float DistanceToEdgeSquared(TectonicEdge edge, ivec2 position)
{
vec2 v = new vec2(edge.A.x, edge.A.y);
vec2 w = new vec2(edge.B.x, edge.B.y);
vec2 p = new vec2(position.x, position.y);
// Return minimum distance between line segment vw and point p
float l2 = (v - w).LengthSqr; // i.e. |w-v|^2 - avoid a sqrt
if (l2 == 0f)
{
return((p - v).LengthSqr); // v == w case
}
// Consider the line extending the segment, parameterized as v + t (w - v).
// We find projection of point p onto the line.
// It falls where t = [(p-v) . (w-v)] / |w-v|^2
float t = glm.Dot(p - v, w - v) / l2;
if (t < 0)
{
return((p - v).LengthSqr); // Beyond the 'v' end of the segment
}
else if (t > 1)
{
return((p - w).LengthSqr); // Beyond the 'w' end of the segment
}
vec2 projection = v + t * (w - v); // Projection falls on the segment
return((p - projection).LengthSqr);
}
void drawLine(TectonicEdge edge, MapPixel[,] map)
{
int x0 = edge.A.x;
int y0 = edge.A.y;
int x1 = edge.B.x;
int y1 = edge.B.y;
int dx = Math.Abs(x1 - x0), sx = x0 < x1 ? 1 : -1;
int dy = -Math.Abs(y1 - y0), sy = y0 < y1 ? 1 : -1;
int err = dx + dy, e2; // error value e_xy
if (dx > map.GetLength(0) * 4 || dy > map.GetLength(1) * 4)
{
//TODO: Investigate broken edge coordinates
return;
}
for (; ;)
{
if (x0 >= 0 && x0 < MapSize.x &&
y0 >= 0 && y0 < MapSize.y)
{
map[x0, y0].Edges.Add(edge);
map[x0, y0].Plate = edge.LeftPlate;
}
if (x0 == x1 && y0 == y1)
{
break;
}
e2 = 2 * err;
// horizontal step?
if (e2 > dy)
{
err += dy;
x0 += sx;
}
else if (e2 < dx)
{
err += dx;
y0 += sy;
}
}
}
// Create a basic set of
public List <TectonicPlate> GeneratePlates()
{
// Spawn some random cell centers within a grid.
// Add one row and column outside of the map so no cells inside the map are border cells.
List <TectonicPlate> plates = new List <TectonicPlate>();
for (int left = -PlateSize; left < MapSize.x + PlateSize; left += PlateSize)
{
for (int bottom = -PlateSize; bottom < MapSize.y + PlateSize; bottom += PlateSize)
{
int right = left + PlateSize;
int top = bottom + PlateSize;
plates.Add(new TectonicPlate
{
Center = new ivec2(rand.Next(left, right), rand.Next(bottom, top)),
AngularVelocity = (float)rand.NextDouble() * maxPlateAngluarVelocity,
LinearVelocity = new vec2((float)rand.NextDouble() * maxPlateLinearVelocity, (float)rand.NextDouble() * maxPlateLinearVelocity),
BaseHeight = (float)rand.NextDouble() + 1f
});
}
}
// Compute voronoi triangulation for plate edges
var plateVectors = new Dictionary <Vector, TectonicPlate>();
foreach (var tectonicPlate in plates)
{
var center = new Vector(tectonicPlate.Center.x, tectonicPlate.Center.y);
plateVectors[center] = tectonicPlate;
}
VoronoiGraph graph = Fortune.ComputeVoronoiGraph(plateVectors.Keys);
foreach (var edge in graph.Edges)
{
ivec2 a = new ivec2((int)edge.VVertexA[0], (int)edge.VVertexA[1]);
ivec2 b = new ivec2((int)edge.VVertexB[0], (int)edge.VVertexB[1]);
// Ignore edges into infinity. We generate cells outside of the map so we have only finite edges in the mep
if (a.x == Int32.MaxValue || a.x == Int32.MinValue ||
a.y == Int32.MaxValue || a.y == Int32.MinValue ||
b.x == Int32.MaxValue || b.x == Int32.MinValue ||
b.y == Int32.MaxValue || b.y == Int32.MinValue)
{
continue;
}
a.x = Math.Min(Math.Max(-200, a.x), MapSize.x + 200);
a.y = Math.Min(Math.Max(-200, a.y), MapSize.y + 200);
b.x = Math.Min(Math.Max(-200, b.x), MapSize.x + 200);
b.y = Math.Min(Math.Max(-200, b.y), MapSize.y + 200);
// left and right cells of the edges given by the fortune voronoi implementation are incorrect, compute the correct cells again
ivec2 middle = (a + b) / 2;
// Find the two plate centers closest to the edge middle point
List <TectonicPlate> neighborCells = new List <TectonicPlate>();
neighborCells.AddRange(plates.OrderBy(p => (p.Center - middle).Length).Take(2));
TectonicPlate left = neighborCells[0];
TectonicPlate right = neighborCells[1];
// left/right correct?
if (EdgeAngle(neighborCells[0].Center, a, b) > 0)
{
right = neighborCells[0];
left = neighborCells[1];
}
float mountainFactor = rand.NextFloat(-1f, 1f);
var tectonicEdge = new TectonicEdge {
A = a, B = b, LeftPlate = left, RightPlate = right, MountainFactor = mountainFactor
};
left.Edges.Add(tectonicEdge);
right.Edges.Add(tectonicEdge);
}
SavePlateImage(plates, "plates.svg");
return(plates);
}
MapPixel[,] GenerateHeightMap(List <TectonicPlate> plates, float progressMin, float progressMax)
{
var map = new MapPixel[MapSize.x, MapSize.y];
UpdateGenerationInfo("Initialize with random heightmap");
for (int x = 0; x < MapSize.x; x++)
{
for (int y = 0; y < MapSize.y; y++)
{
map[x, y] = new MapPixel();
map[x, y].Height = 0.5f + 0.5f * SimplexNoise.RecursiveNoise.Noise2D(x / 200f, y / 200f, 8);
}
}
var drawnEdges = new HashSet <TectonicEdge>();
UpdateGenerationInfo("Initializing tectonic edges");
// Initialize the edges and plate centers
foreach (var tectonicPlate in plates)
{
foreach (var edge in tectonicPlate.Edges)
{
if (drawnEdges.Contains(edge))
{
continue;
}
drawLine(edge, map);
drawnEdges.Add(edge);
}
int x = tectonicPlate.Center.x;
int y = tectonicPlate.Center.y;
if (x >= 0 && x < MapSize.x &&
y >= 0 && y < MapSize.y)
{
map[x, y].Plate = tectonicPlate;
}
}
UpdateGenerationInfo("Computing tectonic surface");
// Flood fill from the plate centers
bool done = false;
for (int i = 1; !done; i++)
{
done = true;
for (int x = 0; x < MapSize.x; x++)
{
for (int y = 0; y < MapSize.y; y++)
{
// Found a pixel without a Plate assigned?
MapPixel p = map[x, y];
if (p.Plate == null)
{
TryFillPixel(map, new ivec2(x, y));
if (p.Plate != null)
{
done = false;
}
}
}
}
for (int x = MapSize.x - 1; x > 0; x--)
{
for (int y = MapSize.y - 1; y > 0; y--)
{
// Found a pixel without a Plate assigned?
MapPixel p = map[x, y];
if (p.Plate == null)
{
TryFillPixel(map, new ivec2(x, y));
if (p.Plate != null)
{
done = false;
}
}
}
}
}
UpdateProgress(progressMin + (progressMax - progressMin) * 0.5f);
// Find missing plates
UpdateGenerationInfo("Find unused tectonic plates");
List <TectonicPlate> missingPlates = FindUnusedPlates(map, plates);
// Set height values depending on the base heights of the plates and the
UpdateGenerationInfo("Set base height of terrain");
Parallel.For(0, MapSize.x, x =>
{
for (int y = 0; y < MapSize.y; y++)
{
var p = map[x, y];
TectonicEdge bestEdge = null;
float bestDistance = Math.Max(MapSize.x, MapSize.y);
float baseHeight = -1f;
if (p.Plate != null)
{
baseHeight = p.Plate.BaseHeight;
foreach (var edge in p.Plate.Edges)
{
if (!missingPlates.Contains(edge.LeftPlate) &&
!missingPlates.Contains(edge.RightPlate))
{
float dist = DistanceToEdgeSquared(edge, new ivec2(x, y));
if (dist < bestDistance)
{
bestDistance = dist;
bestEdge = edge;
}
}
}
}
float tectonicHeight = 0f;
if (bestEdge != null)
{
tectonicHeight = bestEdge.MountainFactor * 3f * (1f / ((float)Math.Pow(1.2f + 0.02f * bestDistance, 2))) *
(1f + SimplexNoise.RecursiveNoise.Noise2D(250f - x / 200f, 250f - y / 200f, 10));
}
float noise = SimplexNoise.RecursiveNoise.Noise2D(x / 100f, y / 100f, 8);
p.Height = baseHeight + tectonicHeight + noise;
}
});
UpdateProgress(progressMax);
return(map);
}
List <TectonicEdge> SplitTectonicEdge(TectonicEdge edge, TectonicEdge originalEdge, int depth)
{
var subEdges = new List <TectonicEdge>();
vec2 a = new vec2(edge.A.x, edge.A.y);
vec2 b = new vec2(edge.B.x, edge.B.y);
// Randomly move on an axis perpendicular to the original voronoi edge
// vector of original edge line
vec2 edgeVector = new vec2(originalEdge.A.x - originalEdge.B.x, originalEdge.A.y - originalEdge.B.y);
// vectors between left/right plate centers and original.A
vec2 leftCenterToA = new vec2(edge.A.x - edge.LeftPlate.Center.x, edge.A.y - edge.LeftPlate.Center.y);
vec2 rightCenterToA = new vec2(edge.A.x - edge.RightPlate.Center.x, edge.A.y - edge.RightPlate.Center.y);
// project centers to origVector
float projectedCenterLeft = (glm.Dot(edgeVector, leftCenterToA) / leftCenterToA.LengthSqr);
float projectedCenterRight = (glm.Dot(edgeVector, rightCenterToA) / rightCenterToA.LengthSqr);
vec2 movementAxis = new vec2(-edgeVector.y, edgeVector.x);
movementAxis = movementAxis.Normalized;
float shift = rand.NextFloat(0.1f, 0.9f);
vec2 vMid = shift * a + (1f - shift) * b;
vMid += movementAxis * rand.NextFloat(0f, depth * depth);
ivec2 middle = new ivec2((int)vMid.x, (int)vMid.y);
TectonicEdge subEdge1 = new TectonicEdge
{
A = edge.A,
B = middle,
LeftPlate = edge.LeftPlate,
RightPlate = edge.RightPlate,
MountainFactor = edge.MountainFactor
};
TectonicEdge subEdge2 = new TectonicEdge
{
A = middle,
B = edge.B,
LeftPlate = edge.LeftPlate,
RightPlate = edge.RightPlate,
MountainFactor = edge.MountainFactor
};
if (depth <= 0)
{
subEdges.Add(subEdge1);
subEdges.Add(subEdge2);
}
else
{
subEdges.AddRange(SplitTectonicEdge(subEdge1, originalEdge, depth - 1));
subEdges.AddRange(SplitTectonicEdge(subEdge2, originalEdge, depth - 1));
}
return(subEdges);
}