Cartographic Objects Digital Images of a Map Vector Data Raster Data Model Model Vector Model vs Raster Model Vector Data Model Raster Data Model • Mapping space in a • Mapping space is plane is a continuous filled by a discrete set set of points of points called a two- dimensional lattice • The basic unit of observation • The basic unit is a corresponds to a line unit of space within a on a map mesh 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 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 Point (0-D) A zero-dimensional object that specifies an absolute location in a two- dimensional space Endpoint (0-D) A point that marks the terminus of a one- dimensional positional object. Lattice Point (0-D) A zero-dimensional object that specifies an absolute location in a tessellation of two-dimensional space Line (1-D) A locus of points that forms a nonintersecting curve in a two- dimensional space terminating at two endpoints. Outline (1-D) A line whose two endpoints have the same absolute location. Straight Line Segment (1-D) A locus of points that does not change its orientation in a two-dimensional space terminating at two endpoints. Alias: line segment String (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. Ring (1-D) A sequence of line segments that intersect once and only once at each line segment endpoint. Directed Objects (1-D) Directed 1-D objects imply movement from the start point to the Right Left terminus point. The Side Side left and right sides of a directed object is uniquely defined. Area (2-D) The interior of a continuous 2-D object (may include rings). Region (2-D) An area having one or more outer outlines and zero or more nonintersecting inner outlines. Background region (2-D) The complement to the set of all regions. Polygon (2-D) An area bounded by one outer ring and zero or more nonintersecting inner rings. Background Polygon (2-D) The complement to the set of all polygons. Pixel (2-D) A regularly shaped 2-D picture element that is the smallest nondivisible element of an image. Cell (2-D) A 2-D object that represents an element of a regular tessellation of space. The most common cells are rectangles, squares, triangles, and hexagons. Basic Analytic Geometry Because analytic geometry can describe the locus of the movement of points, it is widely used in digital cartography. Number Scale The set of all real numbers the set of all points on a number scale P -3 -2 r 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). Cartesian Coordinate System The two axes divide the + coordinate plane into four quadrants (I, II, III, Qua dra nt Quadrant II I and IV). There is a one- to-one relationship - + between the position of (0,0) a point on a plane and Qua dra nt Qua dra nt a pair of real numbers III IV as Cartesian coornidates. - Hardware Space P1 Rm The resolution of Rm + 1 P2 any computer is R2 m limited. And for R2m+ 1 the display P3 R3 m device, it is also R(n-1)m + 1 the case. Pn Rnm Vector A vector is an n-dimensional force emanating from an origin point and having a direction and a fixed length or magnitude. Some Example Vectors Y q Dire c tion p 0 X Halfplane Partition of a Plane Y Counte r c loc kwise Ha lfpla ne q Le ftha nd p Rightha nd X Component Values of a Vector Y y2 Q(x2 , y2 ) x x2 -x1 y y2 -y1 y y1 P( x1 , y1 ) (0,0) x2 x1 X X Vector Starting from Origin Y p 1 (x1 , y 1 ) p 2 (x2 , y2 ) Y1 y2 (0, 0) X X2 X1 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?