//Find the neighboring nodes to a node by checking all nodes around it
private static HashSet <FlowFieldNode> FindNeighboringNodes(FlowFieldNode node, FlowFieldNode[,] nodeArray, int mapWidth, bool includeCorners)
{
HashSet <IntVector2> neighborCells = new HashSet <IntVector2>();
//Get the directions we can move in, which are up, left, right, down
IntVector2[] delta = HelpStuff.delta;
if (includeCorners)
{
delta = HelpStuff.deltaWithCorners;
}
//Will track if at least one neighbor is an obstacle, which may be useful to know later
bool isNeighborObstacle = false;
for (int i = 0; i < delta.Length; i++)
{
IntVector2 cellPos = new IntVector2(node.cellPos.x + delta[i].x, node.cellPos.z + delta[i].z);
//Is this cell position within the grid?
if (IsCellPosWithinGrid(cellPos, mapWidth))
{
//Is not a valid neighbor if its obstacle
if (!nodeArray[cellPos.x, cellPos.z].isWalkable)
{
isNeighborObstacle = true;
}
else
{
neighborCells.Add(cellPos);
}
}
}
//If we are checking 8 neighbors we have to be careful to not jump diagonally if one cell next to the diagonal is obstacle
//This is a costly operation (0.3 seconds if we do it for all cells) so only do it if at least one neighbor is obstacle
if (includeCorners && isNeighborObstacle)
{
HashSet <IntVector2> corners = new HashSet <IntVector2>(HelpStuff.deltaJustCorners);
//Loop through all 8 neighbors
for (int i = 0; i < delta.Length; i++)
{
//Is this neighbor a corner?
if (corners.Contains(delta[i]))
{
IntVector2 cellPos = new IntVector2(node.cellPos.x + delta[i].x, node.cellPos.z + delta[i].z);
//Have we added the corner to the list of neighbors
if (!neighborCells.Contains(cellPos))
{
continue;
}
//Check if neighbors to the corner are obstacles, if so we cant move to this corner
IntVector2 n1 = delta[HelpStuff.ClampListIndex(i + 1, delta.Length)];
IntVector2 n2 = delta[HelpStuff.ClampListIndex(i - 1, delta.Length)];
IntVector2 cellPos_n1 = new IntVector2(node.cellPos.x + n1.x, node.cellPos.z + n1.z);
IntVector2 cellPos_n2 = new IntVector2(node.cellPos.x + n2.x, node.cellPos.z + n2.z);
if (!nodeArray[cellPos_n1.x, cellPos_n1.z].isWalkable || !nodeArray[cellPos_n2.x, cellPos_n2.z].isWalkable)
{
//This is not a valid neighbor so remove it from neighbors
neighborCells.Remove(cellPos);
}
}
}
}
//From cell to node
HashSet <FlowFieldNode> neighborNodes = new HashSet <FlowFieldNode>();
foreach (IntVector2 cell in neighborCells)
{
neighborNodes.Add(nodeArray[cell.x, cell.z]);
}
return(neighborNodes);
}
//Smooth a path with batch gradient descent (x = x - gamma * grad(x))
//https://www.youtube.com/watch?v=umAeJ7LMCfU
public static void GradientDescent(
List <Vector3> path,
List <bool> isNodeFixed,
List <Obstacle> obstacles,
Map map,
bool isCircular,
float alpha, float beta, float gamma, float delta,
bool isDebugOn)
{
//Using map.VoronoiField is slow in each iteration, so should cache
VoronoiFieldCell[,] voronoiField = null;
if (map != null && map.VoronoiField != null)
{
voronoiField = map.VoronoiField;
}
//The list with smooth coordinates
List <Vector3> smoothPath = new List <Vector3>();
//Add the old positions
for (int i = 0; i < path.Count; i++)
{
smoothPath.Add(path[i]);
}
//Stop smoothing when all points have moved a distance less than this distance
//If 0.00001 we need more than 1000 iterations
float tolerance = 0.001f;
//How far has all points together moved this iteration?
//We are comparing the distance sqr instead of magnitude which is faster
float totalChangeSqr = tolerance * tolerance;
//So we dont end up in an infinite loop, is generally < 100
int iterations = 0;
//If we find a nan value its super slow to print that we did each iteration, so we do it once in the end
bool hasFoundNan = false;
while (totalChangeSqr >= tolerance * tolerance)
{
if (iterations > 1000)
{
break;
}
iterations += 1;
totalChangeSqr = 0f;
//We are using surrounding values, so we need an array where we add values found during the iteration
List <Vector3> newValuesThisIteration = new List <Vector3>(smoothPath.Count);
for (int i = 0; i < path.Count; i++)
{
//Dont move nodes that are fixed
if (isNodeFixed[i])
{
newValuesThisIteration.Add(smoothPath[i]);
continue;
}
//Clamp when we reach end and beginning of list
//The first and last node should be set to fixed if the path is not set to circular
int i_plus_one = HelpStuff.ClampListIndex(i + 1, path.Count);
int i_minus_one = HelpStuff.ClampListIndex(i - 1, path.Count);
//Smooth!
//1. Minimize the distance between the smooth path and the original path
Vector3 newSmoothPos = smoothPath[i] + alpha * (path[i] - smoothPath[i]);
//2. Minimize the distance between this position and the surrounding positions
newSmoothPos += beta * (smoothPath[i_plus_one] + smoothPath[i_minus_one] - 2f * smoothPath[i]);
//3. Maximize the distance to the closest obstacle
//Is sometimes unstable because we use the closest obstacle, so is bouncing back and forth
//until the loop stops because of infinite check
//if (obstacles != null)
//{
// Vector3 closestObstaclePos = FindClosestObstaclePos(smoothPath[i], obstacles);
// Vector3 dirToObstacle = closestObstaclePos - smoothPath[i];
// //Ignore obstacles far away
// float maxDist = 10f;
// if (dirToObstacle.sqrMagnitude < maxDist * maxDist)
// {
// float distanceToObstacle = dirToObstacle.magnitude;
// //To make obstacles closer more important
// float scaler = 1f - (distanceToObstacle / maxDist);
// newSmoothPos -= gamma * dirToObstacle.normalized * scaler;
// }
//}
//We can also use the voronoi field to find the closest obstacle
if (voronoiField != null && gamma > 0f)
{
Vector3 nodePos = smoothPath[i];
//Get the data for this cell
IntVector2 cellPos = map.ConvertWorldToCell(nodePos);
//The data for this cell
VoronoiFieldCell v = voronoiField[cellPos.x, cellPos.z];
Vector3 closestObstaclePos = v.ClosestObstaclePos(nodePos, voronoiField);
if (closestObstaclePos.x != -1f)
{
Vector3 dirToObstacle = closestObstaclePos - nodePos;
//Ignore obstacles far away
float maxDist = 10f;
if (dirToObstacle.sqrMagnitude < maxDist * maxDist)
{
float distanceToObstacle = dirToObstacle.magnitude;
//To make obstacles closer more important
float scaler = 1f - (distanceToObstacle / maxDist);
newSmoothPos -= gamma * dirToObstacle.normalized * scaler;
}
}
}
//4. Use the Voronoi field to push vertices away from obstacles
//We need to find the derivative of the voronoi field function with respect to:
//- distance to obstacle edge - should be maximized
//- distance to voronoi edge - should be minimized
//...to optimize the distance to both edges
//This is kinda slow and useless since we are already pushing away the path from obstacles above?
if (voronoiField != null && delta > 0f)
{
Vector3 nodePos = smoothPath[i];
//Get the data for this cell
IntVector2 cellPos = map.ConvertWorldToCell(nodePos);
//The data for this cell
VoronoiFieldCell v = voronoiField[cellPos.x, cellPos.z];
//Same each iteration
float d_max = v.d_obs_max;
float a = v.alpha;
Vector3 closestObstaclePos = v.ClosestObstaclePos(nodePos, voronoiField);
Vector3 closestEdgePos = v.ClosestEdgePos(nodePos, voronoiField);
//If we are inside an obstacle when debugging, we wont have a closest
if (closestObstaclePos.x != -1f && closestEdgePos.x != -1f)
{
//The directions
Vector3 dirToObstacle = closestObstaclePos - nodePos;
Vector3 dirToEdge = closestEdgePos - nodePos;
//The distances
float d_obs = dirToObstacle.magnitude;
float d_edg = dirToEdge.magnitude;
//The distance to voronoi edge
float upper_edge = a * d_obs * (d_obs - d_max) * (d_obs - d_max);
float lower_edge = d_max * d_max * (d_obs + a) * (d_edg + d_obs) * (d_edg + d_obs);
newSmoothPos -= delta * (upper_edge / lower_edge) * (-dirToEdge / d_edg);
//The distance to voronoi obstacle
float upper_obs = a * d_edg * (d_obs - d_max) * ((d_edg + 2f * d_max + a) * d_obs + (d_max + 2f * a) + a * d_max);
float lower_obs = d_max * d_max * (d_obs + a) * (d_obs + a) * (d_obs + d_edg) * (d_obs + d_edg);
newSmoothPos += delta * (upper_obs / lower_obs) * (dirToObstacle / d_obs);
}
}
//Sometimes the algorithm is unstable and shoots the vertices far away
//Maybe better to check for Nan in each part, so if the pos is NaN after optimizing to obstacle, dont add it???
if (float.IsNaN(newSmoothPos.x) || float.IsNaN(newSmoothPos.x) || float.IsNaN(newSmoothPos.x))
{
newSmoothPos = smoothPath[i];
hasFoundNan = true;
}
//Check if the new pos is within the map and if it is a value
if (map != null && !map.IsPosWithinGrid(newSmoothPos))
{
newSmoothPos = smoothPath[i];
}
//How far did we move the position this update?
totalChangeSqr += (newSmoothPos - smoothPath[i]).sqrMagnitude;
newValuesThisIteration.Add(newSmoothPos);
}
//Add the new values we created this iteration
for (int i = 0; i < smoothPath.Count; i++)
{
smoothPath[i] = newValuesThisIteration[i];
}
}
if (isDebugOn)
{
string debugText = DisplayController.GetDisplayText("Smooth path iterations", iterations, null);
Debug.Log(debugText);
}
if (hasFoundNan)
{
Debug.Log("Found Nan value");
}
//Add the new smooth positions to the original waypoints
for (int i = 0; i < path.Count; i++)
{
path[i] = smoothPath[i];
}
}