TTHHEERREE’’SS NNOO DDIIFFFFEERREENNCCEE
BBEETTWWEEEENN GGRRIIDD AANNDD GGRROOUUNNDD
NYSAPLS 2011 Conference
Verona, New York
January 19, 2011
Presenter:
Joseph V.R. Paiva, PhD, PS, PE
1
There’s No Difference There’s No Difference
NYSAPLS 2011 Conference
January 19, 2011
Between Grid and Ground Between Grid and Ground
Joseph V.R. Paiva, PhD, PS, PEJoseph V.R. Paiva, PhD, PS, PE
The grid headacheThe grid headache
Why do we have it anyway?Why do we have it anyway?Is it those darn software Is it those darn software manufacturers?manufacturers?Why can’t we have the good old Why can’t we have the good old “ground” days“ground” days??Dealing with the grid is so expensiveDealing with the grid is so expensive
11
Dealing with the grid is so expensiveDealing with the grid is so expensive
2
TopicsTopics
Surveys of limited scope vs. large Surveys of limited scope vs. large extentextentextentextentPlane surveys vs. geodeticPlane surveys vs. geodeticHow projection makes large surveys How projection makes large surveys easiereasierWhy mixing GPS and total station even Why mixing GPS and total station even
22
ggin small surveys creates a problemin small surveys creates a problemCalculationsCalculationsStrategies for dealing with the Strategies for dealing with the grid/ground grid/ground “thing”“thing”
IntroductionIntroduction
Most smallMost small--area surveys can be done area surveys can be done i th th i fl t ( l i th th i fl t ( l assuming the earth is flat (plane assuming the earth is flat (plane
surveys)surveys)For large areas, Earth’s curvature For large areas, Earth’s curvature hashas to be consideredto be consideredThis usually involves determining This usually involves determining
33
This usually involves determining This usually involves determining geodetic positions (latitude and geodetic positions (latitude and longitude) of survey stationslongitude) of survey stations
3
State Plane Coordinate SystemState Plane Coordinate System
SPCS was designed in the early SPCS was designed in the early 1930 b th (th ) C t d 1930 b th (th ) C t d 1930s by the (then) Coast and 1930s by the (then) Coast and Geodetic survey to solve the problem Geodetic survey to solve the problem of surveys of large extents for the of surveys of large extents for the “local” surveyor“local” surveyorIn addition to allowing plane survey In addition to allowing plane survey
44
In addition to allowing plane survey In addition to allowing plane survey concepts to be used, it delivers concepts to be used, it delivers several additional benefitsseveral additional benefits
SPCS benefitsSPCS benefits
Simplifies calculations for surveys Simplifies calculations for surveys over large distancesover large distancesover large distancesover large distancesProvides common datum of reference Provides common datum of reference for all surveys (if tied in)for all surveys (if tied in)Well suited for engineering projects Well suited for engineering projects of large extent, i.e. highways, but of large extent, i.e. highways, but l h t t l l l h t t l l
55
also photogrammetry, large scale also photogrammetry, large scale cadastral surveys, etc.cadastral surveys, etc.
4
SPCsSPCs
When surveys are tied into the SPCS, When surveys are tied into the SPCS, their locations become (potentially) their locations become (potentially) their locations become (potentially) their locations become (potentially) indestructibleindestructibleWith GPS, the problem of what With GPS, the problem of what coordinates to use once geocentric coordinates to use once geocentric coordinates of GPS have been coordinates of GPS have been transformed in geodetic coordinates transformed in geodetic coordinates
66
transformed in geodetic coordinates transformed in geodetic coordinates makes SPCs a natural choicemakes SPCs a natural choice
ProjectionsProjections
The basic problem with plane The basic problem with plane i i th t it th i i th t it th surveying is that it assumes the surveying is that it assumes the
earth is flatearth is flatSome problems…Some problems…
77
5
ProblemsProblems
meridians convergemeridians converge
88
ProblemsProblems
On the Earth, “straight lines” are not On the Earth, “straight lines” are not t i ht t f idi ( th t i ht t f idi ( th straight except for meridians (or the straight except for meridians (or the
equator) and the difference gets equator) and the difference gets larger as you extend themlarger as you extend them
N
99
6
ProblemsProblems
Changes in elevation cannot be Changes in elevation cannot be i d th t i h ll d ti i d th t i h ll d ti ignored, that is why all geodetic ignored, that is why all geodetic distances are at “sea level”distances are at “sea level”
1010
ProjectionsProjectionsTo have a plane coordinate To have a plane coordinate system it is necessary to system it is necessary to system, it is necessary to system, it is necessary to distort the curved surface of distort the curved surface of the earth to a fit on a planethe earth to a fit on a planeOrange peel analogyOrange peel analogyThis process of flattening This process of flattening
t b t ti i d t b t ti i d
1111
must be systematic in order must be systematic in order to have accuracyto have accuracyIn surveying this process is In surveying this process is called a projectioncalled a projection
7
Projections / 2Projections / 2
Systematic way to portray (curved) Systematic way to portray (curved) f f th th fl t ff f th th fl t fsurface of the earth on a flat surfacesurface of the earth on a flat surface
Distortions inevitableDistortions inevitableDifferent projections are used Different projections are used because each minimizes distortion in because each minimizes distortion in some properties at the expense of some properties at the expense of
1212
some properties at the expense of some properties at the expense of othersothers
Types of projectionsTypes of projections
Different mathematical treatments Different mathematical treatments i t j ti d di i t j ti d di are given to projections depending are given to projections depending
on the result desiredon the result desired
1313
8
Developable surfaceDevelopable surface
A shape that can be made into a A shape that can be made into a llplaneplane
•• Cone Cone •• CylinderCylinder•• Plane (of course)Plane (of course)
1414
General classesGeneral classes
CylindricalCylindrical
Tangent
1515
9
Transverse MercatorTransverse Mercator
A C
1616
B D
Transverse Mercator Transverse Mercator edge viewedge view
CylinderCylinder
1717
Sphere
10
General classesGeneral classes
ConicConic
Secant
1818
Lambert conformalLambert conformal
Varying central Varying central apex angle of cone apex angle of cone apex angle of cone apex angle of cone changes section of changes section of ellipsoid that is ellipsoid that is intersectedintersected
1919
11
2020
PlanarPlanarThis type of projection This type of projection This type of projection This type of projection is created when is created when surveyor sets up surveyor sets up arbitrary coordinate arbitrary coordinate system for a surveysystem for a survey
2121
Plus…many Plus…many miscellaneousmiscellaneous
12
Next stepNext step
Once developable surface Once developable surface parameters are picked plane is parameters are picked plane is parameters are picked, plane is parameters are picked, plane is createdcreatedBecause a developable surface is Because a developable surface is used, while there are distortions in used, while there are distortions in converting coordinates on the earth converting coordinates on the earth to the developable surface there is to the developable surface there is
2222
to the developable surface, there is to the developable surface, there is no further distortion of shape or size no further distortion of shape or size when it is unrolled or “developed”when it is unrolled or “developed”
Most common surfaces in SPCSMost common surfaces in SPCS
Lambert conformal (conic)Lambert conformal (conic)Transverse Mercator (cylinder)Transverse Mercator (cylinder)Also…skewed (or oblique) Also…skewed (or oblique) Mercator Mercator where axis of cylinder is not eastwhere axis of cylinder is not east--westwest
2323
13
State Plane Coordinate State Plane Coordinate Systems (83)Systems (83)
System for specifying System for specifying d ti t ti i l d ti t ti i l geodetic stations using plane geodetic stations using plane
rectangular coordinatesrectangular coordinatesOver 120 zones for U.S.Over 120 zones for U.S.Long Long NN--SS states use states use Transverse MercatorTransverse Mercator
2424
Transverse MercatorTransverse MercatorLong Long EE--WW states use Lambertstates use LambertIf square, use eitherIf square, use either
SPCS (83)SPCS (83)
Alaska, Florida and New York use Alaska, Florida and New York use b th t f j tib th t f j tiboth types of projectionsboth types of projectionsIn addition Alaska has an oblique In addition Alaska has an oblique projection for the southeastern part projection for the southeastern part of the stateof the state
2525
14
SPC83 vs. SPC27SPC83 vs. SPC27
Coordinate values changed (N and E)Coordinate values changed (N and E)MetersMetersTypes of projections changed for Types of projections changed for some statessome statesZones different in someZones different in some
b f h db f h d
2626
Numbers of zones per state changed Numbers of zones per state changed in somein some
Feet!Feet!
U.S. Survey foot = [m] x U.S. Survey foot = [m] x U.S. Survey foot [m] x U.S. Survey foot [m] x 3937/12003937/1200International foot = [m] / International foot = [m] / 0.30480.30482 PPM2 PPM!!
2727
[0.01 ft in a mile][0.01 ft in a mile][but with a [but with a coordcoord value of value of 500,000 m, difference is 1 500,000 m, difference is 1 m!]m!]
15
NOAA/NGS documentNOAA/NGS document
NOAA Manual NOS NGS 5NOAA Manual NOS NGS 5State Plane Coordinate System of State Plane Coordinate System of 19831983http://www.ngs.noaa.gov/http://www.ngs.noaa.gov/[www.ngs.noaa.gov/PUBS_LIB/ManualNOSNGS5.pdf][www.ngs.noaa.gov/PUBS_LIB/ManualNOSNGS5.pdf]
2828
DistortionsDistortions
Scale is exact where cone or Scale is exact where cone or cylinder intersects ellipsoid cylinder intersects ellipsoid cylinder intersects ellipsoid cylinder intersects ellipsoid surfacesurfaceScale is less than one between Scale is less than one between lines of true scale (i.e. length on lines of true scale (i.e. length on ellipsoid is greater than length on ellipsoid is greater than length on plane)plane)
2929
plane)plane)Scale is more than one outside Scale is more than one outside lines of true scale (i.e. length on lines of true scale (i.e. length on ellipsoid is smaller than length on ellipsoid is smaller than length on plane)plane)
16
Zone sizeZone size
Where the zone intersects the Where the zone intersects the Earth and whether it is tangent or Earth and whether it is tangent or Earth, and whether it is tangent or Earth, and whether it is tangent or secant controls the distortionssecant controls the distortionsBy strategic placement, distortions By strategic placement, distortions are minimized, scale differences are minimized, scale differences can be kept to 1:10,000 or lesscan be kept to 1:10,000 or lessDone by keeping zone size to Done by keeping zone size to
3030
Done by keeping zone size to Done by keeping zone size to <158 mi and keeping zone width <158 mi and keeping zone width such that twosuch that two--thirds of the zone is thirds of the zone is between lines of true scale (secant between lines of true scale (secant lines)lines)
More on zone sizeMore on zone size
Zones are designed to overlap each Zones are designed to overlap each th id blth id blother considerablyother considerably
Thus a survey done near a zone Thus a survey done near a zone boundary can be done in either zoneboundary can be done in either zone
3131
17
Transverse Mercator projectionTransverse Mercator projection
Also conformalAlso conformalScale varies east to west but not Scale varies east to west but not north to southnorth to southScale is true at the secant lineScale is true at the secant lineAll geodetic meridians are curved, All geodetic meridians are curved, converging at the poleconverging at the pole
3232
converging at the poleconverging at the pole
Transverse Mercator projection / 2Transverse Mercator projection / 2
All parallels (of latitude) are curvedAll parallels (of latitude) are curvedCM is assigned to a meridian lineCM is assigned to a meridian lineAll lines on the plane parallel to the All lines on the plane parallel to the CM are grid northCM are grid northEastEast--west lines on the plane are west lines on the plane are perpendicular to the CMperpendicular to the CM
3333
perpendicular to the CMperpendicular to the CM
18
Transverse MercatorTransverse Mercator
A C
3434
B D
TM edge viewTM edge view
CylinderCylinder
3535
Sphere
19
When developed…When developed…
A C
Scale greater
than true
Scale greater
than true
Scale less than true
3636
B D
…or…or
CylinderScale greater
than true
Vi di l t i f li d
Scale less than true
3737
View perpendicular to axis of cylinder
20
Mapping angleMapping angle
Also called grid declination or Also called grid declination or i tii tivariationvariation
Greek letter Greek letter -- γγ [gamma][gamma]
3838
Grid overlaid on developed Grid overlaid on developed surfacesurface
CM (C t l M idi )CM (Central Meridian)E0
3939
21
New York SPCS constantsNew York SPCS constantsItem Value
Zone New York E (3101) also NJ( )
Type Transverse Mercator
Central Meridian 74° 30’ W *
Grid origin latitude 38° 50’ N *
Grid origin longitude 74° 30’ W *
Grid origin X coordinate -easting 150,000 m
Grid origin Y coordinate- northing 0 m
Scale at central meridian 1:10,000 *
4040
New York SPCS constantsNew York SPCS constantsItem Value
Zone New York C (3102)( )
Type Transverse Mercator
Central Meridian 76° 35’ W
Grid origin latitude 40° 00’ N
Grid origin longitude 76° 35’ W
Grid origin X coordinate -easting 250,000 m
Grid origin Y coordinate- northing 0 m
Scale at central meridian 1:16,000
4141
22
New York SPCS constantsNew York SPCS constantsItem Value
Zone New York W (3103)( )
Type Transverse Mercator
Central Meridian 78° 35’ W
Grid origin latitude 40° 00’ N
Grid origin longitude 78° 35’ W
Grid origin X coordinate -easting 350,000 m
Grid origin Y coordinate- northing 0 m
Scale at central meridian 1:16,000
4242
New York SPCS constantsNew York SPCS constantsItem Value
Zone Lambert (3104)( )
Type Lambert Conformal
Central Meridian 74° 00’ W
Standard parallel N 41° 02’ N
Standard parallel S 40° 40’ W
Grid origin latitude 40° 10’N *
Grid origin longitude 74° 00’W
Grid origin X coordinate -easting 300,000 m
Grid origin Y coordinate- northing 0 m
Scale at central meridian 1:16,000
4343
23
From Appendix CFrom Appendix C
4444
Calculation of ECalculation of EPP’’
Distance from Central Meridian
N
E0
EP’
CM
4545
E
P
EP
24
Ellipsoid, Geoid, TopographyEllipsoid, Geoid, Topography
Local TopographyLocal Topography
GeoidGeoid
EllipsoidEllipsoid
Mass DeficiencyMass Deficiency
Mass ExcessMass Excess
4646
Reducing surf. dist. to geodetic Reducing surf. dist. to geodetic dist.dist.
.... DistGrndElevR
RDistGeod m ×+
=
RRmm = 20,906,000 ft or 6,372,000 m= 20,906,000 ft or 6,372,000 mApproximate SLF can be Approximate SLF can be calculated for project where relief calculated for project where relief
llll
.....
DistSurfSLFDistGeodElevRm
×=+
4747
is smallis smallIn high relief areas need to In high relief areas need to calculate individually using calculate individually using average elevation of the lineaverage elevation of the line
25
Reducing Reducing geodgeod. dist. to grid dist.. dist. to grid dist.
kDistGeodDistGrid ×= . k is sometimes called SF (scale k is sometimes called SF (scale factor)factor)k is calculated from equations or k is calculated from equations or interpolated from tables in state interpolated from tables in state or NOAA documentsor NOAA documents
4848
Scale factor (Mercator)Scale factor (Mercator)
“k” based on longitude (E“k” based on longitude (EPP’)’)A single Scale Factor (SF), can be A single Scale Factor (SF), can be picked for projects that are not large picked for projects that are not large (under ~8 km)(under ~8 km)
4949
26
Direct conversion from surf. dist. to Direct conversion from surf. dist. to grid dist.grid dist.
Grid Dist = Surf Dist x SLF x SF Grid Dist = Surf Dist x SLF x SF If l ti d E f th If l ti d E f th If average elevation and E for the If average elevation and E for the project are being used, multiply SLF project are being used, multiply SLF and SF and use it as the Grid Factor and SF and use it as the Grid Factor (GF)(GF)Grid factor also sometimes called Grid factor also sometimes called “C bi d S l F t ” (CSF)“C bi d S l F t ” (CSF)
5050
“Combined Scale Factor” (CSF)“Combined Scale Factor” (CSF)SF converts from geodetic to gridSF converts from geodetic to gridGF converts from ground to gridGF converts from ground to grid
Grid AzimuthGrid Azimuth
Grid Az = Geod Az Grid Az = Geod Az -- γγ + Second + Second TTTermTerm
For most surveys Second For most surveys Second Term can be ignored (lines Term can be ignored (lines under 8 km)under 8 km)
5151
27
Why second term?Why second term?
5252
Central Meridian
γ Geodetic azimuth
γGeodetic azimuth
5353
Grid azimuthGrid
azimuth
28
).sin()..( StaLatStaLongCMLong ×−=γ
Varies with longitude but can use Varies with longitude but can use same same γγ for many surveysfor many surveys
)()( ggγ
5454
LaPlace correction may need to be added if using astro-azimuths
General PatternGeneral Patternadjust traverseadjust traversedetermine SLF using elevation determine SLF using elevation determine SLF using elevation determine SLF using elevation (either for project or dist. by (either for project or dist. by dist.)dist.)determine SF using dist. from determine SF using dist. from CM (either for project or dist. CM (either for project or dist. by dist.)by dist.)
5555
calc. GF if desiredcalc. GF if desiredconvert all distances to grid convert all distances to grid distances using GFdistances using GFconvert all azimuths to grid convert all azimuths to grid azimuthsazimuths
29
General pattern / 2General pattern / 2
Assuming one of the traverse points Assuming one of the traverse points h k SPC l f th h k SPC l f th has a known SPC, calc of the has a known SPC, calc of the coordinates (SPC) of the other points coordinates (SPC) of the other points is straightforwardis straightforwardAlways multiply distancesAlways multiply distancesNEVER multiply coordinates!NEVER multiply coordinates!
5656
NEVER multiply coordinates!NEVER multiply coordinates!
Lambert conformal conic projectionLambert conformal conic projection
Conformal: true angular relationships Conformal: true angular relationships are maintained around all points in are maintained around all points in are maintained around all points in are maintained around all points in small regionssmall regionsScale varies north to south but not Scale varies north to south but not east to westeast to westSecant lines, where scale is true, are Secant lines, where scale is true, are
ll d ll d t d d ll lt d d ll l
5757
called called standard parallelsstandard parallelsAll geodetic meridians are straight, All geodetic meridians are straight, converging at the poleconverging at the pole
30
Lambert / 2Lambert / 2
All parallels (of latitude) are arcs of All parallels (of latitude) are arcs of t i i l h th i t t t i i l h th i t t concentric circles have their center at concentric circles have their center at
the apexthe apexCM is assigned to a meridian lineCM is assigned to a meridian lineAll lines on the plane parallel to the All lines on the plane parallel to the CM are grid northCM are grid north
5858
CM are grid northCM are grid northEastEast--west lines on the plane are west lines on the plane are perpendicular to the CMperpendicular to the CM
Lambert conformalLambert conformal
Varying central Varying central apex angle of cone apex angle of cone apex angle of cone apex angle of cone changes section of changes section of ellipsoid that is ellipsoid that is intersectedintersected
5959
31
Standard parallels
6060
p
6161
32
Mapping angleMapping angle
Also called grid declination or Also called grid declination or i tii tivariationvariation
Greek letter Greek letter -- θθ [theta][theta]
6262
Calculations (Lambert)Calculations (Lambert)
Same as for Transverse Mercator Same as for Transverse Mercator ttexcept…except…
Tables for the zone have the value Tables for the zone have the value
lStaLongCMLongAzGeodAzGrid
×−=−=
.)..(....
θθ
6363
of the long. of the CM and of the long. of the CM and llGeneral pattern for calcs is the General pattern for calcs is the samesame
33
Typical calculationsTypical calculations
...
.. DistGrndElevR
RDistGeodm
m ×+
=
Elevation 0 m; ground dist = 1000 Elevation 0 m; ground dist = 1000 mm
.... DistSurfSLFDistGeodm
×=
6464
Elevation 1,000 m; ground dist = Elevation 1,000 m; ground dist = 1000 m1000 m
Scale factorScale factor
Assume distance from CM is 30,000 Assume distance from CM is 30,000 (d ’t tt h th t (d ’t tt h th t m (doesn’t matter whether east or m (doesn’t matter whether east or
west)west)Enter table and pick off value for Enter table and pick off value for 30,000 m: 0.999944430,000 m: 0.9999444If not a round number will have to If not a round number will have to
6565
If not a round number, will have to If not a round number, will have to interpolate!interpolate!
34
InterpolationInterpolation
Dist from CM = 31,457 mDist from CM = 31,457 mT bl l f 30 000 0 9999444T bl l f 30 000 0 9999444Table value for 30,000: 0.9999444Table value for 30,000: 0.9999444Table value for 31,500: 0.9999455Table value for 31,500: 0.9999455Difference (sometimes tabulated): Difference (sometimes tabulated): 0.00000110.0000011SF?SF?
6666
Grid factorGrid factor
GF = SLF x SFGF = SLF x SFAlso called Combined Scale Factor Also called Combined Scale Factor (CSF)(CSF)
6767
35
Mapping angle calcs (Mercator)Mapping angle calcs (Mercator)
).sin()..( StaLatStaLongCMLong ×−=γ
Sta. Long. = 93Sta. Long. = 93°°00’00”00’00”CM = CM = 9292°°30’00”30’00”Sta. Lat = Sta. Lat = 3838°°00’00”00’00”
6868
Which way to apply Which way to apply mapping mapping angle?angle?
6969
36
Practical usePractical use
Tie in to monuments with SPCs, Tie in to monuments with SPCs, therefore don’t need to calculate therefore don’t need to calculate therefore don t need to calculate therefore don t need to calculate mapping anglemapping angleProject coordinates sometime usedProject coordinates sometime used——be careful!be careful!On plats show SPCs. If you must On plats show SPCs. If you must h d di t h d di t h id h id
7070
show ground distances, show ground distances, show grid show grid distances also!distances also!Meta data!Meta data!
WhewWhew
How to use?How to use?M ti ll id ( di t ) M ti ll id ( di t ) My suggestion: use all grid (coordinates) My suggestion: use all grid (coordinates) or all ground (distances)or all ground (distances)If all ground distances, publish a table of If all ground distances, publish a table of grid coordinates of all the pointsgrid coordinates of all the pointsIf all grid coordinates, publish a table of all If all grid coordinates, publish a table of all
d d di tdi t d if d i d d if d i d
7171
ground ground distancesdistances and, if desired, and, if desired, azimuths/bearings on nonazimuths/bearings on non--grid basisgrid basis
37
Grid vs. groundGrid vs. ground
DO NOT publish “ground DO NOT publish “ground di t ” l X d Y l di t ” l X d Y l coordinates” unless X and Y values coordinates” unless X and Y values
are readily differentiableare readily differentiableOn the plat if you show ground On the plat if you show ground values and grid values use a suffix or values and grid values use a suffix or prefix (GRID & ground)prefix (GRID & ground)
7272
prefix (GRID & ground)prefix (GRID & ground)
Grid vs. groundGrid vs. ground
If you have to, use different fonts or If you have to, use different fonts or diff t t l ( l diff t t l ( l it li )it li )different styles (regular vs. different styles (regular vs. italics)italics)But make sure they can be easily But make sure they can be easily differentiateddifferentiatedDo NOT use different colors Do NOT use different colors to to differentiate; remember differentiate; remember that that
7373
differentiate; remember differentiate; remember that that whatever you prepare may become whatever you prepare may become monochromemonochrome
38
Keep in mindKeep in mindA point is a pointA point is a pointIt doesn’t matter whether it is on the It doesn’t matter whether it is on the It doesn t matter whether it is on the It doesn t matter whether it is on the plane (grid), ellipsoid or surfaceplane (grid), ellipsoid or surfaceDo some work on a survey nearby…Do some work on a survey nearby…hand hand calculate grid or ground valuescalculate grid or ground values…then see …then see if your data collector and PC software if your data collector and PC software handle correctlyhandle correctlyNeed to have fairly long distances to see Need to have fairly long distances to see
7474
y gy gdifferences between grid and ground differences between grid and ground (figure PPM to know how long)(figure PPM to know how long)Using a data collector do the math is OK, Using a data collector do the math is OK, as long as it does it correctlyas long as it does it correctlyRemember: GIGORemember: GIGO
TransformationsTransformations
N
Y’
B
X’
A
B
7575
E
X’
Given: A and B in N/E reference frame and X/Y reference frame. Determine the transformation equation to convert any point from the X/Y to N/E system
39
Transformation / 2Transformation / 2N
Y’
AB
EX’
A
Three parts to the transformation:
1. Rotation
2 Scale
7676
2. Scale
3. Translation
Transformation / 3Transformation / 3N
Y’
AB
EX’
A
Rotation:
1. Determine azimuth of AB in XY and NE systems
2 Rotation = azimuth in XY minus azimuth in NE = θ
7777
2. Rotation azimuth in XY minus azimuth in NE θ
40
Transformation / 4Transformation / 4N
Y’
AB
EX’
A
Scale:
1. Determine length of AB in XY and NE systems
2 Scale = length in NE system divided by length in
7878
2. Scale length in NE system divided by length in XY system = s
Transformation / 5Transformation / 5N
Y’
AB
EX’
A
Translation is done in two steps:
1. Calculate coordinates of A and B in X’Y’ system
2 Then determine translation by subtracting
7979
2. Then determine translation by subtracting coordinates in X’Y’ system from coordinates in NE system
3. Result is Tx and TY
41
Determining coordinates in X’Y’ Determining coordinates in X’Y’ frameframe
θθθθ
i'sincos' AAA
XXYsYsXX −=
θθ cossin' AAA sXsXY +=Transforms from XY to X’Y’ coordinates
NY’
BXET '=
8080
EX’
AB
AAY
AAX
YNTXET
'−=−=
Final equations for transformationFinal equations for transformation
XTsYsXE +−= θθ sincos
YTsYsXN ++= θθ cossin
8181
42
Questions?Questions?Questions?Questions?
8282
About the seminar presenter Joseph V. R. Paiva is a consultant in the field of geomatics and general business, particularly to international developers, manufacturers and distributors of instrumentation and other geomatics tools. Prior to this he was managing director of Spatial Data Research, Inc., a GIS data collection, compilation and software development company. Immediately prior, he was at Trimble Navigation Ltd. His roles included senior scientist and technical advisor for Land Survey research & development, VP of the Land Survey group and director of business development for the Engineering and Construction Division. Previous to that, Paiva was vice president and a founder of Sokkia Technology, Inc., guiding development of GPS- and software-based products for surveying, mapping, measurement and positioning. He has also held senior technical management positions in The Lietz Co. and Sokkia Co. Ltd. Dr. Paiva was assistant professor of civil engineering at the University of Missouri-Columbia, and a partner in a surveying/civil engineering consulting firm. Dr. Paiva’s special areas of interest include interface development and design for software and hardware, errors analysis and survey instrumentation of all types. His key contributions in the development field are: design of software flow for the SDR2 and SDR33 Electronic Field Books and the software interface for the Trimble TTS500 total station. He is a member of several professional societies, has presented numerous papers and writes columns for P.O.B. magazine and The Empire State Surveyor. In May 2006 he completed an approximately three year stint as a columnist for Civil Engineering News. He is a Registered Professional Engineer, Registered Land Surveyor, is an ACSM representative to ABET, serving as a program evaluator and team chair on accreditation visits to surveying programs, and has more than 30 years experience working in civil engineering, surveying and mapping. Dr. Paiva is currently working on book to be published soon on the subject of total stations; it is intended to be a practitioner’s guide to help in the understanding, operation, testing and adjustment of these ubiquitous instruments. His contact information is as follows:
• E-mail [email protected]
• Phone (816) 960-6693
• Mobile (816) 225-7163
• Fax (816) 960-6481
• Address 3925 Harrison St Kansas City, MO 64110
• www.josephpaiva.com