13.02 Voronoi diagrams
Consider the following Voronoi diagram for sites \text{A, B} and \text{C}:
What can be said about all the points in cell \text{A}?
What can be said about all the points along the edge between cell \text{A} and cell \text{B}?
What can be said about the vertex?
Consider the following Voronoi diagram:
Which site is the point (-3, 5) closest to? Explain your answer.
Verify your answer to part (a) by finding the distance between point (-3, 5) and each of the sites.
Identify the site which is closest to the following points:
Consider the following Voronoi diagram:
Show that (-3,0) is equidistant to sites \text{A} and \text{B}.
Show that (3,-1) is equidistant to sites \text{B} and \text{D}.
Show that (5,-3) is equidistant to sites \text{B}, \text{C} and \text{D}.
Show that (-3,-3) is equidistant to sites \text{A}, \text{B} and \text{C}.
Does there exist a point that is equidistant to all four sites? Explain your answer.
The following Voronoi diagram shows the locations of four schools in a city. Families are encouraged to send their children to their local (nearest) school. Each unit on the graph represents 1 \text{ km}.
Yosef's house is located at (3,0). Which school should he attend?
Ashleigh lives at (1, 4).
Which school should she attend?
Ashleigh really wants to attend School \text{C} because that is where most of her friends are going. How much further will she have to travel to attend school \text{C}, compared to her local school? Round your answer to two decimal places.
Han lives at (4, 2).
Which school should he attend?
Han and his family move 3 \text{ km} West. Which school should he attend now?
The following Voronoi diagram shows a map of towns, where each unit is a kilometre. We need to find a location for a waste dump, however none of the towns want to be near it.
Suggest a location for the waste dump somewhere on this map. Explain your choice.