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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
MODELIZACION DEL ESPACIOSISTEMAS DE REFERENCIA
Ing. Geomensor:Gabriel Aravena Vallejos
Los s istemas de referencia geodsicos definenla forma y dimensin de la Tierra, as como elorigen y or ientacin de los sistemas decoordenadas.
Los s istemas de referencia geodsicos pueden
ser descritos en base a dos modelosmatemticos: el esfrico y el elipsdico, loscuales son obtenidos en base parmetros f sicosmedidos sobre la superficie terrestre, tales comola aceleracin de gravedad.
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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
Modelo basado en la superficie:
Conceptos principales:El marco de trabajo espacial es unespacio particionado. Ej. Grilla decoordenadas (x,y).
Existen operaciones sobre los campos.Ej: Adicin, composicin, etc.
Caso: Parcela forestal yo puedo conocerla (a) mayor altura entre los rboles, (b)rangos de altura, o bien, (c) el promediode las alturas de los rboles.
Modelo basado en las entidades:
A un nivel conceptual, se consideran objetosespaciales.
Estos son, en el caso de informacin
geogrfica, entidades del mundo real quetienen dos componentes:
- Una descripcin: conjunto de atributos-Componentes espacial: geometra yrelaciones.
Posicin, forma, tamao, densidad,relaciones espaciales.
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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
Modelo basado en las entidades:
Tipos de Objetos EspacialesSimples
1-Dimensiones: puntos2-Dimensin: Lneas3-Dimensiones: polgonos
Complejos
- Multipoint- Multi l ine- Multipolygon
Modelo basado en las entidades:
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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
SISTEMAS DE REFERENCIA
Sistema de referencia en UNA DIMENSION,sistema unidimensional.
Asociamos valores (coordenadas) a cadaelemento a representar.
Se establece una relacin biunvoca entre loselementos a representar y los valoresasignados (coordenadas).
Relacin biunvoca. A cada elemento arepresentar le corresponde uno y solo un valor(coordenadas) y viceversa.
SISTEMAS DE REFERENCIA
Sistema de referencia en UNA DIMENSION,sistema unidimensional.
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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
SISTEMAS DE REFERENCIA
Sistemas de referencia en DOS DIMENSIONES,Ej.: Medidas cancha de ftbol
A
B C
D
120,000,00D
90,00120,00C
90,000,00B
0,000,00A
Norte (m)Este (m)Punto
Definimos:
a) Origen, O.
b) Un par de ejes ortogonales (E, N).
c) Una unidad de longitud (m).
SISTEMAS DE REFERENCIA
Sistemas de referencia en TRES DIMENSIONES, :Ej. Libros en estante.
FILA
S
COLUMNAS
ALT
URA
231A
AlturaColumnaFilaLibro
Definimos:
a) Origen, O.
b) Una terna de ejes ortogonales (Fila, Columna, Altura).
c) Una escala de medicin.
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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
SISTEMAS DE REFERENCIA EN GEODESIA
Definicin de modelos, parmetros, constantes,etc., que sirven como base para la descripcinde los procesos fsicos de la Tierra o de lasuperficie terrestre.
Los sistemas de referencia no se puedendeterminar por medic iones, sino que se definen
convencionalmente.
SISTEMAS DE REFERENCIA EN GEODESIA
Consideramos una terna ortogonal directa deejes cartesianos.
Definimos:
1)Origen
2)Orientacin
3)Escala
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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
SISTEMAS DE REFERENCIA EN GEODESIA
Implica la eleccin de:
- Un elipsoide de referencia.
- Un punto origen o punto DATUM, cuyascoordenadas se determinan medianteobservaciones astronmicas.
- Un acimut de partida, obtenido a partirde observaciones astronmicas.
SISTEMAS DE REFERENCIA EN GEODESIA
Se establece su ubicacin en relacin conla forma fsica de la tierra, el geoide.
Sistema de Referencia 2D: latitud y longitudsobre el elipsoide.
Sistema de Referencia Altimtricoindependiente.
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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
ELEMENTOS GEODESICOS:1. COORDENADAS CARTESIANAS
El punto O, donde se interceptan los ejes, seubica en el centro de la tierra, el eje Z coincidecon el eje de rotacin del planeta y el plano OZXcoincide con el meridiano de Greenwich.
ELEMENTOS GEODESICOS:
1. COORDENADAS CARTESIANAS
Los valores de (X, Y, Z)se miden generalmenteen metros.
Eje Z
Eje Y
Eje X
P (x,y,z)
z
x
yO
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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
En el sistema se define elcentro de la tierra por O,el punto P se sita en lassiguientes coordenadas:
O
Z
Y
X
PN
PS
Q
EQE
P
h
ELEMENTOS GEODESICOS:
2. COORDENADAS GEODESICAS
: latitud geodsica: longitud geodsicah: altura elipsoidal
ELEMENTOS GEODESICOS:
3. COORDENADAS UTM(Universal Transversal Mercator)
La construccin de la proyeccin UTM se basa
en un cilindro transversal, es decir, un cilindrocuyo eje es perpendicular al eje del globo.
Este cilindro es secante, tiene dos crculos detangencia cercanos al meridiano central (MC)del huso, as se logra que las deformacionessean mnimas en esta rea.
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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
ELEMENTOS GEODESICOS:
4. DATUM
Es la superficie de referencia geodsica querepresenta vertical y horizontalmente lacartografa, el Datum define la forma de la tierra,su tamao, origen y la orientacin del sistema decoordenadas.
Generalmente se define en un elipsoide derevolucin y por un punto fundamental, en el quecoinciden las verticales al geoide y al elipsoide.
Cada pas trata de que la superf icie de suelipsoide coincida con el geoide
El ajuste se hace determinando el llamado puntofundamental donde se hace coincidir el geoidecon el elipsoide elegido llamado elipsoide de
referencia.
Al conjunto de parmetros que definen ese puntofundamental se lo llama Datum DATUM.
Todos los Datum estn basados sobre unelipsoide, los cuales se aproximan a la forma dela tierra.
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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
TIPOS DE DATUM:
GEOCENTRICO:Usa el centro de masa de la tierra como or igen(WGS 84)
LOCALES:Al inea su el ipsoide lo ms prximo a la superfic iede la tierra y un rea en particular.
DATUM GEOCENTRICO
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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
DATUM LOCAL
DATUM GEOCENTRICO Y LOCAL
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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
4.1 DATUM HORIZONTAL:
Superficie elipsoidal usada como base parareferenciar coordenadas de localizacin X, Y.
Determina localidades cerca de la superficieterrestre.
Los datos se ajustan matemticamente paraencontrar el mejor elipsoide local, adems de otros
parmetros.
4.2 DATUM VERTICAL:
Esta en desuso, con una excepcin, el NivelMedio del Mar (n.m.m.).
Superficie usada como base para referenciarlocalizaciones de coordenadas Z (actualmentese util iza el geoide o la superficie del agua enreposo de los ocanos idealmente extendida).
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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
OTROS ELEMENTOS:
5. Eje terrestre, Polos:
Es la recta imaginaria, alrededor de la cual girala tierra en su movimiento de rotacin, el cualpermanece paralelo en su movimiento detraslacin, seala a un punto en el espacio quecoincide en la direccin del hemisferio nor te aun punto cercano a la estrella polar. Si bien
este eje tiene otros movimientos, (precesin ynutacin), estos son lentos y no afectan almbito que nos ocupa.
Los extremos de este ejeterrestre en su interseccincon la superficie de la tierrase denominan polos,correspondiendo el nombre
de Polo Norte al que est enel lado de la constelacin dela osa mayor. El otroextremo del eje es el PoloSur.
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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
6. Plano merid iano y meridianos, meridiano cero:
Todo plano que contiene al eje terrestre se llamaPlano Meridiano.
La lnea interseccin de este plano con lasuperficie de la tierra impropiamente sedenomina crculo mximo o meridiano, cuando enrealidad se asemejan ms a una elipse, siendoelipses en el caso de su proyeccin sobre el
elipsoide de referencia.
Pasan por los polos y se toma uno como origendando referencia a los dems; por conveniointernacional corresponde al que pasa por elObservatorio Astronmico de la ciudad Inglesa
de Greenwich, cercana a Londres.
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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
7. Plano Paralelo, Paralelos, Lnea Ecuatorial yTrpicos.
Se denominan Planos Paralelos a todos aquellosque son perpendiculares al Eje de la Tierra,denominndose Plano Ecuator ial al que pasa porel Centro de la Tierra y divide al Globo Terrestreen dos hemisferios, Hemisferio Norte yHemisferio Sur o Austral, que se corresponden acada Polo respectivo.
Todas las intersecciones de los Planos Paraleloscon la superfic ie de la tierra configuran losParalelos recibiendo el nombre de Trpicos,Trpico de Cncer y Trpico de Capricornio, elparalelo correspondiente al equinoccio de veranoy al de invierno, el pr imero en el Hemisferio Nortey el segundo en el Hemisferio Sur.
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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
8. Vertical en un punto. Cenit y Nadir.
La vertical en un punto est determinada porel fenmeno de la gravedad o atraccin terrestre,vertical en el sentido f sico y tambindenominada vertical verdadera, y pasara por elcentro de la tierra.
Si se considera el elipsoide de revolucin, lavertical sera la normal a la superficie en el puntodeterminado del elipsoide, la cual no pasar porel centro del elipsoide y se denomina verticalgeogrfica.
La desviacin o diferencia entre ambases la desviacin relativa de la vertical.Si nos s ituamos sobre un punto de lasuperficie de la Tierra y trazamos un eje verticaltendremos sobre nuestra cabeza el Cenit yatravesando la tierra pasara al otro extremo,
denominado Nadir, recibiendo el nombre deantpodas ambos extremos entre s.
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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
Vertical (Cenit y Nadir) y meridiana de un punto
9. Meridiana y Puntos Cardinales.
Se denomina plano horizontal en un punto alplano tangente a la superficie esfrica en dichopunto.
Meridiana de un punto es la recta de interseccinentre un plano hor izontal y el plano meridianoque pasa por dicho punto.
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2006 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The informationherein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not beinterpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information providedafter the date of this presentation.MICROSOFT MAKES NO WARRANTIES, EXPRESS , IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.
ste nos marca sobre dicho plano horizontal ladireccin Norte-Sur del polo correspondiente.
Una perpendicular a la meridiana definir a unanueva direccin, con lo cual partiendo del puntointerseccin tendramos cuatro direccionescontrapuestas.
Los puntos de proyeccin al infinito de dichasdirecciones se denominan Puntos Cardinales, loscorrespondientes a cada polo reciben de ellos sunombre, Norte y Sur, los otros dos Este y Oeste.
Se corresponden con la derecha e izquierda deun observador que situado en el punto yteniendo al f rente el Norte su espalda quedase alSur.
Por convenio internacional se marcan con lasletras N, S,. E y W.
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Latitud y longitud
Latitud de un punto es la medida, en gradossexagesimales , del arco de meridianointerceptado entre el ecuador y el paralelo dellugar; hacia el Norte se considera posi tiva yhacia el Sur negativa