Finding Shortest Path in 3D Terrain

1
Finding Shortest Path in 3D Terrain

• Marcello Bastéa-Forte
• Lena Lopez
• Angie Madrid
• Marlow Weston

2
The Problem

• Lost hiker
• Location know relative to destination
• Find a way through terrain in the fastest time
• Terrain variation

3
Procedure

• Impossible to find the shortest path possible
  (time-wise) to the hikers destination
• Make estimation
• Create an algorithm using a heuristic
  path-finding algorithm
• Compare this to the optimal solution

4
Terrain Generation

• Generated various random terrains by using a
  divide and conquer algorithm
• Terrain was divided into four pieces and the five
  midpoints were randomized
• Algorithm applied the same division and
  randomization to each of the four pieces for some
  level of iterations

5
Optimal Solution

• Dijkstras Algorithm
• Finds all shortest paths from one fixed starting
  point to every point on the landscape
• Optimal solution used to calculate accuracy of
  the heuristic solution

6
Heuristic Solution

• Greedy algorithm which looks to each cell
  currently surrounding the hiker
• Determines which cell to move to based on three
  factors
• Time it takes to move to that cell
• Distance that cell is from the destination
• Number of times that cell has been visited
• Each of these factors are multiplied by a
  specific constant, which were summed up to yield
  a score

7
Optimizing Heuristic Solution

• Optimization calculates the necessary constant to
  use as a multiplier
• Optimized according to the time it takes to move
  to a cell and the distance the cell is from the
  destination
• Randomly generated 300 sets of numbers
• Ran each on a pool of 300 3d terrains, all of
  which were 25 percent water

8
Results

• No obvious correlation between distance from the
  end, time taken to move into a new cell, or a
  combination of the two
• Optimal numbers found are to weight distance
  0.469164 and to weight difficulty 0.671543

9
Results
10
Results
11
Results
12
Conclusion

• Further optimization of the heuristic by
• Changing look ahead distance
• Increasing the distance that can be seen over
  water
• Other clever adjustments