private static void DropSedimentFromKernel(Field2d <float> field, IField2d <float> kernel, int centerX, int centerY, float targetSediment)
{
for (int y = 0; y < kernel.Height; y++)
{
for (int x = 0; x < kernel.Width; x++)
{
int cX = centerX + x - kernel.Width / 2;
int cY = centerY + y - kernel.Height / 2;
if (cX >= 0 && cY >= 0 && cX < field.Width && cY < field.Height)
{
field[cY, cX] += targetSediment * kernel[y, x];
}
}
}
}
public IField2d <T> RenderToField()
{
Field2d <T> output = new Field2d <T>(new Common.ConstantField <T>(this.Width, this.Height, default(T)));
foreach (var chunk in this.chunks)
{
for (int y = 0; y < chunk.Field.Height; y++)
{
for (int x = 0; x < chunk.Field.Width; x++)
{
output[y + chunk.MinPoint.Y, x + chunk.MinPoint.X] = chunk.Field[y, x];
}
}
}
return(output);
}
// TODO: Don't allow the field to erode below zero.
// TODO: Here, at last, is the source of the insane bug. The way this bug works is easiest to understand
// if one envisions a kernel of small radius and a "trough" consisting of two elevated walls and a lower
// middle. The nature of a trough is that a particle can become "trapped" in one, rolling back and forth
// as each wall turns the particle back. If a trough is narrow enough that a particle dropping sediment in
// the middle will also drop sediment on both walls by virtue of its kernel, then oscillation in the trough
// can cause the particle to "build towers." This happens because when the particle is picking up sediment--
// i.e., when it's beginning to go down-hill--its kernel covers part of the trough and a little bit outside;
// however, when the particle is depositing sediment--i.e., when it's beginning to go uphill--its kernel is
// entirely over the trough. By repeated action, this allows the particle to "dig" sediment from just outside
// the walls of its trough and bring that sediment back into the trough, creating the extremely
// characteristic "bars" of high and low elevation in extremely close proximity. The solution to this,
// presumably, is to prevent this "digging" behavior, presumably by taking sediment in a more cautious
// manner that won't allow erosion computed from a high place to induce the removal of sediment from a low
// place.
private static void PickUpSedimentFromKernel(Field2d <float> field, IField2d <float> kernel, int centerX, int centerY, float targetSediment)
{
if (targetSediment == 0)
{
return;
}
float targetMin = field[centerY, centerX] - kernel[kernel.Height / 2, kernel.Width / 2] * targetSediment;
float collected = 0f;
for (int y = 0; y < kernel.Height; y++)
{
for (int x = 0; x < kernel.Width; x++)
{
int cX = centerX + x - kernel.Width / 2;
int cY = centerY + y - kernel.Height / 2;
if (cX >= 0 && cY >= 0 && cX < field.Width && cY < field.Height && field[cY, cX] >= targetMin)
{
collected += targetSediment * kernel[y, x];
}
}
}
float scalar = targetSediment / collected;
for (int y = 0; y < kernel.Height; y++)
{
for (int x = 0; x < kernel.Width; x++)
{
int cX = centerX + x - kernel.Width / 2;
int cY = centerY + y - kernel.Height / 2;
if (cX >= 0 && cY >= 0 && cX < field.Width && cY < field.Height && field[cY, cX] >= targetMin)
{
field[cY, cX] -= targetSediment * kernel[y, x] * scalar;
}
}
}
}
// Based on the approach by Hans Theobald Beyer, "Implementation of a method for hydraulic erosion," 2015
public static Field2d <float> DropletHydraulic(IField2d <float> inputHeightmap, int numDroplets, int iterationsPerDrop, float minSlope = 0f, float maxHeight = 1f, int radius = 0)
{
Random random = new Random();
float pFriction = 0.3f;
float pCapacity = 1f;
float pErode = 0.3f;
float pDeposit = 0.3f;
float pGravity = 0.8f / maxHeight;
float pEvaporate = 0.01f;
const int STARTING_DIRECTION_GRANULARITY = 32;
var kernel = GetKernel(radius);
Field2d <float> heightmap = new Field2d <float>(inputHeightmap);
for (int idx = 0; idx < numDroplets; idx++)
{
Droplet droplet = new Droplet()
{
Position = new vFloat(random.Next(heightmap.Width), random.Next(heightmap.Height)),
Direction = new vFloat(random.Next(STARTING_DIRECTION_GRANULARITY) - STARTING_DIRECTION_GRANULARITY / 2,
random.Next(STARTING_DIRECTION_GRANULARITY) - STARTING_DIRECTION_GRANULARITY / 2).norm(),
Speed = 0,
Water = 1,
Sediment = 0,
};
for (int iteration = 0; iteration < iterationsPerDrop; iteration++)
{
(int x, int y)oldPos = ((int)droplet.Position[0], (int)droplet.Position[1]);
float oldHeight = heightmap[oldPos.y, oldPos.x];
var gradient = heightmap.GradientAtPoint(droplet.Position);
droplet.Direction = (droplet.Direction + gradient) * (1 - pFriction);
if (droplet.Direction.magSq() > 0)
{
droplet.Position += droplet.Direction.norm();
}
if (droplet.Position[0] < 0f || droplet.Position[1] < 0f ||
droplet.Position[0] >= heightmap.Width || droplet.Position[1] >= heightmap.Height)
{
break;
}
(int x, int y)newPos = ((int)droplet.Position[0], (int)droplet.Position[1]);
float newHeight = heightmap[newPos.y, newPos.x];
if (newHeight > oldHeight)
{
float droppedSediment = Math.Min(newHeight - oldHeight, droplet.Sediment);
DropSedimentFromKernel(heightmap, kernel, oldPos.x, oldPos.y, droppedSediment);
droplet.Sediment -= droppedSediment;
}
else if (newHeight < oldHeight)
{
float capacity = Math.Max(oldHeight - newHeight, minSlope) * droplet.Speed * droplet.Water * pCapacity;
if (droplet.Sediment > capacity)
{
float droppedSediment = (droplet.Sediment - capacity) * pDeposit;
DropSedimentFromKernel(heightmap, kernel, oldPos.x, oldPos.y, droppedSediment);
droplet.Sediment -= droppedSediment;
}
else
{
float pickedUpSediment = Math.Min((capacity - droplet.Sediment) * pErode, oldHeight - newHeight);
PickUpSedimentFromKernel(heightmap, kernel, oldPos.x, oldPos.y, pickedUpSediment);
droplet.Sediment += pickedUpSediment;
}
}
// This is from the paper, but it's super weird. So, the drops will pick up speed even if they go uphill?
// I think speed is the wrong term for this variable. In fact, this whole concept is very magical. Speed should
// be determined by the magnitude of the velocity, not by some random accumulator. On the other hand, I tried
// that, and this works way better. So...
droplet.Speed = (float)Math.Sqrt(droplet.Speed * droplet.Speed + Math.Abs(newHeight - oldHeight) * pGravity);
droplet.Water = droplet.Water * (1 - pEvaporate);
}
}
return(heightmap);
}
public static List <Point2d> FindPath(Rectangle area, Point2d from, Point2d to, Func <Point2d, Point2d, float> getCostOfStep = null, Func <Point2d, Point2d, float> estimateCostOfStep = null)
{
getCostOfStep = getCostOfStep ?? Point2d.Distance;
estimateCostOfStep = estimateCostOfStep ?? Point2d.Distance;
Field2d <float> visited = new Field2d <float>(new ConstantField <float>(area.Width, area.Height, float.NaN));
visited[from.y, from.x] = 0f;
BinaryHeap <CostedPoint> toVisit = new BinaryHeap <CostedPoint>();
toVisit.Push(new CostedPoint()
{
point = from, cost = visited[from.y, from.x] + estimateCostOfStep(from, to)
});
Field2d <Point2d> cameFrom = new Field2d <Point2d>(new ConstantField <Point2d>(area.Width, area.Height, new Point2d(-1, -1)));
cameFrom[from.y, from.x] = from;
while (toVisit.Count > 0)
{
var curr = toVisit.Pop().point;
for (int j = -1; j <= 1; j++)
{
for (int i = -1; i <= 1; i++)
{
if (i == 0 && j == 0)
{
continue;
}
Point2d next = new Point2d(curr.x + i, curr.y + j);
if (next.x <= area.Left || next.x >= area.Right || next.y <= area.Top || next.y >= area.Bottom)
{
continue;
}
if (next == to)
{
List <Point2d> path = new List <Point2d>();
path.Add(next);
path.Add(curr);
Point2d it = curr;
while (cameFrom[it.y, it.x] != it)
{
it = cameFrom[it.y, it.x];
path.Add(it);
}
path.Reverse();
return(path);
}
float cost = visited[curr.y, curr.x] + getCostOfStep(curr, next);
if (float.IsNaN(visited[next.y, next.x]) || visited[next.y, next.x] > cost)
{
visited[next.y, next.x] = cost;
cameFrom[next.y, next.x] = curr;
toVisit.Push(new CostedPoint()
{
point = next, cost = cost + estimateCostOfStep(next, to)
});
}
}
}
}
return(null);
}