1. Cartographic Objects Digital Images of a Map Vector Data Model Raster Data Model

2. Vector Model vs Raster Model Vector Data ModelRaster 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

3. Requirements for Definition of Digital 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

4. Definitions 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

5. Point (0-D) A zero-dimensional object that specifies an absolute location in a two- dimensional space

6. Endpoint (0-D) A point that marks the terminus of a one- dimensional positional object.

7. Lattice Point (0-D) A zero-dimensional object that specifies an absolute location in a tessellation of two-dimensional space

8. Line (1-D) A locus of points that forms a nonintersecting curve in a two- dimensional space terminating at two endpoints.

9. Outline (1-D) A line whose two endpoints have the same absolute location.

10. 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)

11. 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)

12. A sequence of line segments that intersect once and only once at each line segment endpoint. Ring (1-D)

13. 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 (1-D)

14. The interior of a continuous 2-D object (may include rings). Area (2-D)

15. An area having one or more outer outlines and zero or more nonintersecting inner outlines. Region (2-D)

16. The complement to the set of all regions. Background region (2-D)

17. An area bounded by one outer ring and zero or more nonintersecting inner rings. Polygon (2-D)

18. The complement to the set of all polygons. Background Polygon (2-D)

19. Pixel (2-D) A regularly shaped 2-D picture element that is the smallest nondivisible element of an image.

20. 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)

21. Basic Analytic Geometry Because analytic geometry can describe the locus of the movement of points, it is widely used in digital cartography.

22. Number Scale The set of all real numbers the set of all points on a number scale

23. Cartesian 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).

24. 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 System

25. Hardware Space The resolution of any computer is limited. And for the display device, it is also the case.

26. Vector A vector is an n-dimensional force emanating from an origin point and having a direction and a fixed length or magnitude.

27. Some Example Vectors

28. Halfplane Partition of a Plane

29. Component Values of a Vector

30. Vector Starting from Origin

31. Questions 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?