodiment, the present invention is directed to a kind of golf, with the outer surface for including multiple dents.It is recessed Multiple replication forms that trace covers the irregular domain of outer surface with uniform pattern are arranged.The irregular domain is by vertex to edge method Formed, this method based on the faces n dipyramid to be projected to the vertical line opened as the n same intervals from pole to pole on sphere, The vertical line is by the line segmentation around equator, and to limit the Northern Hemisphere and the Southern Hemisphere, the wherein patterns of indentations on the Northern Hemisphere is south The mirror image of patterns of indentations on hemisphere.

In another embodiment, the present invention be directed to a kind of golf, have include true parting line, it is multiple virtually The outer surface of parting line and multiple dents.Dent with uniform pattern by inlaying irregular domain to cover what outer surface limited Patterns of indentations is arranged.Irregular domain passes through the segmentation that is generated by vertex to edge method and its multiple multiple according to the faces n dipyramid System defines.Segmentation and its multiple duplications form the true and virtual parting line of ball.

In another embodiment, the present invention is directed to a kind of method for arranging multiple dents on golf ball surface.It should Method includes generating irregular domain according to the faces n dipyramid using vertex to edge method, fills irregular domain with dent, and inlay Embedding irregular domain to cover the surface of golf in an uniform way.The method at vertex to edge includes projecting dipyramid Onto sphere, each face of dipyramid has vertex connection at one end and by another base edge connection brought out Two lateral edges；The point P that the vertex is connected to base edge is segmented by non-rectilinear, and in a manner of generating irregular domain Pattern is formed to the segmentation.

Description of the drawings

The following drawings constitutes the part of this specification and specification is combined to read, wherein identical reference numeral is come Same parts are indicated in multiple views.

Figure 1A shows the golf with method arrangement dent through the invention；Figure 1B shows face of a polyhedron； Fig. 1 C show the element of the present invention in the face of a polyhedron of Figure 1B；Fig. 1 D show that method through the invention is filled out with dent Fill the domain to be formed and be formed by two elements of Fig. 1 C；

Fig. 2 shows polyhedral single faces thereon with control point；

Fig. 3 A show face of a polyhedron；Fig. 3 B show the element of the present invention filled with dent；Fig. 3 C show with by The domain of the present invention for the dent filling that the element of Fig. 3 B is formed；Fig. 3 D show that method through the invention is formed by the domain of Fig. 3 C Golf；

Fig. 4 A show two face of a polyhedrons；Fig. 4 B show first of the present invention in two face of a polyhedrons of Fig. 4 A Domain；Fig. 4 C show the first domain and the second domain of the present invention in three face of a polyhedrons；Fig. 4 D show side through the invention The golf that method is formed by the domain of Fig. 4 C；

Fig. 5 A show face of a polyhedron；Fig. 5 B show the first domain of the present invention in face of a polyhedron；Fig. 5 C show three The first domain and the second domain of the present invention in a face of a polyhedron；Fig. 5 D show that the method using the present invention is formed by the domain of Fig. 5 C Golf；

Fig. 6 A show face of a polyhedron；Fig. 6 B show the part in the domain of the present invention in the face of a polyhedron of Fig. 6 A；Figure 6C shows the domain that method through the invention is formed；Fig. 6 D show the height that the method using the present invention is formed by the domain of Fig. 6 C Golf ball；

Fig. 7 A show face of a polyhedron；Fig. 7 B show the domain of the present invention in the face of a polyhedron of Fig. 7 A；Fig. 7 C are shown The golf that method through the invention is formed；

Fig. 8 A show the first element of the present invention in face of a polyhedron；Fig. 8 B show the sheet in the face of a polyhedron of Fig. 8 A First and second elements of invention；Fig. 8 C show two domains of the present invention of the first and second elements including Fig. 8 B；Fig. 8 D Show the individual domain of the present invention in two domains based on Fig. 8 C；Fig. 8 E show the domain shape by Fig. 8 D using method of the invention At golf；

Fig. 9 A show face of a polyhedron；Fig. 9 B show the element of the present invention in the face of a polyhedron of Fig. 9 A；Fig. 9 C are shown Combination is to form two elements of Fig. 9 B in the domain of the present invention；Fig. 9 D show member of the method through the invention based on Fig. 9 C The domain that part is formed；Fig. 9 E show the golf that the method using the present invention is formed by the domain of Fig. 9 D；

Figure 10 A show the face of granatohedron；Figure 10 B show the segmentation of the present invention in the face of Figure 10 A；Figure 10C shows to form the segmentation and its duplication of Figure 10 B in the domain of the present invention；Figure 10 D show method base through the invention In the domain that the segmentation of Figure 10 C is formed；And Figure 10 E show the golf that method through the invention is formed by the domain of Figure 10 D Ball；

Figure 11 A show the octahedral plane being projected on sphere；Figure 11 B show this hair in the octahedral plane of Figure 11 A The first bright domain；Figure 11 C show the first domain and the second domain for the present invention being projected on sphere；Figure 11 D, which are shown, to be panelized To cover the domain of Figure 11 C on the surface of sphere；Figure 11 E show one of the golf that the method using the present invention is formed Point；Figure 11 F show that the another of golf that the method using the present invention is formed is not；And Figure 11 G, which are shown, uses this The golf that the method for invention is formed；

Figure 12 A show the icosahedron face being projected on sphere；Figure 12 B are shown in the icosahedron face of Figure 12 A The first domain of the present invention；Figure 12 C show the first domain and the second domain for the present invention being projected on sphere；Figure 12 D show by Inlay the domain of Figure 12 C on the surface to cover sphere；Figure 12 E show the one of the golf that the method using the present invention is formed Part；Figure 12 F show the another part for the golf that the method using the present invention is formed；And Figure 12 G show use The golf that the method for the present invention is formed.

Figure 13 A show cube dignity being projected on sphere；Figure 13 B show this hair in cube dignity of Figure 13 A The first bright domain；Figure 13 C show the first domain and the second domain for the present invention being projected on sphere；Figure 13 D, which are shown, to be panelized To cover the domain of Figure 13 C on the surface of sphere；Figure 13 E show the first domain of the present invention filled with dent；Figure 13 F are shown With the second domain for the present invention that dent is filled；And Figure 13 G show the golf that the method using the present invention is formed；

Figure 14 A show six face dipyramids being projected on sphere；Figure 14 B show an implementation according to the present invention Segmentation in the face of the dipyramid of Figure 14 A of mode；Figure 14 C are shown to be generated not according to embodiment of the present invention Regular domain；Figure 14 D show the irregular domain that another embodiment according to the present invention generates；Figure 14 E are shown to be filled out with dent The irregular domain of Figure 14 C filled；Figure 14 F show the irregular domain of Figure 14 D filled with dent；Figure 14 G are shown using root The golf formed according to the method for an embodiment of the invention；And Figure 14 H are shown using according to the present invention another The golf that the method for one embodiment is formed.

Specific implementation mode

The present invention provide it is a kind of on golf ball surface with from by rule or irregular polyhedrons generate it is at least one The method of pattern arrangement dent derived from irregular domain.This method includes selecting polyhedral control point, by control point with it is non-straight The sketch line of line connects, and forms pattern to generate irregular domain, optionally in a second manner to grass to sketch line in the first way Figure line forms pattern, to create additional irregular domain, fills irregular domain with dent, and inlay irregular domain, so as to Uniform pattern covers the surface of golf.Control point includes the center, polyhedral vertex, polyhedron edge of face of a polyhedron Midpoint or other points etc..This method ensures to minimize or eliminate due to big circular caused by the parting line of molding process Keep following polyhedral symmetry simultaneously.

In special embodiment, as shown in Figure 1A, the present invention includes the golf 10 for having dent 12.Dent 12 It is arranged by filling irregular domain 14 with dent, as Fig. 1 D are clearly seen.Irregular domain 14 creates as follows, that is, is inlaying When on the surface of golf 10, compared with the ball of the prior art, they assign the symmetry of bigger grade to surface.Domain 14 irregular shape is shaped with rule furthermore such that the appearance of the golf parting line of molding process and minimised Domain is obtained to be compared, and the bigger flexibility for arranging dent is allowed.

For purposes of the present invention, term " irregular domain " refers to wherein at least one and preferably all of defined domain The segmentation on boundary is not the domain of straight line.

Irregular domain can be limited by using any example method described herein.In one embodiment, should Method generates one or more unique domains based on the external sphere in vertex by regular polyhedron.Based on origin（0,0,0） Corresponding polyhedral vertex external sphere vertex table 1 below in limit.

Table 1

The vertex of external sphere based on corresponding polyhedron vertex

In another embodiment, this method, which forms to be based on dipyramid being projected on sphere, generates unique domain.

Each method has one group of unique rule, and domain forms symmetrical pattern according to the rule on the surface of golf. Each method is limited by the combination at least two control points.It is obtained from one or more faces of rule or irregular polyhedrons These control points include at least with Types Below：The side of the center C of face of a polyhedron, the vertex V in regular polyhedron face, face of a polyhedron Point P on the base edge E of the midpoint M of edge, the vertex V of dipyramid and dipyramid.

Fig. 2 shows polyhedrons（Regular dodecahedron in this）Exemplary face 16 and face 16 on each of in One in heart C, midpoint M, vertex V and edge E.Two control points C, M or V can be identical or different types.Therefore, Six kinds of methods for regular polyhedron have been defined below：

1. center to midpoint（C→M）；

2. center to center（C→C）；

3. center to vertex（C→V）；

4. midpoint to midpoint（M→M）；

5. midpoint to vertex（M→V）；And

6. vertex to vertex（V→V）.

Figure 14 B are shown on the base edge E of illustrative dipyramid, the vertex V of dipyramid and dipyramid Point P.Therefore, vertex is limited to edge method for a kind of method of dipyramid（V→E）.

Although the details of each method is different, they follow identical basic ideas.First, non-linear sketch line quilt It is depicted as two control points of connection.This sketch line can have any shape, including but not limited to arc, spline shape, two Or more straight line or camber line or curve, or a combination thereof.Secondly, method forms pattern to sketch line in a particular manner, with wound Domain is built, described below.Third, when needed, sketch line form pattern in a second manner, to create the second domain.

Although the basic ideas of each method of six kinds of methods are consistent, each method preferably follows different step, To form domain from the sketch line between two control points, individually described below with reference to each method.

Center is to vertex method

Referring again to Figure 1A -1D, center to vertex method forms a kind of domain, inlays to cover the table of golf 10 Face.The domain is as defined below：

1. selecting regular polyhedron（Figure 1A -1D use icosahedron）；

2. selecting the single face 16 of regular polyhedron, as shown in Figure 1B；

3. the center C in the face 16 and first vertex V in face 16₁It is connected by any non-linear sketch line, is hereinafter referred to as divided Section 18；

4. the duplication 20 of segmentation 18 is rotated around center C so that replicate 20 by center C and close vertex V₁Vertex V₂Even It connects.Two segmentations 18 and 20 and connection vertex V₁And V₂Edge limited element 22, shown as Fig. 1 C understand；And

5. element 22 is rotated around the midpoint M of edge E to create domain 14, shown as Fig. 1 D understand.

When being panelized the surface to cover golf 10 in domain 14, as shown in Figure 1A, according to as control point C and V₁Basis selection regular polyhedron, the overall domain 14 of different number will be obtained.For covering the surface of golf 10 The quantity in domain 14 is equal to selected polyhedral face P_FQuantity be multiplied by the edge P in polyhedral each face_EQuantity divided by 2, As shown in following table 2.

Table 2

The domain obtained using specific polyhedron when the heart in use is to vertex mode

Polyhedron type	Face PFQuantity	Edge PEQuantity	The quantity in domain 14
				Tetrahedron	4	3	6
Cube	6	4	12
				It is octahedra	8	3	12
Dodecahedron	12	5	30
				Icosahedron	20	3	30

Center is to midpoint method

Referring again to Fig. 3 A-3D, center to midpoint method forms a kind of can be panelized to cover the table of golf 10 The single irregular domain in face.The domain is as defined below：

1. selecting regular polyhedron（Fig. 3 A-3D use dodecahedron）；

2. the single face 16 of the regular dodecahedron of selection, as shown in Figure 3A；

3. the first edge E of the center C knead doughs 16 in face 16₁Midpoint M₁Pass through 18 connection of segmentation；

4. the duplication 20 of segmentation 18 is rotated around center C so that replicate 20 by center C and close first edge E₁Second Edge E₂Midpoint M₂Connection.Two 16 and 18 and edge E of segmentation₁With edge E₂In midpoint M₁And M₂Between part limit member Part 22；And

5. element 22 surrounds the vertex V-arrangement in face 16 into pattern, the vertex V in the face 16 is included in element 22, and connects side Edge E₁And E₂To form domain 14.

When the surface to cover golf 10 is inlayed in domain 14 around golf 10, as shown in Figure 3D, according to work To be used for control point C and M₁Basis selection regular polyhedron, the overall domain 14 of different number will be obtained.For covering Gao Er The quantity in the domain 14 on the surface of husband's ball 10 is equal to selected polyhedral vertex P_VQuantity, as shown in following table 3.

Table 3

The heart in use is to the domain obtained using specific polyhedron when midpoint method

Polyhedron type	Vertex PVQuantity	The quantity in domain 14
			Tetrahedron	4	4
Cube	8	8
			It is octahedra	6	6
Dodecahedron	20	20
			Icosahedron	12	12

Center to center method

Referring again to Fig. 4 A-4D, center to center method, which is formed, can be panelized with the surface that covers golf 10 Two domains.The domain is as defined below：

1. selecting regular polyhedron（Fig. 4 A-4D use dodecahedron）；

2. selecting two adjacent surfaces 16a and 16b of regular polyhedron, as shown in Figure 4 A；

3. the center C of face 16a₁The center C of knead dough 16b₂Pass through 18 connection of segmentation；

4. the duplication 20 of segmentation 18 surrounds center C₁And C₂Between midpoint M rotate 180 degree so that replicate 20 also by center C₁With center C₂Connection, as shown in Figure 4 B.Two segmentations 16 and 18 limit the first domain 14a；And

5. segmentation 18 is rotated to limit the second domain 14b, as shown in Figure 4 C also around vertex V.

When the first domain 14a and the second domain 14b are panelized the surface to cover golf 10, as shown in Figure 4 D, according to As for control point C₁And C₂Basis selection regular polyhedron, the overall domain 14a and 14b of different number will be obtained.It is used for The quantity for covering first and second the domain 14a and 14b on the surface of golf 10 is that the quantity of the first domain 14a is P_F*P_E/ 2 and The quantity of second domain 14b is P_V, as shown in following table 4.

Table 4

The domain obtained using specific polyhedron using center to center method

Polyhedron type	Vertex PVQuantity	The quantity of first domain 14a	Face PFQuantity	Edge PEQuantity	The quantity of second domain 14b
						Tetrahedron	4	6	4	3	4
Cube	8	12	6	4	8
						It is octahedra	6	9	8	3	6
Dodecahedron	20	30	12	5	20
						Icosahedron	12	18	20	3	12

Midpoint is to midpoint method

With reference to figure 5A-5D, 11A-11G, 12A-12G and 13A-13G, midpoint to midpoint method, which is formed, can be panelized to cover Two domains on the surface of lid golf 10.The domain is as defined below：

1. selecting regular polyhedron（Fig. 5 A-5D use dodecahedron, Figure 11 A-11G to make using octahedron, Figure 12 A-12G With icosahedron, Figure 13 A-13G use cube）；

2. the single face 16 of regular polyhedron is projected on sphere, as shown in Fig. 5 A, 11A, 12A and 13A；

3. the first edge E in face 16₁Midpoint M₁With neighbouring first edge E₁Second edge E₂Midpoint M₂Pass through segmentation 18 connections, as shown in Fig. 5 A, 11A, 12A and 13A；

4. segmentation 18 is to be equal to 360/P_E, rotational angle around face 16 center C formed pattern, to form the first domain 14a, such as Fig. 5 B, 11B, 12B and 13B；

5. being segmented 18 and first edge E₁With second edge E₂In midpoint M₁M between and₂Part limit element 22, such as Fig. 5 B, 11B, 12B and 13B；And

6. element 22 is around connection edge E₁And E₂Vertex V-arrangement at pattern, to create the second domain 14b, as Fig. 5 C, 11C, 12C and 13C（In Figure 12 C, 12D and 13D, each section in the second domain is denoted as 14b）.It is formed in the pattern in the second domain Number of fragments be equal to P_F*P_E/P_V。

When the first domain 14a and the second domain 14b are panelized the surface to cover golf 10, as Fig. 5 D, 11D, 12D and Shown in 13D, according to as control point M₁And M₂Basis selection regular polyhedron, the overall domain of different number will be obtained 14a and 14b.For cover golf 10 surface the first and second domain 14a and 14b quantity be the first domain 14a number Amount is P_FAnd second domain 14b quantity be P_V, as shown in following table 5.

In the particular aspects of embodiment shown in Figure 11 A-11G, segmentation 18 forms the very real or imaginary of golf 10 The part of quasi- parting line.Therefore, 18 are segmented and domain is replicated in by each of formation of above step 4 and 6 and is panelized to cover The true parting line and three virtual parting lines of ball are formed when the surface of ball.

In the particular aspects of embodiment shown in Figure 12 A-12G, it is segmented 18 and passes through the formation of above step 4 and 6 Each of be replicated in the true parting line and five virtual parting lines that ball is formed when domain is panelized the surface to cover ball.

In the particular aspects of embodiment shown in Figure 13 A-13G, it is segmented 18 and passes through the formation of above step 4 and 6 Each of be replicated in the true parting line and three virtual parting lines that ball is formed when domain is panelized the surface to cover ball.

Table 5

The domain obtained using specific polyhedron using midpoint to midpoint method

Polyhedron type	Face PFQuantity	The quantity of first domain 14a	Vertex PVQuantity	The quantity of second domain 14b
					Tetrahedron	4	4	4	4
Cube	6	6	8	8
					It is octahedra	8	8	6	6
Dodecahedron	12	12	20	20
					Icosahedron	20	20	12	12

Midpoint is to vertex method

With reference to figure 6A-6D, midpoint to vertex method forms a domain for being panelized the surface to cover golf 10.It should Domain is as defined below：

1. selecting regular polyhedron（Fig. 6 A-6D use dodecahedron）；

2. selecting the single face 16 of regular polyhedron, as shown in Figure 6A；

3. the edge E in face 16₁Midpoint M₁With edge E₁On vertex V₁Pass through 18 connection of segmentation；

4. center C of the duplication 20 of segmentation 18 around face 16 forms pattern, each midpoint M is used respectively₂The top of knead dough 16 Point V₂, so as to a part for defined domain 14, as shown in Figure 6B；And

5. segmentation 18 and duplication 20 then rotate 180 degree respectively around its respective midpoint, to realize domain 14, such as Fig. 6 C It is shown.

When being panelized the surface to cover golf 10 in domain 14, as shown in Figure 6 D, according to as control point M₁ And V₁Basis selection regular polyhedron, the overall domain 14 of different number will be obtained.For covering the surface of golf 10 The quantity in domain 14 be P_F, as shown in following table 6.

Table 6

The domain that point is obtained to vertex method using specific polyhedron in use

Polyhedron type	Face PFQuantity	The quantity in domain 14
			Tetrahedron	4	4
Cube	6	6
			It is octahedra	8	8
Dodecahedron	12	12
			Icosahedron	20	20

Vertex is to vertex method

With reference to figure 7A-7C, vertex to vertex method forms two domains for being panelized the surface to cover golf 10.It should Domain is as defined below：

1. selecting regular polyhedron（Fig. 7 A-7C use icosahedron）；

2. selecting the single face 16 of regular polyhedron, as shown in Figure 7 A；

3. the first vertex V in face 16₁With neighbouring first vertex V₁The second vertex V₂Pass through 18 connection of segmentation；

4. center C of the segmentation 18 around face 16 forms pattern, to form the first domain 14a, as shown in Fig. 7 B；

5. being segmented 18 and vertex V₁And V₂Between edge limited element 22；And

6. element 22 surrounds edge E₁Midpoint M₁Rotation is to create the second domain 14b.

When the first domain 14a and the second domain 14b are panelized the surface to cover golf 10, as seen in figure 7 c, according to As for control point V₁And V₂Basis selection regular polyhedron, the overall domain 14a and 14b of different number will be obtained.It is used for The quantity for covering the first domain 14a and the second domain 14b on the surface of golf 10 is that the quantity of the first domain 14a is P_F, Yi Ji The quantity of two domain 14b is P_F*P_E/ 2, as shown in following table 7.

Table 7

The domain obtained using specific polyhedron when using vertex to vertex method

Polyhedron type	Face PFQuantity	The quantity of first domain 14a	The edge P in each faceEQuantity	The quantity of second domain 14b
					Tetrahedron	4	4	3	6
Cube	6	6	4	12
					It is octahedra	8	8	3	12
Dodecahedron	12	12	5	30
					Icosahedron	20	20	3	30

Although the six kinds of methods described utilize two control points before, can also be created not based on more than two control point Regular domain.It is, for example, possible to use three or even more control points.It is allowed for irregular domain using additional control point Possible different shape.It is described below and uses midpoint M, center C and vertex V as three controls for creating an irregular domain Make the illustrative methods of point.

Midpoint is to center to vertex method

With reference to figure 8A-8E, midpoint to center to vertex method, which is formed, is panelized one of the surface to cover golf 10 A domain.The domain is as defined below：

1. selecting regular polyhedron（Fig. 8 A-8E use icosahedron）；

2. selecting the single face 16 of regular polyhedron, as shown in Figure 8 A；

3. the edge E in face 16₁On midpoint M₁, face 16 center C and edge E₁On vertex V₁Connected by segmentation 18 It connects, and is segmented 18 and edge E₁In midpoint M₁With vertex V₁Between part limit first element 22a, as shown in Figure 8 A；

4. the duplication 20 of segmentation 18 is rotated around center C so that replicate 20 by center and neighboring edge E₁Edge E₂On Midpoint M₂Connection, and by center C and in edge E₁And E₂Cross part vertex V₂Connection, and 18 are segmented in midpoint M₁With in Part, duplication 20 between heart C is in vertex V₂Part between the C of center and edge E₁In midpoint M₁With vertex V₂Between Part limits second element 22b, as shown in Figure 8 B；

5. first element 22a and second element 22b surrounds edge E₁Midpoint M₁Rotation, as shown in Figure 8 C, to limit two A domain 14, wherein individual domain 14 are only defined by the rotation 18 ' of the part and segmentation 18 of segmentation 18 and duplication 20, such as Fig. 8 D institutes Show.

When being panelized the surface to cover golf 10 in domain 14, as illustrated in fig. 8e, according to as control point M, C With the regular polyhedron of the basis selection of V, the overall domain 14 of different number will be obtained.For covering the surface of golf 10 The quantity in domain 14 is equal to selected polyhedral face P_FQuantity be multiplied by the edge P in polyhedral each face_EQuantity, it is as follows Shown in face table 8.

Table 8

The domain obtained using specific polyhedron when the method to center to vertex is put in use

Polyhedron type	Face PFQuantity	Edge PEQuantity	The quantity in domain 14
				Tetrahedron	4	3	12
Cube	6	4	24
				It is octahedra	8	3	24
Dodecahedron	12	5	60
				Icosahedron	20	3	60

Although the method offer described uses the frame of center C, vertex V and midpoint M as unique control point before, also may be used To use other control points.Such as control point can be any point P on the edge E of selected face of a polyhedron.Using this When kind control point, another type of domain can be generated, although the mechanism for creating irregular domain can be different.It retouches below It states using the point P on center C and edge to create a kind of illustrative methods in such irregular domain.

Center is to edge method

With reference to figure 9A-9E, center to edge method forms a domain for being panelized the surface to cover golf 10.It should Domain is as defined below：

1. selecting regular polyhedron（Fig. 9 A-9E use icosahedron）；

2. selecting the single face 16 of regular polyhedron, as shown in Figure 9 A；

3. the center and peripheral E in face 16₁On point P₁Pass through 18 connection of segmentation；

4. the duplication 20 of segmentation 18 is rotated around center C so that replicate 20 by center C and neighboring edge E₁Edge E₂On Point P₂Connection, midpoint P₂Relative to edge E₂With point P₁Relative to edge E₁It positions in the same manner so that two segmentations 18 and 20 And edge E₁And E₂Respectively in point P₁And P₂Between part and connection edge E₁And E₂Vertex V limit element 22, such as scheme Shown in 9B, and

5. element 22 surrounds edge E₁Midpoint M₁Or edge E₂Midpoint M₂Rotation, the midpoint are all located in element 22, As shown in Fig. 9 B-9C, to create domain 14, as shown in fig. 9d.

When being panelized the surface to cover golf 10 in domain 14, as shown in fig. 9e, according to as control point C and P₁Basis selection regular polyhedron, the overall domain 14 of different number will be obtained.For covering the surface of golf 10 The quantity in domain 14 is equal to selected polyhedral face P_FQuantity be multiplied by the edge P in polyhedral each face_EQuantity divided by 2, As shown in following table 9.

Table 9

The heart in use is to the domain obtained using specific polyhedron when edge method

Polyhedron type	Face PFQuantity	Edge PEQuantity	The quantity in domain 14
				Tetrahedron	4	3	6
Cube	6	4	12
				It is octahedra	8	3	12
Dodecahedron	12	5	30
				Icosahedron	20	3	30

Although each method described illustrates by reference to regular polyhedron before, it is irregular more that they can also be used for some Face body, such as Archimedes's entity, Taka are blue three-dimensional（Catalanta Solids）Deng.Method for exporting irregular domain will Some modifications are usually required, to consider the shape in the irregular face of irregular entity.It is blue three-dimensional described below for Taka（Such as Granatohedron）Illustrative methods.

Vertex for granatohedron is to vertex method

With reference to figure 10A-10E, it is panelized to vertex method formation to cover golf based on the vertex of granatohedron One domain on the surface of ball 10.The domain is as defined below：

1. selecting the single face 16 of granatohedron, as shown in Figure 10 A；

2. the first vertex V in face 16₁With neighbouring first vertex V₁The second vertex V₂By 18 connection of segmentation, such as Figure 10 B institutes Show；

3. the first of segmentation 18, which replicates 20, surrounds vertex V₂, rotate, make the vertex V of its joint face 16₂With vertex V₃, segmentation The second of 18 replicates 24 and is rotated around center C, makes the vertex V of its joint face₃With vertex V₄, the third for being segmented 18 replicates and 26 surrounds Vertex V₁Rotation makes it connect vertex V₁With vertex V₄, as illustrated in figure 10 c, to form domain 14, as shown in Figure 10 D；

When being panelized the surface to cover golf 10 in domain 14, as shown in figure 10e, 12 domains will be used for covering height The surface of golf ball 10 is respectively used to each face of granatohedron.

Vertex for dipyramid is to edge method

With reference to figure 14A-14H, vertex to edge method forms a domain for being panelized the surface to cover golf 10. The domain is as defined below：

It is opened as n same intervals on sphere 1. the faces the n dipyramid by the total quantity with face equal to 2n is projected in Vertical line, the vertical line extend from pole to pole, are divided by limiting the line in equator in the Northern Hemisphere and the Southern Hemisphere.In Figure 14 A-14H In, n=6.As shown in Figure 14 A, each face 16 of dipyramid, which has, connects at vertex V at one end and passes through base in the other end Two lateral edges S of portion edge E connections₁And S₂。

2. as shown in Figure 14B, selecting the single face 16 of dipyramid, and the vertex V in face 16 is connected to by segmentation 18 Point P on the base edge E in face 16.

3. forming pattern to segmentation 18 in a manner of forming irregular domain 14.

A. in the embodiment shown in Figure 14 C, irregular domain 14 is by making segmentation 18 surround base edge E mirror image shapes At with the duplication 18a of restriction segmentation 18, and around the axis rotation segmentation 18 and duplication that vertex V is connected to sphere origin 18a replicates 18b and 18c to limit.Rotational angle is equal to 360/n.In Figure 14 C, each section in domain is denoted as 14.

B. in the embodiment shown in Figure 14 D, irregular domain 14 passes through the axis around tie point P and the center of sphere The pattern that 180 degree is formed to segmentation 18 replicates 18a to limit, and turns around the axis for the origin that vertex V is connected to sphere Dynamic segmentation 18 and duplication 18a replicate 18b and 18c to limit.Rotational angle is equal to 360/n.In Figure 14 D, each section in domain It is denoted as 14.

It is panelized to cover the surface of ball for forming pattern n times, irregular domain 14 by surrounding central axis, is such as schemed Shown in 14C and 14D.

In the particular embodiment for the vertex of the faces n dipyramid to edge method, dipyramid has even number Face, and it is segmented a part for the true or virtual parting line that 18 form golf 10.Therefore, more than being segmented 18 and its passing through Step 3 formed it is each replicate formed one of ball it is true with multiple virtual parting lines, the quantity of virtual parting line is equal to（ⁿ/₂）- 1, and n >=4, or >=6, or>6.

After forming irregular domain using any the method, domain can fill dent for forming golf 10.In Figure 11 E-11G, the first domain and the second domain are based on octahedron and are formed to midpoint method using midpoint.Figure 11 E, which are shown, to be filled out A part of pitted first domain 14a and the second domain 14b are filled, wherein the dent of the first domain 14a is indicated by alphabetical a.Figure 11 F The part for filling pitted second domain 14b and the first domain 14a is shown, wherein the dent of the second domain 14b is marked by alphabetical b Show.Figure 11 G show filled with dent and are panelized the first domain 14a and second domain on surface to cover golf 10 14b.In Figure 12 E-12G, the first domain and the second domain are formed using midpoint to midpoint method based on icosahedron.Figure 12 E are shown The the first domain 14a and the second domain 14b of filling dent, wherein the dent of the first domain 14a is indicated by alphabetical a.Figure 12 F are shown Filling pitted second domain 14b and the first domain 14a, wherein the dent of the second domain 14b is indicated by alphabetical b.Figure 12 G show First domain and the second domain on the surface to cover golf 10 are gone out filled with dent and have been panelized.In Figure 13 E-13G, the One domain and the second domain are formed using midpoint to midpoint method based on cube.Figure 13 E show the pitted first domain 14a of filling With the second domain 14b.Figure 13 F show the pitted second domain 14b and the first domain 14a of filling.Figure 13 G are shown filled with dent And it is panelized first domain and the second domain on the surface to cover golf 10.Figure 14 C-14H are shown based on six face bipyramids Body uses the domain that vertex is created to edge method.Figure 14 E show the domain for filling pitted Figure 14 C.Figure 14 F show filling The domain of pitted Figure 14 D.Figure 14 G show filled with dent and form pattern six times around central axis to cover golf The domain of Figure 14 C on the surface of ball 10.Figure 14 H show filled with dent and form pattern six times around central axis to cover height The domain of Figure 14 D on the surface of golf ball 10.In the specific embodiments of the present invention, the patterns of indentations on the Northern Hemisphere is the Southern Hemisphere On patterns of indentations mirror image, as shown in Figure 14 E and 14G.

In one embodiment, how filling dent, there is no limit.In another embodiment, dent is not so that have The mode that dent intersects with line segmentation is filled.

For by the dimple shape of selection region filling or profile there is no limit.Although the present invention is included in a kind of embodiment Include roughly circular dent, dent or protruding portion with any wishes feature and/or performance can be used（Stirrup）.Example Such as, in one embodiment, dent can have a variety of shapes and sizes, including different depth and perimeter.In particular, dent Can be recessed hemispherical or they can be that triangle, rectangular, hexagon, catenary, polygon or this field are common Other shapes known to technical staff.They can also have straight line, bending or sloping edge or side.Generally speaking, this field Any kind of dent or protruding portion known to those of ordinary skill（Stirrup）It can be used for the present invention.Dent can be fully enclosed each In domain, as shown in Figure 1A, 1D, 11E-11G, 12E-12G, 13E-13G, 14E-14H or dent can be in one or more Share between domain, as shown in Fig. 3 C-3D, as long as the surface of the dent arrangement and specific golf that are arranged on each independent domain On all duplications in domain be consistent.Alternatively, inlay can create covering more than about 60%, be preferably above about 70%, The patterns of indentations of more preferably greater than about 80% golf ball surface.

In other embodiments, domain can be not filled with dent, and the boundary in irregular domain may include convex ridge or lead to Road.In the golf with this irregular domain, one or more domains or multigroup domain are preferably overlapped, to increase channel Surface coverage.Alternatively, the boundary in irregular domain may include convex ridge or channel, and domain is filled with dent.

In domain when forming pattern on golf ball surface, the arrangement by its shape and the domain of following polyhedron determination is true Protecting obtained golf has advanced symmetry, equals or exceeds 12.The golf that the method for all present invention is formed The rule or irregular polygon that the grade of symmetry will be based on depending on irregular domain.It is formed based on five regular polyhedrons Golf symmetry grade and type listed in table 10.

Table 10

The symmetry of golf of the present invention as polyhedral function

Polyhedron type	Symmetry class	Symmetry orders
			Tetrahedron	Chiral tetrahedral symmetry	12
Cube	It is chiral octahedra symmetrical	24
			It is octahedra	It is chiral octahedra symmetrical	24
Dodecahedron	Chiral icosahedral symmetry	60
			Icosahedron	Chiral icosahedral symmetry	60

It is this it is advanced it is symmetrical has many advantages, including more consistent dent distribution, possible higher charging efficiency with And cover the Improving Measurements of the parting line of ball.In addition, due to higher symmetrical degree, the patterns of indentations formed by this method can be with With improved flight stability and symmetry.

In other embodiments, the surface of the endless all standing ball in irregular domain, and can with or cannot fill recessed There is open space between the domain of trace.This allows asymmetry being attached in ball.

The patterns of indentations of the present invention on seamless golf especially suitable for filling dent.Seamless golf and its system It makes method for example further to disclose in United States Patent (USP) No.6,849,007 and 7,422,529, the full disclosure content of the patent It is incorporated herein by reference.

When providing numerical lower limits and numerical upper limits herein, it is envisioned that any combinations of these numerical value can be used.

All patents, open source literature, test process and other bibliography incorporated herein（Including priority document）It is logical It crosses reference to be completely combined, degree is these open source literatures and the present invention and all law regulations phases of this combination of permission Hold.

Although particularly describing exemplary embodiments of the present invention, it will be appreciated that those of ordinary skill in the art are readily apparent that And be easy to carry out other multigroup modifications, without departing from the spirit and scope of the present invention.Therefore, it is not intended that by appended claims Range is confined to example given here and description, but thinks that claim includes patent novelty possessed by the present invention All features, including all features that those of ordinary skill in the art treat as equivalent.

Claims (21)

1. a kind of golf, with the appearance for including true parting line, one or more virtual parting lines and multiple dents Face, wherein the multiple dent is by inlaying the patterns of indentations that irregular domain limits to be arranged, so as to comprising irregular domain and The uniform pattern of multiple duplications in irregular domain covers the outer surface, wherein the irregular domain is by two borders, often A boundary extends to pole from pole, is limited wherein the first boundary is replicated by the first rotation of non-straight line segment and non-straight line segment, Yi Ji Two boundaries are replicated by the second rotation of non-straight line segment and the rotation of the third of non-straight line segment is replicated and limited, wherein the irregular domain Multiple duplications in boundary and the irregular domain correspond to the true and virtual parting line of the ball；The wherein described irregular domain is logical It crosses and is generated by vertex to edge method.

2. golf according to claim 1, wherein the outer surface of golf includes 342 dents.

3. golf according to claim 1, wherein the outer surface of golf includes 328 dents.

4. golf according to claim 1, wherein golf has the plane parting line along equator.

5. golf according to claim 1, wherein there is golf the part by the boundary in irregular domain to limit On-plane surface parting line.

6. a kind of golf, with outer surface, which includes the patterns of indentations to be limited by inlaying irregular domain Multiple dents of arrangement, to cover the outer surface with uniform pattern, irregular domain according to the faces n dipyramid by by vertex to The segmentation and its multiple duplications that edge method generates are defined, wherein segmentation and its it is multiple replicate generate one of the ball it is true and Multiple virtual parting lines.

7. golf according to claim 6, wherein the dipyramid to be projected on sphere as from pole to pole The vertical line opened of n same intervals, the vertical line is by the line segmentation around equator, to limit the Northern Hemisphere and the Southern Hemisphere, Patterns of indentations wherein on the Northern Hemisphere is the mirror image of the patterns of indentations on the Southern Hemisphere.

8. golf according to claim 6, wherein the outer surface of golf includes 342 dents.

9. golf according to claim 6, wherein the outer surface of golf includes 328 dents.

10. golf according to claim 6, wherein the quantity of virtual parting line is equal to (n/2) -1, and wherein n It is greater than or equal to 4 even number.

11. golf according to claim 6, wherein the quantity of virtual parting line is equal to (n/2) -1, and wherein n It is greater than or equal to 6 even number.

12. golf according to claim 6, wherein the quantity of virtual parting line is equal to (n/2) -1, and wherein n It is greater than or equal to 8 even number.

13. the method for arranging multiple dents on golf ball surface, this method include：

Using vertex to edge method, irregular domain is generated according to the faces n dipyramid, the vertex includes to edge method：

Dipyramid is projected on sphere, there is vertex at one end to connect and pass through the other end in each face of dipyramid Two lateral edges of the base edge connection at place；

By non-rectilinear be segmented point P vertex being connected in base edge；And

Segmentation is set to form pattern in a manner of generating irregular domain；

Irregular domain is filled with dent；And

Irregular domain is inlayed, to cover golf ball surface in a manner of uniform pattern.

14. according to the method for claim 13, wherein irregular domain surrounds base edge by making the first of segmentation to replicate Mirror image is simultaneously replicated around the additional copy and first that the axis for the origin that vertex is connected to sphere is rotated to the segmentation to generate, Middle rotational angle is equal to 360/n.

15. according to the method for claim 14, wherein the segmentation, the first duplication and additional copy generate one of ball very Real and multiple virtual parting lines.

16. according to the method for claim 15, wherein the quantity of virtual parting line is equal to (n/2) -1, and wherein n is Even number more than or equal to 4.

17. according to the method for claim 15, wherein the quantity of virtual parting line is equal to (n/2) -1, and wherein n is Even number more than or equal to 8.

18. according to the method for claim 13, wherein irregular domain by around will point P and sphere origin connection The first of axis rotation segmentation replicates 180 ° and rotates the additional of the segmentation around by the axis for the origin that vertex is connected to sphere It replicates and first replicates to generate, wherein rotational angle is equal to 360/n.

19. according to the method for claim 18, wherein the segmentation, the first duplication and additional copy generate one of ball very Real and multiple virtual parting lines.

20. according to the method for claim 19, wherein the quantity of virtual parting line is equal to (n/2) -1, and wherein n is Even number more than or equal to 4.

21. according to the method for claim 19, wherein the quantity of virtual parting line is equal to (n/2) -1, and wherein n is Even number more than or equal to 8.