public Vector3 CalculateSpin(Vector3 position)
{
// Combine transverse movement about center and pivot.
// First project center onto position vector to get an orthogonal spin vector.
Vector3 spin = Math2.ProjectOnVector(Traits.Center, position) - Traits.Center;
if (spin.Length > 0.0001f)
{
Vector3 tangent = Vector3.Cross(spin, position);
tangent.Normalize();
tangent *= spin.Length * (float)Math.Tan(Traits.CenterRotation);
return(tangent);
}
return(Vector3.Zero);
}
static Stress calculateStress(Vector3 movement0, Vector3 movement1, Vector3 boundaryVector, Vector3 boundaryNormal)
{
var relativeMovement = movement0 - movement1;
var pressureVector = Math2.ProjectOnVector(relativeMovement, boundaryNormal);
var pressure = pressureVector.Length;
if (Vector3.Dot(pressureVector, boundaryNormal) > 0)
{
pressure = -pressure;
}
var shear = Math2.ProjectOnVector(relativeMovement, boundaryVector).Length;
return(new Stress(2.0f / (1.0f + (float)Math.Exp(-pressure / 30.0f)) - 1.0f,
2.0f / (1.0f + (float)Math.Exp(-shear / 30.0f)) - 1.0f));
}
public Geometry <Vertex3DColor> GenerateDistanceDebugGeom()
{
List <Vertex3DColor> verts = new List <Vertex3DColor>();
List <uint> indices = new List <uint>();
for (int plateIndex = 0; plateIndex < plates.Length; ++plateIndex)
{
Vector3 center = plates[plateIndex].Traits.Center;
int cornerIndex = 0;
foreach (int corner in plates[plateIndex].Corners)
{
float hue = (float)cornerIndex / (float)plates[plateIndex].Corners.Count;
Vector3 color3 = Math2.HSV2RGB(new Vector3(hue, 0.7f, 0.5f));
Vector4 color = new Vector4(color3.X, color3.Y, color3.Z, 1.0f);
Centroid centroid = geometry.Topology.Centroids[corner];
Vector3 cornerPos = centroid.position;
Vector3 direction = cornerPos - center;
direction.Normalize();
float theta = centroid.PlateDistances[plateIndex];
float distance = 2.0f * (float)Math.Sin(theta * 0.5f);
direction *= distance;
cornerPos = center + direction;
cornerPos.Normalize();
int vertexStart = verts.Count;
GeometryFactory.AddArcVerts(verts, center, cornerPos, 1.001f, color);
for (int vertexIndex = vertexStart; vertexIndex < verts.Count - 1; ++vertexIndex)
{
indices.Add((uint)vertexIndex);
indices.Add((uint)vertexIndex + 1);
}
++cornerIndex;
}
}
Mesh <Vertex3DColor> mesh = new Mesh <Vertex3DColor>(verts.ToArray());
Geometry <Vertex3DColor> geom = new Geometry <Vertex3DColor>(mesh, indices.ToArray());
geom.PrimitiveType = OpenTK.Graphics.OpenGL.PrimitiveType.Lines;
return(geom);
}
public Scene(World world, float width, float height)
{
this.world = world;
camera = new Camera
{
Position = Vector3.UnitZ * 2.0f,
Width = width,
Height = height
};
ambientColor = Math2.ToVec3(Color.Aquamarine) * 0.25f;
Shader quadShader = new Shader(SHADER_PATH + "quadVertShader.glsl", SHADER_PATH + "texFragShader.glsl");
Shader shader = new Shader(SHADER_PATH + "Vert3DColorUVShader.glsl", SHADER_PATH + "shadedFragShader.glsl");
Shader pointShader = new Shader(SHADER_PATH + "pointVertShader.glsl", SHADER_PATH + "pointFragShader.glsl");
Shader lineShader = new Shader(SHADER_PATH + "pointColorVertShader.glsl", SHADER_PATH + "pointFragShader.glsl");
Shader texShader2 = new Shader(SHADER_PATH + "Vert3DColorUVShader.glsl", SHADER_PATH + "texFragShader.glsl");
Shader borderShader = new Shader(SHADER_PATH + "Vert3DColorShader.glsl", SHADER_PATH + "pointFragShader.glsl");
Texture cellTexture = new Texture("Edge.png");
Texture arrowTexture = new Texture("Arrow.png");
var node = new Node
{
Position = new Vector3(0, 0, -3)
};
node.Model = Matrix4.CreateTranslation(node.Position);
nodes.Add(node);
worldRenderGeometry = world.geometry.GenerateDualMesh <Vertex3DColorUV>();
worldRenderer = new Renderer(worldRenderGeometry, shader);
worldRenderer.AddUniform(new UniformProperty("lightPosition", lightPosition));
worldRenderer.AddUniform(new UniformProperty("ambientColor", ambientColor));
worldRenderer.AddTexture(cellTexture);
worldRenderer.CullFaceFlag = true;
node.Add(worldRenderer);
borderGeometry = world.plates.GenerateBorderGeometry <Vertex3DColor>();
borderGeometry.PrimitiveType = PrimitiveType.Triangles;
borderRenderer = new Renderer(borderGeometry, borderShader)
{
DepthTestFlag = true,
CullFaceFlag = true,
CullFaceMode = CullFaceMode.Back
};
node.Add(borderRenderer);
worldVertsDebugRenderer = new Renderer(world.geometry, pointShader);
worldVertsDebugRenderer.AddUniform(new UniformProperty("color", new Vector4(0, 0.2f, 0.7f, 1)));
worldVertsDebugRenderer.AddUniform(new UniformProperty("pointSize", 3f));
//node.Add(worldVertsDebugRenderer);
Geometry <Vertex3D> centroidGeom = new Geometry <Vertex3D>(world.geometry.GenerateCentroidPointMesh())
{
PrimitiveType = PrimitiveType.Points
};
worldCentroidDebugRenderer = new Renderer(centroidGeom, pointShader)
{
DepthTestFlag = false,
CullFaceFlag = false
};
worldCentroidDebugRenderer.AddUniform(new UniformProperty("color", new Vector4(0.5f, 0.5f, 0.5f, 1)));
worldCentroidDebugRenderer.AddUniform(new UniformProperty("pointSize", 3f));
worldCentroidDebugRenderer.AddUniform(new UniformProperty("zCutoff", -2.8f));
//node.Add(worldCentroidDebugRenderer);
var spinGeom = world.plates.GenerateSpinDriftDebugGeom(true);
worldPlateSpinDebugRenderer = new Renderer(spinGeom, texShader2)
{
DepthTestFlag = false,
CullFaceFlag = false,
BlendingFlag = true
};
worldPlateSpinDebugRenderer.AddTexture(arrowTexture);
worldPlateSpinDebugRenderer.AddUniform(new UniformProperty("color", new Vector4(1, 1, 1, 1.0f)));
node.Add(worldPlateSpinDebugRenderer);
var driftGeom = world.plates.GenerateSpinDriftDebugGeom(false);
worldPlateDriftDebugRenderer = new Renderer(driftGeom, texShader2)
{
DepthTestFlag = false,
CullFaceFlag = false,
BlendingFlag = true
};
worldPlateDriftDebugRenderer.AddTexture(arrowTexture);
worldPlateDriftDebugRenderer.AddUniform(new UniformProperty("color", new Vector4(.75f, 0.75f, 0.0f, 1.0f)));
node.Add(worldPlateDriftDebugRenderer);
var equatorGeom = GeometryFactory.GenerateCircle(Vector3.Zero, Vector3.UnitY, 1.001f, new Vector4(1.0f, 0, 0, 1.0f));
var equatorRenderer = new Renderer(equatorGeom, lineShader);
equatorRenderer.AddUniform(new UniformProperty("zCutoff", -2.8f));
node.Add(equatorRenderer);
//var plateDistanceGeom = world.plates.GenerateDistanceDebugGeom();
//var plateDistanceRenderer = new Renderer(plateDistanceGeom, lineShader)
//{
// DepthTestFlag = true;
//}
//plateDistanceRenderer.AddUniform(new UniformProperty("zCutoff", -2.8f));
//node.Add(plateDistanceRenderer);
}
public float RelaxTriangles(float multiplier)
{
NeedsUpdate = true;
double totalSurfaceArea = 4.0 * Math.PI;
double idealFaceArea = totalSurfaceArea / (indices.Length / 3);
double idealEdgeLength = Math.Sqrt(idealFaceArea * 4.0 / Math.Sqrt(3.0));
double idealDistanceToCentroid = idealEdgeLength * Math.Sqrt(3) / 3.0 * 0.9;
Vector3[] shiftPositions = new Vector3[mesh.vertices.Length];
for (int i = 0; i < mesh.vertices.Length; ++i)
{
shiftPositions[i] = new Vector3(Vector3.Zero);
}
int numIndices = indices.Length;
TVertex[] centroidVerts = new TVertex[numIndices / 3];
TVertex centroidVertex = new TVertex();
for (int i = 0; i < numIndices; i += 3)
{
Vector3 centroid = Topology.CalculateCentroid(i / 3);
centroid.Normalize();
MeshAttr.SetPosition(ref centroidVertex, ref centroid);
Vector3[] oldPositions = new Vector3[3]
{
new Vector3(MeshAttr.GetPosition(ref mesh.vertices[indices[i]])),
new Vector3(MeshAttr.GetPosition(ref mesh.vertices[indices[i + 1]])),
new Vector3(MeshAttr.GetPosition(ref mesh.vertices[indices[i + 2]])),
};
for (int j = 0; j < 3; ++j)
{
Vector3 midLine = centroid - oldPositions[j];
float midLength = midLine.Length;
midLine *= (float)(multiplier * (midLength - idealDistanceToCentroid) / midLength);
shiftPositions[indices[i + j]] += midLine;
}
}
var origin = Vector3.Zero;
Plane p = new Plane(Vector3.UnitY, Vector3.Zero);
for (int i = 0; i < mesh.vertices.Length; ++i)
{
Vector3 vertexPosition = MeshAttr.GetPosition(ref mesh.vertices[i]);
p.Redefine(vertexPosition, origin);
shiftPositions[i] = vertexPosition + p.ProjectPoint(shiftPositions[i]);
shiftPositions[i].Normalize();
}
// Stop poylgons rotating about their centroid.
// Doesn't stop triangles flipping.
float[] rotationSuppressions = new float[mesh.vertices.Length];
rotationSuppressions.Initialize();
Topology.GenerateEdges();
float minEdgeLength = (float)idealEdgeLength * 0.8f;
float maxEdgeLength = (float)idealEdgeLength * 1.2f;
foreach (var iter in Topology.Edges)
{
Int64 key = iter.Key;
int index1 = (int)(key & 0xffffffff);
int index2 = (int)((key >> 32) & 0xffffffff);
Vector3 oldPos1 = MeshAttr.GetPosition(ref mesh.vertices[index1]);
Vector3 oldPos2 = MeshAttr.GetPosition(ref mesh.vertices[index2]);
Vector3 newPos1 = shiftPositions[index1];
Vector3 newPos2 = shiftPositions[index2];
Vector3 oldEdge = oldPos2 - oldPos1;
Vector3 newEdge = newPos2 - newPos1;
if (newEdge.Length < minEdgeLength)
{
// Move shift positions back out to ensure that the edge is never too small.
Vector3 midPt = newPos1 + 0.5f * newEdge;
newEdge.Normalize();
newEdge *= minEdgeLength * 0.5f;
shiftPositions[index1] = midPt - newEdge;
shiftPositions[index2] = midPt + newEdge;
newEdge = shiftPositions[index2] - shiftPositions[index1];
}
if (newEdge.Length > maxEdgeLength)
{
// Move shift positions back in to ensure that the edge is never too large.
Vector3 midPt = newPos1 + 0.5f * newEdge;
newEdge.Normalize();
newEdge *= (maxEdgeLength * 0.5f);
shiftPositions[index1] = midPt - newEdge;
shiftPositions[index2] = midPt + newEdge;
newEdge = shiftPositions[index2] - shiftPositions[index1];
}
oldEdge.Normalize();
newEdge.Normalize();
float suppression = (1.0f - Vector3.Dot(oldEdge, newEdge)) * 0.5f;
rotationSuppressions[index1] = Math.Max(suppression, rotationSuppressions[index1]);
rotationSuppressions[index2] = Math.Max(suppression, rotationSuppressions[index2]);
}
for (int i = 0; i < mesh.vertices.Length; ++i)
{
Vector3 pos = MeshAttr.GetPosition(ref mesh.vertices[i]);
Vector3 delta = pos;
pos = Math2.Lerp(pos, shiftPositions[i], (float)(1.0f - Math.Sqrt(rotationSuppressions[i])));
pos.Normalize();
shiftPositions[i] = pos;
}
float totalShift = 0;
for (int i = 0; i < mesh.vertices.Length; ++i)
{
Vector3 delta = MeshAttr.GetPosition(ref mesh.vertices[i]);
MeshAttr.SetPosition(ref mesh.vertices[i], ref shiftPositions[i]);
delta -= shiftPositions[i];
totalShift += delta.Length;
}
Topology.Regenerate();
return(totalShift);
}
public Geometry <AltVertex> GenerateBorderGeometry <AltVertex>()
where AltVertex : struct, IVertex
{
if (borders == null || borders.Count == 0)
{
return(null);
}
else
{
List <AltVertex> vertices = new List <AltVertex>();
List <uint> newIndices = new List <uint>();
const float h = 0.1f;
foreach (var iter in borders)
{
Int64 borderKey = iter.Key;
int v1index = (int)(borderKey & 0xffffffff);
int v2index = (int)((borderKey >> 32) & 0xffffffff);
Border border = iter.Value;
// The border lies along an edge in the dual geometry.
int plateIndex1 = border.plate0;
int plateIndex2 = border.plate1;
Vector3 v1Pos = geometry.Mesh.GetPosition(v1index);
Vector3 v2Pos = geometry.Mesh.GetPosition(v2index);
Vector3 centroid1 = geometry.Topology.Centroids[border.c1Index].position;
Vector3 centroid2 = geometry.Topology.Centroids[border.c2Index].position;
Vector3 v1g1prime = Math2.BaseProjection(v1Pos, centroid1, centroid2, h);
Vector3 v1g2prime = Math2.BaseProjection(v1Pos, centroid2, centroid1, h);
Vector3 v2g1prime = Math2.BaseProjection(v2Pos, centroid1, centroid2, h);
Vector3 v2g2prime = Math2.BaseProjection(v2Pos, centroid2, centroid1, h);
centroid1 *= 1.01f; // Project the centroids out of the sphere slightly
centroid2 *= 1.01f;
bool edgeOrderIsAnticlockwise = false;
for (int i = 0; i < 3; i++)
{
if (geometry.Indices[border.c1Index * 3 + i] == v1index)
{
if (geometry.Indices[border.c1Index * 3 + (i + 1) % 3] == v2index)
{
edgeOrderIsAnticlockwise = true;
}
break;
}
}
int index = vertices.Count;
geometry.AddTriangle(ref vertices, ref newIndices, ref v1g2prime, ref centroid2, ref centroid1, edgeOrderIsAnticlockwise);
geometry.AddTriangle(ref vertices, ref newIndices, ref v1g2prime, ref centroid1, ref v1g1prime, edgeOrderIsAnticlockwise);
geometry.AddTriangle(ref vertices, ref newIndices, ref v2g1prime, ref centroid1, ref centroid2, edgeOrderIsAnticlockwise);
geometry.AddTriangle(ref vertices, ref newIndices, ref v2g1prime, ref centroid2, ref v2g2prime, edgeOrderIsAnticlockwise);
float p1 = Math2.Clamp(Math.Abs(borderCorners[border.c1Index].stress.pressure) * 1000.0f, 0, 1.0f);
float p2 = Math2.Clamp(Math.Abs(borderCorners[border.c2Index].stress.pressure) * 1000.0f, 0, 1.0f);
float hue1 = borderCorners[border.c1Index].stress.pressure > 0 ? 0 : 0.5f;
float hue2 = borderCorners[border.c2Index].stress.pressure > 0 ? 0 : 0.5f;
Vector3 rgb1 = Math2.HSV2RGB(new Vector3(hue1, p1, 1.0f - p1));
Vector3 rgb2 = Math2.HSV2RGB(new Vector3(hue2, p2, 1.0f - p2));
Vector4 c1Color = new Vector4(rgb1.X, rgb1.Y, rgb1.Z, 1);
Vector4 c2Color = new Vector4(rgb2.X, rgb2.Y, rgb2.Z, 1);
AltVertex v;
for (int i = 0; i < 12; ++i)
{
Vector4 color = new Vector4(1.0f, 1.0f, 1.0f, 1.0f);
if (i == 0 || i == 1 || i == 3 || i == 8 || i == 10 || i == 11)
{
color = c2Color;
}
else if (i == 2 || i == 4 || i == 5 || i == 6 || i == 7 || i == 9)
{
color = c1Color;
}
v = vertices[index + i]; MeshAttr.SetColor(ref v, ref color); vertices[index + i] = v;
}
}
Mesh <AltVertex> newMesh = new Mesh <AltVertex>(vertices.ToArray());
return(new Geometry <AltVertex>(newMesh, newIndices.ToArray()));
}
}