CartographiCartographic Objectsc Objects
Digital Images of a Map
Vector Data Model
Raster Data Model
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
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
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
Point (0-D)Point (0-D)
A zero-dimensional object that specifies an absolute location in a two-dimensional space
Endpoint (0-D)Endpoint (0-D)
A point that marks the terminus of a one-dimensional positional object.
Lattice Point (0-D)Lattice Point (0-D)
A zero-dimensional object that specifies an absolute location in a tessellation of two-dimensional space
Line (1-D)Line (1-D)
A locus of points that forms a nonintersecting curve in a two-dimensional space terminating at two endpoints.
Outline (1-D)Outline (1-D)
A line whose two endpoints have the same absolute location.
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)
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)
A sequence of line segments that intersect once and only once at each line segment endpoint.
Ring (1-D)Ring (1-D)
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
The interior of a continuous 2-D object (may include rings).
Area (2-D)Area (2-D)
An area having one or more outer outlines and zero or more nonintersecting inner outlines.
Region (2-D)Region (2-D)
The complement to the set of all regions.
Background region (2-D)Background region (2-D)
An area bounded by one outer ring and zero or more nonintersecting inner rings.
Polygon (2-D)Polygon (2-D)
The complement to the set of all polygons.
Background Polygon (2-D)Background Polygon (2-D)
Pixel (2-D)Pixel (2-D)A regularly shaped 2-D picture element that is the smallest nondivisible element of an image.
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)
Basic Analytic GeometryBasic Analytic Geometry
Because analytic geometry can describe the locus of the movement of points, it is widely used in digital cartography.
Number ScaleNumber Scale
The set of all real numbers
the set of all points on a number scale
P
r-2-3
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).
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
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
VectorVector
A vector is an n-dimensional force emanating from an origin point and having a direction and a fixed length or magnitude.
Some Example VectorsSome Example Vectors
Direction
p
q
X
Y
0
Halfplane Partition of a PlaneHalfplane Partition of a Plane
X
Y
CounterclockwiseHalfplane
p
q
Lefthand
Righthand
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
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
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?