O
`(19) United States
`0
`(12) Reissued Patent
`Shannon, Sr.
`
`USO0RE44963E
`
`(10) Patent Number:
`(45) Date of Reissued Patent:
`
`US RE44,963 E
`Jun. 24, 2014
`
`(54) SYSTEM AND METHOD FOR
`(IOMPU'l'ERlZl-JD l11\’.-\LUA'l‘l01\‘ OF
`GE\lS-IONES
`'
`
`Inventor:
`(75)
`(73) Assignce:
`
`Paul T. Shannon, Sr.. Macon. GA (US)
`Igiamond Technologies, Inc.. Macon.
`(L'\ (US)
`
`3.970.391 A *
`4-031633 A
`4.049.350 A "'
`4.056.952 A
`4.152.069 A
`
`35611413
`711976 Johnsoiict a1.
`_
`711977 Tamed:
`9‘ 1977 Bnlck ........................... .. 356-'30
`ll“l977 ()l(lld¢'I
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`(C I, n:d)
`on mu
`FOREIGN PATENT DOCUMENTS
`3600115 Al
`751987
`
`DE
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`(22)
`
`Filed:
`
`Dec. 6, 2010
`Related US. Patent Documents
`
`(“""i"1'°<‘)
`OTHER PUBLICATIONS
`
`Reissue Of:
`(64)
`Palenl No.2
`Issued:
`Appl. No.:
`Filed:
`
`5,966,673
`Oct‘ 12’ 1999
`08/782,889
`Jan. 10, 1997
`
`(2005-01)
`(2000-01)
`
`(51)
`
`<50
`
`1113- CL
`0011‘! 21/00
`0077"‘?!/3 7
`(52) US- 0-
`(‘PC .................................... .. GOIN2I/87 (2013.01)
`USPC ......... .. 702/81; 356./30'. 703/1: 703/6: 702/35
`(58) Field of Classification Search
`G01-N 211,87
`CPC ..................................................
`USPC "" ",““““““““““““““““" 7028]: 35‘ 356'“)
`see apphcauon me for complete Search hlsmr-V‘
`'*°'"°"°**“'*“*
`U_S_ PATENT DOCUMENTS
`
`Dodson J .S(l978).A Statistical Assessment of Brillianceand Fire for
`Polishing Gem Diamond on the Basis ofGeoine1i'ie:«il Optics. PhD
`Thesis. L'iiivei'sity of London.‘
`
`(Continued)
`
`I’ri'mar_T E,\'ami'ner — John Breene
`Assistant Examiner — Timothy II llwang
`(74) Atlorney. Agent, ornrm — Blakcly. Sokolofll Taylor&
`Zafinzin LLP
`
`(57)
`ABSTRACT
`A system and method for computerized grading ofthe cut of
`3 gemstona The system includes a gemstone mode] and an
`illuminzilion model. The gemstone model defines the cut of
`the gemstone in three dimensions with reference to the facets
`Eicififi§§31SI§§Zell§o‘l§"$3‘i§?é1iiI1Z‘l1fil°t$§°3J§§l1§p‘Z’3}-
`deteriiiiiiiiiga beam of light refracted into the gemstone from
`the illumination model for at least one of the facets. tracing
`reflections of the beam of light within the gemstone, and
`measuring at least one light beam refracted out of the gem-
`_
`,
`_
`_
`~
`~
`_
`~
`,
`_
`stone model.The mt'<I5ll1't‘[1)('.‘l1lS ol the retracted lighlare used
`to evaluate the gemstone.
`
`3.744.919 A
`3~79‘l'47-4 A '
`3.X35.665 A “
`3.858.979 A
`3'86-/-.032 A
`3.944.368 A
`3947.120 A "
`
`71973 Babb
`3" 1974 5101010’S‘ 9‘ 01»
`9-" I974 Kilchel
`. . . . .
`.
`. . . . . .
`I: 1975 Elbe
`3,1975 Bmck
`3-‘ I976 Beasley
`31-1976 Bar-Issac et a1.
`
`.
`
`. . . . . .
`
`35030
`. . . .. 63-"32
`
`356530
`
`352 Claims, 56 Drawing Sheets
`
`
`
`Arundsd
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`Page 1 of 117
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`GIA EXHIBIT 1001
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`

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`US RE44,963 E
`Page 2
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`(56)
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`FOREIGN PATENT DOCUMENTS
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`Page 2 of 117
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`

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`US RE44,963 E
`Page 3
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`(56)
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`U.S. Patent
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`Jun. 24, 2014
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`Sheet 1 of 56
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`US RE44,963 E
`
`._.m.
`4..
`f,
`
`.»
`
`g.%_%«...
`
`
`104
`
`108
`
`
`
`
`
`
`FIG. 1
`
`Amended
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`Page 5 of 117
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`U.S. Patent
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`Jun. 24, 2014
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`Sheet 2 of 56
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`Us RE44,963 E
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`
`BUILD DATA MODEL
`
`
`
`FOR GEMSTONE TO
`
`
`
`BE EVALUATED
`
`
`
`
`
`ILLUMINATE STONE
`
`WITH AN
`
`
`ILLUMINATION
`MODEL
`
`
`
`
`
`
`TRACE THE
`PROPAGATION OF
`
`
`LIGHT WITHIN THE
`
`
`
`STONE AND EXITING
`
`
`THE STONE
`
`
`
`
`
`DETERMINE LIGHT
`
`EXITING THE
`
`
`GEMSTONE
`
`
`
`
`GRADE GEMSTONE
`
`BASED ON LIGHT
`
`
`
`EXITING THE STONE
`
`
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`
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`
`
`204
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`208
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`212
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`216
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`220
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`FIG. 2
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`Page 6 of 117
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`Sheet 3 of 56
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`US RE44,963 E
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` 304
`
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`BUILD DATA
`
`STRUCTURE
`
`
`
`
`
`CREATE MAP OF Ff
`
`
`STONE
`
`
`
`
`
`
`
`308
`
`
`
`CONSTRUCT /
`
`CAMERA MODEL
`
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`312
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`
`
`
`
`
`CREATE ZONE MAP
`I=oR EACH CAMERA /
`
`
`
`
`
`
`316
`
`
`
`/-
`
`
`
`320
`
`
`
`: D
`
`EFINE OPTICAL
`
`
`PROPERTIES OF
`
`
`GEMSTONE
`
`
`DETERMINE
`
`DISPERSION f
`
`INDICES
`
`
`324
`
`
`
`
`
`1
`
`
`FIG. 3(a)
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`Page 7 of 117
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`Sheet 4 of 56
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`US RE44,963 E
`
`
`
`DETERMINE
`
`ILLUMINATION
`MODEL
`
`
`
`
`
`
`ILLUMINATE STONE
`
`USING
`
`ILLUMINATION
`MODEL
`
`
`
`
`
`MODEL
`PROPAGATION OF
`
`
`UGHTTHROUGH
`
`
`THE GEMSONE
`
`
`MODEL
`
`
`EVALUATE THE
`
`
`LIGHT OUTPUT
`
`
`FROM THE MODEL
`
`
`
`
`
`GRADE THE STONE
`
`
`BASED ON THE
`
`
`
`LIGHT OUTPUT
`
`
`
`
`
`328
`
`
`
`
`
`
`
`
`
`
`
`
`332
`
`336
`
`
`340
`
`
`
`344
`
`
`
`
`
`FIG. 3(b) (Amended)
`
`
`
`
`
`Page 8 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 5 of 56
`
`US RE44,963 E
`
`ILLUMINATION
`MODEL
`
`E
`
`GEMSTONE
`MODEL
`
`@
`
`CAMERA MODEL
`
`E
`
`FIG. 4
`
`Page 9 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 6 of 56
`
`US RE44,963 E
`
`502
`
`
`
`504
`
`506
`
`508
`
`510
`
`512
`
`M4
`
`516
`
`
`
`NEXTFACET
`
`EXTRACTFACET
`VERWCES
`
`
`
`EXTRACTFACET
`TYPE
`
`EXTRACTFACET
`LAYER
`
`
`
`COMPUTEFACET
`DOMNN
`
`COMPUTE
`NORMALVECTOR
`FORFACETPLANE
`
`COMPUTEFACET
`LOCAL
`COORDWATE
`SYSTEM
`
`FIG. 5 (Amended)
`
`Page 10 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 7 of 56
`
`Us RE44,963 E
`
`602
`
`START
`
`NEXT FAC ET
`
`604
`
`606
`
`608
`
`610
`
`
`
`FACET IN
`CROWN?
`
`YES
`
`CREATE ZONE
`
`LINK ZONE TO
`
`FACET
`
`612
`
`NO
`
`YES
`
`END
`
`614
`
`FIG. 6
`
`Page 11 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 8 of 56
`
`US RE44,963 E
`
`702
`
`704
`
`CR EATE CAMERA
`
`ARRAY
`
`DEFINE LOCAL
`
`COORDINATE
`
`SYSTEM FOR
`
`EACH CAMERA
`
`-I 706
`
`BUILD CAMERA-
`SPECIFIC COPY OF
`
`708
`
`MASTER ZONE
`
`LIST FOR EACH
`
`CAMERA
`
`710
`
`FIG. 7
`
`Page 12 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 9 of 56
`
`US RE44,963 E
`
`FIG. 8
`
`Page 13 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 10 of 56
`
`US RE44,963 E
`
`902
`
`START
`
`DETERMINE
`
`
`
`
`
`
`
`WHICH FACETS
`
`
`
`ARE VISIBLE TO
`CAMERA
`
`COMPUTE ZONE
`
`AREA FOR EACH
`ZONE AND TOTAL
`
`ZONE AREA FOR
`CAMERA
`
`904
`
`906
`
`908
`
`
`
`
`COMPUTE
`
`PERCENTAGE OF
`
`
`
`
`
`
`TOTAL ZONE AREA
`OCCUPIED BY
`
`
`
`EACH ZONE
`
`910
`
`FIG. 9
`
`Page 14 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 11 of 56
`
`US RE44,963 E
`
`FIG. 10
`
`Page 15 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 12 of 56
`
`US RE44,963 E
`
`Page 16 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 13 of 56
`
`US RE44,963 E
`
`GET DISPERSION
`CONSTANTS FOR
`GEMSTONE
`MATERIAL
`
`ASSIGN
`WAVELENGTHS
`FOR DISPERSION
`COMPONENTS
`
`COMPUTE INDICES
`OF REFRACTION
`FOR EACH
`DISPERSION
`COMPONENT
`
`1202
`
`1204
`
`1206
`
`1208
`
`1210
`
`FIG. 12 (Amended)
`
`Page 17 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 14 of 56
`
`US RE44,963 E
`
`START
`ILLUMINATE
`MODEL
`
`1302
`
`1304
`
`GET FACET SELECTION
`METHOD
`
`1352
`
`1308
`
`1305
`
`AUTO-
`MATIC
`
`DISPLAY
`
`GRADE
`
`
`1312
`
`POINT IN
`A FACET?
`
`
`
`
`
`
`YES
`HIGHLIGHT
`SELECTED FACET
`
`1314
`
`SELECT A
`LIGHT VECTOR
`
`LIGHT
`DIFF I CONICULAR
`
`1316
`
`‘|_3f;"°”'
`
`
`COMPUTE PASS TH RU
`VISIBILITY POINT IN
`FACET PLANE
`
`
`
`COMPUTE FACET
`|L|-\/UEIg*8FT{|é3N
`
`SELECT A LIGHT
`VECTOR
`
`133°
`
`1332
`
`1334
`
`1336
`
`DOES
`
`LIGHT VECTOR
`TOUCH
`
`
`
`REFRACT LIGHT
`VECTOR INTO MODEL
`
`
`
`IS LAST
`LIGHT
`VECTOR?
`
`
`
`
`
`PR°iffDS,§$;;fiiI'°”S
`IS LAST
`
`REFRACTIONS TO
`UGHT 7
`
`
`
`
`
`
`
`
`FACET?
`YES
`
`REFRACT LIGHT
`VECTOR INTO MODEL
`
`PROCESS REFLECTIONS AND
`INTERNAL REFRACTIONS TO
`CAMERAS
`
`1338
`
`1340
`
`FIG. 13(a)
`
`Page 18 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 15 of 56
`
`US RE44,963 E
`
`AUTOMATIC
`
`YES
`
`‘I386
`
`1360
`
`1384
`
`NO
`
`SELECT A
`FACET
`
`
`
`
`
`
`EXIT
`
`
`ILLUMINATION
`LOOP
`
`
`
`
`
`COMPUTE FACET
`ILLUMINATION
`VECTORS
`
`
`
`SELECT A LIGHT
`VECTOR
`
`
`
`
`
`COMPUTE PASS THRU
`VISIBILITY POINT IN
`FACET PLANE
`
`SELECT A
`LIGHT VECTOR
`
`LIGHT
`DIFF I CONICULAR
`
`
`
`
`
`
`
`
`1 374
`
`1376
`
`1373
`
`1330
`
`REFRACT LIGHT
`VECTOR INTO MODEL
`
`
`
`9055
`LIGHT VECTOR
`
`
`TOUCH
`FACET?
`PROCESS REFLECTIONS AND
`INTERNAL REFRACTIONS TO
`CAMERAS
`
`1370
`
`
`
`ES
`
`Y
`
`REFRACT LIGHT
`VECTOR INTO MODEL
`
`IS LAST
`LIGHT
`VECTOR?
`
`
`
`
`
`PROCESS REFLECTIONS
`
`IS LAST
`AND INTERNAL
`LIGHT
`REFRACTIONS TO
`VECTOR?
`CAMERAS
`
`
`
`FIG. 13(b)
`
`Page 19 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 16 of 56
`
`US RE44,963 E
`
`1411
`
`1412
`
`1414
`
`1416
`
`1418
`
`SELECT A BEAM
`COMPONENT
`
`COMPUTE ANGLE OF
`REFRACTION
`
`
`
`COMPUTE REFRACTED
`DIRECTION COSINES
`
`COMPUTE REFRACTED
`ANGLE OF DEVIATION
`
`TRANSLATE DIRECTION
`COSINES TO GLOBAL
`COORDINATE SYSTEM
`
`SELECTED
`
`LAST
`DISPERSION
`BUFFER
`
`Yes
`
`COMPUTF DISP
`BEAM INTENSITY
`COMPONENTS
`
`COMPUTE DISP.
`BEAM
`POLARIZATION
`
`COMPUTE DISP.
`BEAM AMPLITUDE
`
`START
`
`1402
`
`1404
`
`TRANSLATE LIGHT
`VECTOR TO FACET LOCAL
`
`COORDINATE SYSTEM
`
`1406
`
`COMPUTE DIRECTION
`COSINES FOR LIGHT
`
`VECTOR
`
`1408
`
`COMPUTE ANGLE OF
`INCIDENCE WITH FACET
`
`NORMAL
`
`1410
`
`COMPUTE FACET AREA
`
`COMPUTE BEAM
`INTENSITY
`COMPONENTS
`
`COMPUTE BEAM
`POLARIZATION
`
`COMPUTE BEAM
`AMPLITUDE
`
`FIG. 14
`
`Page 20 of 117
`
`

`
`U.S.
`
`Patent
`
`Jun. 24, 2014
`
`Sheet 17 of 56
`
`US RE44,963 E
`
`1504
`
`1505
`
`1508
`
`1510
`
`sTART
`
`1502
`
`NExT BOUNCE
`
`
`
`NEXT BEAM
`
`NEXT FACET
`
`
`'3
`BEAM PARALLEL TO
`
`FACET?
`
`NO
`
`PROJECT REFLECTION BOUNDING Box
`INTO RECEIVING FACET PLANE
`
`1512
`
`1516
`
`1520
`
`BOUNDING
`
`BOX OVERLAP?
`
`
`
`
`
`BEAM
`
`AMPLITUDE
`< MIN?
`
`NO
`
`
`
`
`
`PROJECT REFLECTION ONTO PLANE OF
`RECEIVING FACET
`
`1514
`
`1515
`
`NON-ZERO OVERLAP?
`
`1518
`
`YES
`
`CREATE REFLECTED LIGHT BEAM
`
`1522
`
`2224
`
`PROPAGATE REFRACTED
`LIGHT TO CAMERAS
`
`
`INCIDENT ANGLE <
`RITICAL ANGLE? ‘
`
`YES
`
` 1526
`
`NO
`
`LAST BEAM?
`
`NO
`
`LAST BOUNCE?
`
`1528
`
`1530
`
`NO
`
`END
`
`1532
`
`FIG. 15 (Amended)
`
`Page 21 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 18 of 56
`
`US RE44,963 E
`
`1602
`
`
`
`
`
`C REATE X-Y
`BOUNDING BOX
`
`FOR RECEIVING
`
`
`
`FACET
`
`
`
`
`CREATE X-Y-Z
`BOUNDING BOX
`
`FOR REFLECTION
`
`
`
`
`
`1504
`
`1505
`
`1608
`
`
`
`PROJECT
`
`REFLECTION
`
`
`
`
`
`
`BOUNDING BOX
`ONTO RECEIVING
`
`
`
`FACET PLANE
`
`1610
`
`FIG. 16
`
`Page 22 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 19 of 56
`
`US RE44,963 E
`
`COMPARE
`VERTICES OF
`PROJECTED
`BOUNDING BOX TO
`SIDES OF FACET
`BOUNDING BOX
`
`COMPARE
`VERTICES OF
`FACET BOUNDING
`BOX TO SIDES OF
`PROJECTED
`BOUNDING BOX
`
`COMPARE SIDES
`OF FACT
`BOUNDING BOX TO
`SIDES OF
`PROJECTED
`BOUNDING BOX
`
`1702
`
`1704
`
`1706
`
`1708
`
`1710
`
`FIG. 17 (Amended)
`
`Page 23 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 20 of 56
`
`US RE44,963 E
`
`1 802
`
`N EXT VERTEX
`
`
`
`/ 1806
`
`
`VERTEX
`NO
`BETWEEN X
`
`SIDES?
`
` 1804
`
`
` VERTEX
`BET\NEEN Y
`SIDES?
`
`
`
`1808
`
`INDICATE
`OVERLAF’
`
`
`
`
`1812
`
`1814
`
`FIG. 18
`
`Page 24 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 21 of 56
`
`US RE44,963 E
`
`1902
`
` 1 904
`
`
`
`FACET X
`SIDES BETWEEN
`PROJECTION X
`
`SIDES?
`
`
`
`
`1908
`
`FACET Y
`INDICATE
`SIDES BETWEEN
`BOUNDING BOX
`PROJECTION Y
`
`OVERLAP
`SIDES?
`
`
`
`
`
`FIG. 19 (Amended)
`
`Page 25 of 117
`
`1906
`
`PROJECTION Y
`
`SIDES BETWEEN
`FACET Y SIDES?
`
`YES
`
`PROJECTION X
`SIDES BETWEEN
`FACET X SIDES?
`
`
`
`

`
`
`U.S. Patent
`
`
`
`Jun. 24, 2014
`
`
`
`Sheet 22 of 56
`
`
`
`
`
`
`
`
`US RE44,963 E
`
`X
`
`
`
`
`
`
`
`»
`
`
`
`2
`
`
`:\\\—20o4
`
`
`
`
`FIG. 20
`
`
`
`‘\\\—2oo2
`
`
`
`2004
`
`
`
`
`
`FIG. 21
`
`
`
`Page 26 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 23 of 56
`
`US RE44,963 E
`
`START
`
`2202
`
`NEXT BEAM COMPONENT
`
`2204
`
`2206
`
`2208
`
`2210
`
`2212
`
`2214
`
`2216
`
`2220
`
`
`
`CONVERT DIRECTION
`COSINES FROM GCS TO
`FACET LCS
`
`COMPUTE ANGLE OF
`INCIDENCE
`
`COMPUTE ANGLE or=
`REFRACTION
`
`CONVERT DIRECTION
`COSINES FROM FACET LCS
`TO GCS
`
`COMPUTE XSEC INTENSITY
`
`COMPUTE DEGREE OF
`POLARIZATION
`
`2218
`
` LAST BEAM
`COMPONENT?
`
`
`YES
`
`COMPUTE ACCUMULATED
`BEAM VOLUME FOR CHILD
`
`BEAM
`
`2222
`
`
`
`IS BEAM
`
`AMPLITUDE LESS THAN
`
`A MINIMUM?
`
`
`YES
`
`
`
`DISCARD
`REF RACTED
`
`BEAM
`
`
`NO
`
`2226
`
`
`
`IS BEAM
`
`PROJECTED BELOW
`
`
`HORIZON?
`
`NO
`
`
`
`2228
`
`FIG. 22 (Amended)
`
`Page 27 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 24 of 56
`
`US RE44,963 E
`
`CREATE
`REFRACTED BEAM
`
`LOCATE CAMERA
`ILLUMINATED BY
`REFRACTED BEAM
`
`CAPTURE
`REFRACTED
`BEAM DATA USING
`CAMERA
`
`2302
`
`2304
`
`2306
`
`2308
`
`2310
`
`FIG. 23 (Amended)
`
`Page 28 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 25 of 56
`
`US RE44,963 E
`
`2402
`
`START
`
`DEFINE VIEWING
`PLANE
`
`PROJECT
`REFRACTED BEAM
`ONTO VIEWING
`PIANE
`
`24 04
`
`2405
`
`2408
`
`2410
`
`
`
`
`
`
`
`
`DETERMINE
`ANGULAR EXTENT
`OF PROJECTION
`OF WHITE BEAM
`
`
`
`COMPARE
`PROJECTION
`ANGLES TO
`CAMERA ANGLES
`
`
`
`2412
`
`FIG. 24
`
`Page 29 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 26 of 56
`
`US RE44,963 E
`
`Page 30 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 27 of 56
`
`US RE44,963 E
`
`2602
`
`START
`
`DETERMINE ZONE
`CORRESPONDING
`TO REFRACTING
`FACET
`
`UPDATE ZONE
`AVERAGE ANGLE
`OF DISPERSION
`
`COMPUTE BEAM
`EN ERGY DATA
`
`UPDATE CAMERA
`ZONE DATA USING
`BEAM DATA
`
`Page 31 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 28 of 56
`
`US RE44,963 E
`
`START
`
`
`
`2702
`
`
`
`2704
`
`2706
`
`2708
`
`2710
`
`DEFINE
`DISPERSION AXIS
`ON VIEWING
`PLANE
`
`
`
`COMPUTE PATH
`WIDTH
`
`COMPUTE PATH
`LENGTH
`
`
`
`COMPUTE
`INCIDENT FLUX AT
`VIEVVING PLANE
`
`
`
`2712
`
`FIG. 27
`
`Page 32 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 29 of 56
`
`US RE44,963 E
`
`2808
`
`2804
`
`28(a)
`
`23°‘
`
`
`
`2808
`
`280:)
`
`2808
`
`/\/
`/
`
`2301)
`
`2804
`
`FIG. 28
`
`Page 33 of 117
`
`

`
`
`U.S. Patent
`
`
`
`Jun. 24, 2014
`
`
`
`Sheet 30 of 56
`
`
`
`
`
`
`
`
`Us RE44,963 E
`
`
`
`2808
`
`29(a)
`
`
`
`2808
`
`
`
`
`
`29(b)
`
`
`
`
`
`FIG. 29
`
`
`
`Page 34 of 117
`
`

`
`U.S. Patent
`
`Jun. 24, 2014
`
`Sheet 31 of 56
`
`US RE44,963 E
`
`DETERMINE
`SEGMENTS OF
`FACET AND
`PROJECTION OF
`BEAM
`
`DETERMINE
`WHETHER VERTEX
`OF PROJECTI