The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2020 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

We proposed a new methodology for reducing multiple types of rasterization errors to simultaneously preserve the spatial properties of area, shape, and topology in polygon-to-raster conversion. By reassigning cells of the rasterized outcome, the method first compensates for the loss in shape properties. Topological changes are then corrected by comparing the topological relations of raster regions and their corresponding polygons. Finally, the areas between pairs of neighboring regions are coordinated to maintain area properties.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2020 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. The Topological Faces / Area Landmark Relationship File (FACESAL.dbf) contains a record for each face / area landmark relationship. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The face to which a record in the Topological Faces / Area Landmark Relationship File (FACESAL.dbf) applies can be determined by linking to the Topological Faces Shapefile (FACES.shp) on the permanent topological face identifier (TFID) attribute. The area landmark to which a record in the Topological Faces / Area Landmark Relationship File (FACESAL.dbf) applies can be determined by linking to the Area Landmark Shapefile (AREALM.shp) on the area landmark identifier (AREAID) attribute. A face may be part of multiple area landmarks. An area landmark may consist of multiple faces.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. The Topological Faces / Military Installation Relationship File (FACESMIL.dbf) contains a record for each face / military installation relationship. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The face to which a record in the Topological Faces / Military Installation Relationship File (FACESMIL.dbf) applies can be determined by linking to the Topological Faces Shapefile (FACES.shp) on the permanent topological face identifier (TFID) attribute. The military installation to which a record in the Topological Faces / Military Installation Relationship File (FACESMIL.dbf) applies can be determined by linking to the Military Installation Shapefile (MIL.shp) on the military installation identifier (AREAID) attribute. A face may be part of multiple military installations. A military installation may consist of multiple faces.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for almost all geographic areas for which the Census Bureau tabulates data for both the 2010 Census and Census 2000. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2020 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for almost all geographic areas for which the Census Bureau tabulates data for both the 2010 Census and Census 2000. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2020 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for almost all geographic areas for which the Census Bureau tabulates data for both the 2010 Census and Census 2000. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for almost all geographic areas for which the Census Bureau tabulates data for both the 2010 Census and Census 2000. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2020 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2020 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2020 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2020 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2020 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2020 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2020 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2020 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2020 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.