cartographic objects digital images of a map vector data model raster data model
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CartographiCartographic Objectsc Objects
Digital Images of a Map
Vector Data Model
Raster Data Model
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Vector Model vs Raster ModelVector Model vs Raster Model
Vector Data Model Raster Data Model
• Mapping space in a plane is a continuous set of points
• The basic unit of observation corresponds to a line on a map
• Mapping space is filled by a discrete set of points called a two-dimensional lattice
• The basic unit is a unit of space within a mesh
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Requirements for Definition of Requirements for Definition of Digital Cartographic ObjectsDigital Cartographic Objects
• Can combine the spatial properties of absolute location and relative location
• Must be modular so that lower dimensional objects can be used to define higher dimensional objects
• Can be studied in planar, hyperbolic and elliptic geometry
• Must be expandable at a later date
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Definitions from NCDCDSDefinitions from NCDCDS• Zero-Dimensional Objects
- Point, Endpoint, Lattice Point• One-Dimensional Objects
- Line, Outline, Straight Line Segment, String, Ring
• Two-Dimensional Objects
- Area, Region, Background Region, Polygon, Background Polygon, Pixel, Cell
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Point (0-D)Point (0-D)
A zero-dimensional object that specifies an absolute location in a two-dimensional space
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Endpoint (0-D)Endpoint (0-D)
A point that marks the terminus of a one-dimensional positional object.
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Lattice Point (0-D)Lattice Point (0-D)
A zero-dimensional object that specifies an absolute location in a tessellation of two-dimensional space
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Line (1-D)Line (1-D)
A locus of points that forms a nonintersecting curve in a two-dimensional space terminating at two endpoints.
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Outline (1-D)Outline (1-D)
A line whose two endpoints have the same absolute location.
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A locus of points that does not change its orientation in a two-dimensional space terminating at two endpoints.
Alias: line segment
Straight Line Segment (1-D)Straight Line Segment (1-D)
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A sequence of line segments that intersect once and only once at each line segment endpoint excluding two segment endpoints that form the endpoints of the string.
String (1-D)String (1-D)
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A sequence of line segments that intersect once and only once at each line segment endpoint.
Ring (1-D)Ring (1-D)
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Directed 1-D objects imply movement from the start point to the terminus point. The left and right sides of a directed object is uniquely defined.
Directed Objects Directed Objects (1-D)(1-D)
Left Side
Right Side
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The interior of a continuous 2-D object (may include rings).
Area (2-D)Area (2-D)
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An area having one or more outer outlines and zero or more nonintersecting inner outlines.
Region (2-D)Region (2-D)
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The complement to the set of all regions.
Background region (2-D)Background region (2-D)
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An area bounded by one outer ring and zero or more nonintersecting inner rings.
Polygon (2-D)Polygon (2-D)
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The complement to the set of all polygons.
Background Polygon (2-D)Background Polygon (2-D)
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Pixel (2-D)Pixel (2-D)A regularly shaped 2-D picture element that is the smallest nondivisible element of an image.
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A 2-D object that represents an element of a regular tessellation of space. The most common cells are rectangles, squares, triangles, and hexagons.
Cell (2-D)Cell (2-D)
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Basic Analytic GeometryBasic Analytic Geometry
Because analytic geometry can describe the locus of the movement of points, it is widely used in digital cartography.
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Number ScaleNumber Scale
The set of all real numbers
the set of all points on a number scale
P
r-2-3
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Cartesian CoordinatesCartesian Coordinates
If two number scales are drawn at a right angle with respect to each other, these number scales are called coordinate axes – one for X-axis and another for Y-axis. Any point on a 2-D plane has Cartesian coordinates (x,y).
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The two axes divide the coordinate plane into four quadrants (I, II, III, and IV). There is a one-to-one relationship between the position of a point on a plane and a pair of real numbers as Cartesian coornidates.
Cartesian Coordinate SystemCartesian Coordinate System
+-
+
-
(0,0)
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
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Hardware SpaceHardware Space
The resolution of
any computer is
limited. And for
the display
device, it is also
the case.
Rm
Rm+1
R2m
R2m+1
R3m
R(n-1)m+1
Rnm
P1
P2
P3
Pn
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VectorVector
A vector is an n-dimensional force emanating from an origin point and having a direction and a fixed length or magnitude.
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Some Example VectorsSome Example Vectors
Direction
p
q
X
Y
0
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Halfplane Partition of a PlaneHalfplane Partition of a Plane
X
Y
CounterclockwiseHalfplane
p
q
Lefthand
Righthand
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Component Values of a VectorComponent Values of a Vector
x
y
x -x2 1
y -y2 1
X
Y
(0,0) x1x2
X
y1
y2
y
P x y( , )1 1
Q(x , y )2 2
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Vector Starting from OriginVector Starting from Origin
X
Y
(0, 0)
X1
Y1
X2
y2
p (x , y )1 1 1
p (x , y )2 2 2
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Questions for ReviewQuestions for Review• How many basic data models are there to represent
the digital images on a map?(a vector and raster data model )
• According to NCDCDS, which objects belong to the 0-D objects?
• Which objects belong to the 1-D objects?• Which objects belong to the 2-D objects?• Can you explain the incorrespondency between the
real numbers and the positions of the points in the hardware space?