private void InitializePlates()
{
// Initialize vertexToPlate array to a value that isn't a valid plate index
vertexToPlate = new int[geometry.Mesh.Length];
for (int i = 0; i < geometry.Mesh.Length; ++i)
{
vertexToPlate[i] = -1;
}
borders.Clear();
for (int plateIndex = 0; plateIndex < plates.Length; ++plateIndex)
{
int plate = -1;
do
{
int vertexIndex = rand.Next(geometry.Mesh.Length);
// prevent 2 plates spawning at the same vertex.
plate = vertexToPlate[vertexIndex];
if (plate == -1)
{
var traits = new PlatePhysicsTraits();
traits.Pivot = new Vector3(rand.Next(100) - 50, rand.Next(100) - 50, rand.Next(100) - 50);
traits.Pivot.Normalize();
traits.Center = geometry.Mesh.GetPosition(vertexIndex);
if (Vector3.Dot(traits.Center, traits.Pivot) < 0)
{
traits.Pivot *= -1.0f; // Ensure pivot is at least in the same hemisphere as the plate center.
}
traits.CenterRotation = (rand.Next(200) - 100) * (float)Math.PI / 6000.0f; // -3 -> 3 degrees
traits.PivotRotation = (rand.Next(200) - 100) * (float)Math.PI / 6000.0f;
traits.Elevation = 0.0f;
plates[plateIndex] = new Plate(vertexToPlate, geometry, traits, plateIndex, vertexIndex, ref rand);
break;
}
} while (plate != -1);
}
}
public void CalculateBorderTileHeights()
{
// if perpendicular motion is +ve, it's a collision.
// -ve, it's a rift (which would form basaltic volcanoes)
// If collision, then
// if heights sufficiently close & same sign, treat as height increase
// mountain formation; folding;
// if heights opposite sign; subduct the lower under the higher.
// tilt upper plate (calc for all boundaries)
foreach (int borderCornerKey in borderCorners.Keys)
{
List <Int64> borderIndices = borderCorners[borderCornerKey].borderIndices;
if (borderIndices.Count == 3)
{
// At 3 plate boundaries, just take some maxima / averages:
Plate plate0 = plates[vertexToPlate[geometry.Topology.Centroids[borderCornerKey].Faces[0]]];
Plate plate1 = plates[vertexToPlate[geometry.Topology.Centroids[borderCornerKey].Faces[1]]];
Plate plate2 = plates[vertexToPlate[geometry.Topology.Centroids[borderCornerKey].Faces[2]]];
Stress stress = borderCorners[borderCornerKey].stress;
if (stress.pressure > 0.3)
{
borderCorners[borderCornerKey].elevation = Math.Max(plate0.Traits.Elevation, Math.Max(plate1.Traits.Elevation, plate2.Traits.Elevation)) + stress.pressure;
}
else if (stress.pressure < -0.3)
{
borderCorners[borderCornerKey].elevation = Math.Max(plate0.Traits.Elevation, Math.Max(plate1.Traits.Elevation, plate2.Traits.Elevation)) + stress.pressure / 4;
}
else if (stress.shear > 0.3)
{
borderCorners[borderCornerKey].elevation = Math.Max(plate0.Traits.Elevation, Math.Max(plate1.Traits.Elevation, plate2.Traits.Elevation)) + stress.shear / 8;
}
else
{
borderCorners[borderCornerKey].elevation = (plate0.Traits.Elevation + plate1.Traits.Elevation + plate2.Traits.Elevation) / 3.0f;
}
}
else
{
Border border0 = borders[borderIndices[0]];
Border border1 = borders[borderIndices[1]];
int plateIndex0 = border0.plate0;
int plateIndex1 = border1.plate0 == plateIndex0 ? border1.plate1 : border0.plate1;
Plate plate0 = plates[plateIndex0];
Plate plate1 = plates[plateIndex1];
ElevationCalculation elevationCalculation = ElevationCalculation.DORMANT;
Stress stress = borderCorners[borderCornerKey].stress;
if (stress.pressure > 0.3)
{
borderCorners[borderCornerKey].elevation = Math.Max(plate0.Traits.Elevation, plate1.Traits.Elevation) + stress.pressure;
if (plate0.Traits.Elevation < 0 && plate0.Traits.Elevation < 0)
{
elevationCalculation = ElevationCalculation.COLLIDING;
}
else if (plate0.Traits.Elevation < 0)
{
elevationCalculation = ElevationCalculation.SUBDUCTING;
}
else if (plate1.Traits.Elevation < 0)
{
elevationCalculation = ElevationCalculation.SUPERDUCTING;
}
else
{
elevationCalculation = ElevationCalculation.COLLIDING;
}
}
else if (stress.pressure < -0.3)
{
borderCorners[borderCornerKey].elevation = Math.Max(plate0.Traits.Elevation, plate1.Traits.Elevation) + stress.pressure / 4;
elevationCalculation = ElevationCalculation.DIVERGING;
}
else if (stress.shear > 0.3)
{
borderCorners[borderCornerKey].elevation = Math.Max(plate0.Traits.Elevation, plate1.Traits.Elevation) + stress.shear / 8;
elevationCalculation = ElevationCalculation.SHEARING;
}
else
{
borderCorners[borderCornerKey].elevation = (plate0.Traits.Elevation + plate1.Traits.Elevation) / 2.0f;
elevationCalculation = ElevationCalculation.DORMANT;
}
// Queue up:
// next corner: Inner corner: the corner that isn't the opposite corner of border0 and border1
// (i.e. remove the opposite corners from Centroid neighbours, and it's the remaining one).
// origin: { this corner, stress, plate, elevationType }
// border: inner border
// corner: this corner
// distanceToPlateBoundary: inner border length, i.e. of next corner.
}
}
}
public void CalculateStresses()
{
// for each vertex in plate boundaries,
// calculate relative motion between tiles
// both parallel to (shear) and perpendicular to (pressure) edge.
foreach (int borderCornerKey in borderCorners.Keys)
{
List <Int64> borderIndices = borderCorners[borderCornerKey].borderIndices;
var centroid = geometry.Topology.Centroids[borderCornerKey];
var pos = centroid.position;
Dictionary <int, Vector3> plateMovement = new Dictionary <int, Vector3>();
foreach (Int64 borderKey in borderIndices)
{
Border border = borders[borderKey];
// Calculate movement only once for each plate
for (int i = 0; i < 2; ++i)
{
int plateIndex = (i == 0) ? border.plate0 : border.plate1;
Vector3 movement;
if (!plateMovement.TryGetValue(plateIndex, out movement))
{
Plate plate = plates[plateIndex];
movement = plate.CalculateSpin(pos) + plate.CalculateDrift(pos);
plateMovement[plateIndex] = movement;
}
}
}
if (borderIndices.Count == 3)
{
// 3 separate plates. Find movement from each plate at this corner and average it
Stress[] stresses = new Stress[3];
int stressIdx = 0;
foreach (Int64 borderKey in borderIndices)
{
Border border = borders[borderKey];
int oppositeCornerIndex = border.OppositeCorner(borderCornerKey);
var oppositeCornerPosition = geometry.Topology.Centroids[oppositeCornerIndex].position;
Vector3 boundary = oppositeCornerPosition - pos;
Vector3 boundaryNormal = Vector3.Cross(boundary, pos);
stresses[stressIdx++] = calculateStress(plateMovement[border.plate0], plateMovement[border.plate1], boundary, boundaryNormal);
}
borderCorners[borderCornerKey].stress.pressure = (stresses[0].pressure + stresses[1].pressure + stresses[2].pressure) / 3.0f;
borderCorners[borderCornerKey].stress.shear = (stresses[0].shear + stresses[1].shear + stresses[2].shear) / 3.0f;
}
else // Border between only 2 plates.
{
// generate average vector, calculate stress once.
Border border0 = borders[borderIndices[0]];
Border border1 = borders[borderIndices[1]];
int plate0 = border0.plate0;
int plate1 = border1.plate0 == plate0 ? border1.plate1 : border0.plate1;
int oppositeCornerIndex0 = border0.OppositeCorner(borderCornerKey);
int oppositeCornerIndex1 = border0.OppositeCorner(borderCornerKey);
var oppositeCornerPosition0 = geometry.Topology.Centroids[oppositeCornerIndex0].position;
var oppositeCornerPosition1 = geometry.Topology.Centroids[oppositeCornerIndex1].position;
Vector3 boundary = oppositeCornerPosition1 = oppositeCornerPosition0;
Vector3 boundaryNormal = Vector3.Cross(boundary, pos);
borderCorners[borderCornerKey].stress = calculateStress(plateMovement[plate0], plateMovement[plate1], boundary, boundaryNormal);
}
}
}