1. COMP261 Lecture 4
Graphs 3 of 3

2. Outline Graph display Different coordinate systems Location class
Redraw graph under movements

3. Program Summary Load the files Store the information into a graph
Roads: roadID-roadInfo.tab
Nodes: nodeID-lat-lon.tab
Road segments: roadSeg-roadID-length-nodeID-nodeID-coords.tab
Store the information into a graph
Data structure needed
Display (part of) the graph in the drawing area
Redraw the graph after movements (e.g. left, right, zoom in/out)

4. Display Graph

5. Display Graph Important parameters Size of the drawing area
Location of the drawing area
Scale of the drawn graph (zoom in/out)
Different coordinate systems
Drawing area: 800x800 pixels
Locations in graph: latitude/longitude, x/y kms, …
Transformation
Graph area ↔ Drawing area
Use origin location + scale

6. Location vs Pixels. ORIGIN: pixel coordinates: 0, 0 location:,
SCALE:
800 pixels
97.5 km

7. Location Class Provided to help display
Three representations of a location/place/point
latitude/longitude
Absolute location on a sphere
This is what is in the data
Location fields: x/y in kilometers
Relative location to Aukland center
x kms to the east, y kms to the north
Assume Auckland region is a flat plane (not quite true, but good enough)
This is what you need for finding shortest paths
Point (x/y in pixels): pixel coordinates
for drawing points and lines
mouse click positions
y (north)
AukCenter
x (east)

8. Location Class Read lat/lon from data
Transform to x/y kms and store in the object
Formula already provided in the class
For display, transform x/y kms to pixel coordinates
Current origin and scale
Look at the Location.java

9. Display Graph
public void drawLocations(Graph g, Location origin, double scale) {
for each location in g:
Point pt = location.asPoint(origin, scale);
drawPoint(pt); }
public Point asPoint(Location origin, double scale) {
int u = (int) ((x - origin.x) * scale);
int v = (int) ((origin.y - y) * scale);
return new Point(u, v);

10. Redraw Graph Under Movements
public Point asPoint(Location origin, double scale) {
int u = (int) ((x - origin.x) * scale);
int v = (int) ((origin.y - y) * scale);
return new Point(u, v); }
Drawing requires transforming from x/y kms or lat/lon to pixel coordinates
Depends on origin and scale
Move left/right/up/down change origin
Zoom in/out change both origin and scale
How to adjust origin?

11. Redraw Graph Under Movements
Zoom in/out from the current center
Zoom in: zoom < 1
Zoom out: zoom > 1
dy = (height – height * zoom) / 2
old origin
new origin
dx = (width – width * zoom) / 2
width * zoom
height
width
New origin = (origin.x + dx, origin.y + dy)

12. Redraw Graph Under Movements
Notice: use the same coordinate system for all the calculations
x/y kms
Need to get xmin, xmax, ymin, ymax
Pixel coordinates
Need to transform back from Point to Location
See the method
newFromPoint(Point point, Location origin, double scale)
in Location.java

13. Redraw Graph Under Movements
Using the x/y kms Get the pixel width and height of the drawing area vertices ← {(0,0), (0,height), (width, 0), (width, height)} for i = 0 to 3: loc[i] ← Location.newFromPoint(vertices[i], origin, scale) locWidth ← loc[2].x – loc[0].x locHeight ← loc[1].y – loc[0].y dx ← (locWidth – locWidth * zoom) / 2 dy ← (locHeight – locHeight * zoom) / 2 newOrigin.x ← origin.x + dx newOrigin.y ← origin.y + dy

14. Redraw Graph Under Movements
Using pixel coordinates directly?
How about zoom out?

15. Summary of Display Load the Road, Node, Segment files
Use Location object to represent the locations of the nodes and segments
Convert lat/lon to x/y kms in the objects
Store into a graph object
Use data structures discussed before
Set proper initial origin location and scale (e.g. 1)
Auto-display the loaded graph using the origin and scale
Under any movement
Recalculate the origin and scale (depending on movement)
Redraw the graph using the new origin and scale