Path Following

1
Path Following
2
Requirement

• Given start and goal point, find path computed by
  any path finding algorithm the result is a
  polyline
• As the performing character is orientable, the
  orientation needs to be updated along the path
• Fit Catmull-Rom spline through the polyline and
  traverse in (nearly) constant speed
• The character may detour in any frame, following
  a different path (due to the movement of goal)
• If no detour has occurred, the character stops at
  the goal point.

3
Polyline
Intermediate tangent vectors are defined as usual
Start tangent scaled first segment current
velocity for detoured segment
End tangent scaled last segment
4
Details

• (nearly) constant speed traversal
• Use cumulative chord length as the key value
• Increment the key (t), determine which Hermite
  segment it is in, compute the frame (tangent
  sufficient in this case)

5
Prototype
y
(3,2)
(4,2)
x
(-5,-2)
(2,-1)
(-2,-3)
(-7,-4)
6
(-10,5)
(-2,5)
(9,3)
3
(3,3)
0
7
(3,1.5)
(-2,1.5)
4
5
(2,-2)
(-2,-2)
1
2
6
(-10,-5)
(-2,-5)
(2,-6)
(6.5,-6)
7
to
0 1 2 3 4 5 6 7
0 0 1 1 3 3 3 3 3
1 0 1 2 0 4 4 4 4
2 1 1 2 3 4 4 4 4
3 0 0 2 3 4 4 4 4
4 3 1 2 3 4 5 5 7
5 4 4 4 4 4 5 6 7
6 4 5 5 5 5 5 6 7
7 4 4 4 4 4 5 6 7
from