protected void Start()
{
var hexGridSurface = RectangularHexGrid.Create(
HexGridDescriptor.CreateSideUp(true, HexGridAxisStyles.StaggeredSymmetric),
Vector3.zero, Quaternion.Euler(90f, 0f, 0f),
false, false,
new IntVector2(topologyWidth, topologyHeight));
_surface = hexGridSurface;
Vector3[] vertexPositionsArray;
_topology = hexGridSurface.CreateManifold(out vertexPositionsArray);
_vertexPositions = vertexPositionsArray.AsVertexAttribute();
_facePositions = FaceAttributeUtility.CalculateFaceCentroidsFromVertexPositions(_topology.internalFaces, _vertexPositions);
_faceCornerBisectors = EdgeAttributeUtility.CalculateFaceEdgeBisectorsFromVertexPositions(_topology.internalFaces, _vertexPositions, _facePositions);
_faceBlockedStates = new bool[_topology.internalFaces.Count].AsFaceAttribute();
var triangulation = new SeparatedFacesUmbrellaTriangulation(2,
(Topology.FaceEdge edge, DynamicMesh.IIndexedVertexAttributes vertexAttributes) =>
{
vertexAttributes.position = _vertexPositions[edge];
vertexAttributes.normal = Vector3.up;
vertexAttributes.color = borderColor;
vertexAttributes.Advance();
vertexAttributes.position = _vertexPositions[edge] + _faceCornerBisectors[edge] * 0.05f;
vertexAttributes.normal = (vertexAttributes.position + Vector3.up - _facePositions[edge.nearFace]).normalized;
vertexAttributes.color = normalColor;
vertexAttributes.Advance();
},
(Topology.Face face, DynamicMesh.IIndexedVertexAttributes vertexAttributes) =>
{
vertexAttributes.position = _facePositions[face];
vertexAttributes.normal = Vector3.up;
vertexAttributes.color = normalColor;
vertexAttributes.Advance();
});
_dynamicMesh = DynamicMesh.Create(
_topology.enumerableInternalFaces,
DynamicMesh.VertexAttributes.Position |
DynamicMesh.VertexAttributes.Normal |
DynamicMesh.VertexAttributes.Color,
triangulation);
foreach (var mesh in _dynamicMesh.submeshes)
{
var meshFilter = Instantiate(submeshPrefab);
meshFilter.mesh = mesh;
meshFilter.transform.SetParent(transform, false);
}
var partioning = UniversalFaceSpatialPartitioning.Create(_surface, _topology, _vertexPositions);
var picker = GetComponent <FaceSpatialPartitioningPicker>();
picker.partitioning = partioning;
}
public static IEdgeAttribute <TAttributeValue>[] GetRingAttributes <TAttributeValue>(Topology topology, InputSlot[] inputSlots)
{
if (inputSlots.Length == 0)
{
return(null);
}
var array = new IEdgeAttribute <TAttributeValue> [inputSlots.Length];
for (int i = 0; i < inputSlots.Length; ++i)
{
var attribute = inputSlots[i].GetAsset <IEdgeAttribute <TAttributeValue> >();
if (attribute is IFaceAttribute <TAttributeValue> )
{
attribute = new TwinEdgeAttributeWrapper <TAttributeValue>(topology, attribute);
}
array[i] = attribute;
}
return(array);
}
private void DestroyOldGame()
{
if (_surface == null)
{
return;
}
var existingMeshCount = gameBoardMeshes.childCount;
for (int i = 0; i < existingMeshCount; ++i)
{
Destroy(gameBoardMeshes.GetChild(i).gameObject);
}
foreach (var face in _topology.internalFaces)
{
if (_facePieces[face] != null)
{
Destroy(_facePieces[face].gameObject);
}
}
_surface = null;
_topology = null;
_vertexPositions = null;
_facePositions = null;
_innerAngleBisectors = null;
_facePieces = null;
_faceBoardStates = null;
_partitioning = null;
_dynamicMesh = null;
_picker.partitioning = null;
_picker.enabled = false;
_gameActive = false;
}
public void SubdividedIcosahedronFaceEdgeMidpointWeightedIntersections()
{
CreateSubdividedIcosahedron(1f);
edgeMidpoints = EdgeAttributeUtility.CalculateVertexEdgeMidpointsFromVertexPositions(topology.vertexEdges, vertexPositions);
FaceEdgeMidpointWeightedIntersections();
}
public void CubeFaceEdgeMidpointWeightedIntersections()
{
CreateCube(1f);
edgeMidpoints = EdgeAttributeUtility.CalculateVertexEdgeMidpointsFromVertexPositions(topology.vertexEdges, vertexPositions);
FaceEdgeMidpointWeightedIntersections();
}
public void LargeDistortedHexGridFaceEdgeMidpointWeightedIntersections()
{
CreateDistortedHexGrid(8, 8, 1);
edgeMidpoints = EdgeAttributeUtility.CalculateVertexEdgeMidpointsFromVertexPositions(topology.vertexEdges, vertexPositions);
FaceEdgeMidpointWeightedIntersections();
}
public void SmallHexGridFaceEdgeMidpointWeightedIntersections()
{
CreateHexGrid(2, 2);
edgeMidpoints = EdgeAttributeUtility.CalculateVertexEdgeMidpointsFromVertexPositions(topology.vertexEdges, vertexPositions);
FaceEdgeMidpointWeightedIntersections();
}
protected void Start()
{
orbitalCamera.enabled = !isInverted;
pivotalCamera.enabled = isInverted;
exteriorLight.enabled = !isInverted;
interiorLight.enabled = isInverted;
_lightVector = (isInverted ? interiorLight : exteriorLight).transform.position;
_lightAxis = Vector3.Cross(Vector3.Cross(Vector3.up, _lightVector), _lightVector);
RenderSettings.ambientLight = new Color(0.3f, 0.4f, 0.5f);
RenderSettings.ambientIntensity = 0.25f;
RenderSettings.customReflection = whiteCubeMap;
RenderSettings.reflectionIntensity = 0.125f;
RenderSettings.defaultReflectionMode = UnityEngine.Rendering.DefaultReflectionMode.Custom;
_picker = GetComponent <FaceSpatialPartitioningPicker>();
_surface = SphericalSurface.Create(Vector3.up, Vector3.right, 10f, isInverted);
Vector3[] baseVertexPositionsArray;
Topology baseTopology;
SphericalManifoldUtility.CreateIcosahedron(_surface, out baseTopology, out baseVertexPositionsArray);
Vector3[] vertexPositionsArray;
SphericalManifoldUtility.Subdivide(_surface, baseTopology, baseVertexPositionsArray.AsVertexAttribute(), topologySubdivision, out _topology, out vertexPositionsArray);
_vertexPositions = PositionalVertexAttribute.Create(_surface, vertexPositionsArray);
SphericalManifoldUtility.MakeDual(_surface, _topology, _vertexPositions, out vertexPositionsArray);
_vertexPositions = PositionalVertexAttribute.Create(_surface, vertexPositionsArray);
var regularityWeight = 0.5f;
var equalAreaWeight = 1f - regularityWeight;
var regularityRelaxedVertexPositions = new Vector3[_topology.vertices.Count].AsVertexAttribute();
var equalAreaRelaxedVertexPositions = new Vector3[_topology.vertices.Count].AsVertexAttribute();
var relaxedVertexPositions = regularityRelaxedVertexPositions;
var faceCentroids = PositionalFaceAttribute.Create(_surface, _topology.internalFaces.Count);
var faceCentroidAngles = new float[_topology.faceEdges.Count].AsEdgeAttribute();
var vertexAreas = new float[_topology.vertices.Count].AsVertexAttribute();
FaceAttributeUtility.CalculateFaceCentroidsFromVertexPositions(_topology.internalFaces, _vertexPositions, faceCentroids);
VertexAttributeUtility.CalculateVertexAreasFromVertexPositionsAndFaceCentroids(_topology.vertices, _vertexPositions, faceCentroids, vertexAreas);
Func <float> relaxIterationFunction = () =>
{
SphericalManifoldUtility.RelaxVertexPositionsForRegularity(_surface, _topology, _vertexPositions, true, regularityRelaxedVertexPositions);
SphericalManifoldUtility.RelaxVertexPositionsForEqualArea(_surface, _topology, _vertexPositions, true, equalAreaRelaxedVertexPositions, faceCentroids, faceCentroidAngles, vertexAreas);
for (int i = 0; i < relaxedVertexPositions.Count; ++i)
{
relaxedVertexPositions[i] = regularityRelaxedVertexPositions[i] * regularityWeight + equalAreaRelaxedVertexPositions[i] * equalAreaWeight;
}
var relaxationAmount = SphericalManifoldUtility.CalculateRelaxationAmount(_vertexPositions, relaxedVertexPositions);
for (int i = 0; i < _vertexPositions.Count; ++i)
{
_vertexPositions[i] = relaxedVertexPositions[i];
}
return(relaxationAmount);
};
Func <bool> repairFunction = () =>
{
return(SphericalManifoldUtility.ValidateAndRepair(_surface, _topology, _vertexPositions, 0.5f, true));
};
Action relaxationLoopFunction = TopologyRandomizer.CreateRelaxationLoopFunction(20, 20, 0.95f, relaxIterationFunction, repairFunction);
TopologyRandomizer.Randomize(
_topology, 1, 0.1f,
3, 3, 5, 7, true,
_random,
relaxationLoopFunction);
_facePositions = PositionalFaceAttribute.Create(_surface, _topology.internalFaces.Count);
FaceAttributeUtility.CalculateFaceCentroidsFromVertexPositions(_topology.internalFaces, _vertexPositions, _facePositions);
_maximumFaceDistance = 0f;
foreach (var edge in _topology.faceEdges)
{
var distance = Geometry.AngleBetweenVectors(_facePositions[edge.nearFace], _facePositions[edge.farFace]) * _surface.radius;
_maximumFaceDistance = Mathf.Max(_maximumFaceDistance, distance);
}
_innerAngleBisectors = EdgeAttributeUtility.CalculateFaceEdgeBisectorsFromVertexPositions(_topology.internalFaces, _vertexPositions, _facePositions);
_innerVertexPositions = new Vector3[_topology.faceEdges.Count].AsEdgeAttribute();
foreach (var edge in _topology.faceEdges)
{
_innerVertexPositions[edge] = _vertexPositions[edge] + _innerAngleBisectors[edge] * 0.03f;
}
_faceNormals = FaceAttributeUtility.CalculateFaceNormalsFromSurface(_topology.faces, _surface, _facePositions);
_faceUVFrames = FaceAttributeUtility.CalculatePerFaceSphericalUVFramesFromFaceNormals(_topology.faces, _faceNormals, Quaternion.identity);
_faceOuterEdgeUVs = EdgeAttributeUtility.CalculatePerFaceUnnormalizedUVsFromVertexPositions(_topology.faces, _vertexPositions, _faceUVFrames);
_faceInnerEdgeUVs = EdgeAttributeUtility.CalculatePerFaceUnnormalizedUVsFromVertexPositions(_topology.faces, _innerVertexPositions, _faceUVFrames);
_faceCenterUVs = FaceAttributeUtility.CalculateUnnormalizedUVsFromFacePositions(_topology.faces, _facePositions, _faceUVFrames);
var faceMinUVs = new Vector2[_topology.faces.Count].AsFaceAttribute();
var faceRangeUVs = new Vector2[_topology.faces.Count].AsFaceAttribute();
FaceAttributeUtility.CalculateFaceEdgeMinAndRangeValues(_topology.faces, _faceOuterEdgeUVs, faceMinUVs, faceRangeUVs);
foreach (var face in _topology.faces)
{
var uvMin = faceMinUVs[face];
var uvRange = faceRangeUVs[face];
var adjusted = AspectRatioUtility.Expand(new Rect(uvMin.x, uvMin.y, uvRange.x, uvRange.y), 1f);
faceMinUVs[face] = adjusted.min;
faceRangeUVs[face] = adjusted.size;
}
_faceOuterEdgeUVs = EdgeAttributeUtility.CalculatePerFaceUniformlyNormalizedUVsFromFaceUVMinAndRange(_topology.faces, faceMinUVs, faceRangeUVs, _faceOuterEdgeUVs);
_faceInnerEdgeUVs = EdgeAttributeUtility.CalculatePerFaceUniformlyNormalizedUVsFromFaceUVMinAndRange(_topology.faces, faceMinUVs, faceRangeUVs, _faceInnerEdgeUVs);
_faceCenterUVs = FaceAttributeUtility.CalculateUniformlyNormalizedUVsFromFaceUVMinAndRange(_topology.faces, faceMinUVs, faceRangeUVs, _faceCenterUVs);
_partitioning = UniversalFaceSpatialPartitioning.Create(_surface, _topology, _vertexPositions);
_picker.partitioning = _partitioning;
_picker.enabled = true;
_faceTerrainIndices = new int[_topology.faces.Count].AsFaceAttribute();
var terrainWeights = new int[] { grassWeight, waterWeight, desertWeight, mountainWeight };
int terrainWeightSum = 0;
foreach (var weight in terrainWeights)
{
terrainWeightSum += weight;
}
var rootFaces = new List <Topology.Face>();
var rootFaceEdges = new List <Topology.FaceEdge>();
for (int regionIndex = 0; regionIndex < geographicalRegionCount; ++regionIndex)
{
Topology.Face face;
do
{
face = _topology.internalFaces[_random.Index(_topology.internalFaces.Count)];
} while (rootFaces.Contains(face));
rootFaces.Add(face);
foreach (var edge in face.edges)
{
rootFaceEdges.Add(edge);
}
_faceTerrainIndices[face] = _random.WeightedIndex(terrainWeights, terrainWeightSum);
}
TopologyVisitor.VisitFacesInRandomOrder(rootFaceEdges, (FaceEdgeVisitor visitor) =>
{
_faceTerrainIndices[visitor.edge.farFace] = _faceTerrainIndices[visitor.edge.nearFace];
visitor.VisitInternalNeighborsExceptSource();
},
_random);
_faceSeenStates = new bool[_topology.faces.Count].AsFaceAttribute();
_faceSightCounts = new int[_topology.faces.Count].AsFaceAttribute();
var triangulation = new SeparatedFacesUmbrellaTriangulation(2,
(Topology.FaceEdge edge, DynamicMesh.IIndexedVertexAttributes vertexAttributes) =>
{
var face = edge.nearFace;
var faceNormal = _faceNormals[face];
var gridOverlayU = GetGridOverlayU(false, _faceSeenStates[face], _faceSightCounts[face]);
vertexAttributes.position = _vertexPositions[edge];
vertexAttributes.normal = faceNormal;
vertexAttributes.uv1 = AdjustSurfaceUV(_faceOuterEdgeUVs[edge], _faceTerrainIndices[face]);
vertexAttributes.uv2 = new Vector2(gridOverlayU, 0f);
vertexAttributes.Advance();
vertexAttributes.position = _innerVertexPositions[edge];
vertexAttributes.normal = faceNormal;
vertexAttributes.uv1 = AdjustSurfaceUV(_faceInnerEdgeUVs[edge], _faceTerrainIndices[face]);
vertexAttributes.uv2 = new Vector2(gridOverlayU, 0.5f);
vertexAttributes.Advance();
},
(Topology.Face face, DynamicMesh.IIndexedVertexAttributes vertexAttributes) =>
{
vertexAttributes.position = _facePositions[face];
vertexAttributes.normal = _faceNormals[face];
vertexAttributes.uv1 = AdjustSurfaceUV(_faceCenterUVs[face], _faceTerrainIndices[face]);
vertexAttributes.uv2 = new Vector2(GetGridOverlayU(false, _faceSeenStates[face], _faceSightCounts[face]), 1f);
vertexAttributes.Advance();
});
_dynamicMesh = DynamicMesh.Create(
_topology.enumerableInternalFaces,
DynamicMesh.VertexAttributes.Position |
DynamicMesh.VertexAttributes.Normal |
DynamicMesh.VertexAttributes.UV1 |
DynamicMesh.VertexAttributes.UV2,
triangulation);
foreach (var mesh in _dynamicMesh.submeshes)
{
var meshObject = Instantiate(planetMeshPrefab);
meshObject.mesh = mesh;
meshObject.transform.SetParent(planetMeshes, false);
}
_faceUnits = new Transform[_topology.faces.Count].AsFaceAttribute();
for (int i = 0; i < unitCount; ++i)
{
Topology.Face face;
do
{
face = _topology.internalFaces[_random.Index(_topology.internalFaces.Count)];
} while (_faceTerrainIndices[face] == 1 || _faceUnits[face] != null);
var unit = Instantiate(unitPrefab);
unit.SetParent(units, false);
unit.transform.position = _facePositions[face] + _faceNormals[face] * 0.15f;
_faceUnits[face] = unit;
RevealUnitVicinity(face);
}
_dynamicMesh.RebuildMesh(DynamicMesh.VertexAttributes.UV2);
}
public void StartNewGame()
{
DestroyOldGame();
Vector3[] vertexPositionsArray;
if (squaresToggle.isOn)
{
IntVector2 boardSize;
if (smallToggle.isOn)
{
boardSize = new IntVector2(9, 9);
}
else if (mediumToggle.isOn)
{
boardSize = new IntVector2(13, 13);
}
else
{
boardSize = new IntVector2(19, 19);
}
_surface = RectangularQuadGrid.Create(Vector2.right, Vector2.up, Vector3.zero, Quaternion.identity, false, false, boardSize);
_topology = ((RectangularQuadGrid)_surface).CreateManifold(out vertexPositionsArray);
_vertexPositions = PositionalVertexAttribute.Create(_surface, vertexPositionsArray);
}
else if (hexesToggle.isOn)
{
IntVector2 boardSize;
if (smallToggle.isOn)
{
boardSize = new IntVector2(9, 9);
}
else if (mediumToggle.isOn)
{
boardSize = new IntVector2(13, 13);
}
else
{
boardSize = new IntVector2(19, 19);
}
_surface = RectangularHexGrid.Create(
HexGridDescriptor.CreateCornerUp(true, HexGridAxisStyles.StaggeredSymmetric),
Vector3.zero, Quaternion.identity,
false, false,
boardSize);
_topology = ((RectangularHexGrid)_surface).CreateManifold(out vertexPositionsArray);
_vertexPositions = PositionalVertexAttribute.Create(_surface, vertexPositionsArray);
}
else
{
IntVector2 boardSize;
if (smallToggle.isOn)
{
boardSize = new IntVector2(9, 9);
}
else if (mediumToggle.isOn)
{
boardSize = new IntVector2(13, 13);
}
else
{
boardSize = new IntVector2(19, 19);
}
_surface = RectangularHexGrid.Create(
HexGridDescriptor.CreateCornerUp(true, HexGridAxisStyles.StaggeredSymmetric),
Vector3.zero, Quaternion.identity,
false, false,
boardSize);
_topology = ((RectangularHexGrid)_surface).CreateManifold(out vertexPositionsArray);
_vertexPositions = PositionalVertexAttribute.Create(_surface, vertexPositionsArray);
var regularityWeight = 0.5f;
var equalAreaWeight = 1f - regularityWeight;
var regularityRelaxedVertexPositions = new Vector3[_topology.vertices.Count].AsVertexAttribute();
var equalAreaRelaxedVertexPositions = new Vector3[_topology.vertices.Count].AsVertexAttribute();
var relaxedVertexPositions = regularityRelaxedVertexPositions;
var faceCentroids = PositionalFaceAttribute.Create(_surface, _topology.internalFaces.Count);
var vertexAreas = new float[_topology.vertices.Count].AsVertexAttribute();
FaceAttributeUtility.CalculateFaceCentroidsFromVertexPositions(_topology.internalFaces, _vertexPositions, faceCentroids);
VertexAttributeUtility.CalculateVertexAreasFromVertexPositionsAndFaceCentroids(_topology.vertices, _vertexPositions, faceCentroids, vertexAreas);
var totalArea = 0f;
foreach (var vertexArea in vertexAreas)
{
totalArea += vertexArea;
}
Func <float> relaxIterationFunction = () =>
{
PlanarManifoldUtility.RelaxVertexPositionsForRegularity(_topology, _vertexPositions, true, regularityRelaxedVertexPositions);
PlanarManifoldUtility.RelaxVertexPositionsForEqualArea(_topology, _vertexPositions, totalArea, true, equalAreaRelaxedVertexPositions, faceCentroids, vertexAreas);
for (int i = 0; i < relaxedVertexPositions.Count; ++i)
{
relaxedVertexPositions[i] = regularityRelaxedVertexPositions[i] * regularityWeight + equalAreaRelaxedVertexPositions[i] * equalAreaWeight;
}
var relaxationAmount = PlanarManifoldUtility.CalculateRelaxationAmount(_vertexPositions, relaxedVertexPositions);
for (int i = 0; i < _vertexPositions.Count; ++i)
{
_vertexPositions[i] = relaxedVertexPositions[i];
}
return(relaxationAmount);
};
Func <bool> repairFunction = () =>
{
return(PlanarManifoldUtility.ValidateAndRepair(_topology, _surface.normal, _vertexPositions, 0.5f, true));
};
Action relaxationLoopFunction = TopologyRandomizer.CreateRelaxationLoopFunction(20, 20, 0.95f, relaxIterationFunction, repairFunction);
TopologyRandomizer.Randomize(
_topology, 1, 0.1f,
3, 3, 5, 7, true,
_random,
relaxationLoopFunction);
}
_facePositions = PositionalFaceAttribute.Create(_surface, _topology.internalFaces.Count);
FaceAttributeUtility.CalculateFaceCentroidsFromVertexPositions(_topology.internalFaces, _vertexPositions, _facePositions);
_innerAngleBisectors = EdgeAttributeUtility.CalculateFaceEdgeBisectorsFromVertexPositions(_topology.internalFaces, PlanarSurface.Create(Vector3.zero, Quaternion.identity), _vertexPositions);
_faceBoardStates = new BoardState[_topology.internalFaces.Count].AsFaceAttribute();
foreach (var face in _topology.internalFaces)
{
_faceBoardStates[face] = BoardState.Empty;
}
_facePieces = new Transform[_topology.internalFaces.Count].AsFaceAttribute();
_partitioning = UniversalFaceSpatialPartitioning.Create(_surface, _topology, _vertexPositions);
_picker.partitioning = _partitioning;
_picker.enabled = true;
var centerVertexNormal = _surface.normal.normalized;
var triangulation = new SeparatedFacesUmbrellaTriangulation(2,
(Topology.FaceEdge edge, DynamicMesh.IIndexedVertexAttributes vertexAttributes) =>
{
vertexAttributes.position = _vertexPositions[edge];
vertexAttributes.normal = (_vertexPositions[edge] + _surface.normal * 5f - _facePositions[edge.nearFace]).normalized;
vertexAttributes.uv = new Vector2(0.25f, 0f);
vertexAttributes.Advance();
vertexAttributes.position = _vertexPositions[edge] + _innerAngleBisectors[edge] * 0.05f;
vertexAttributes.normal = (vertexAttributes.position + _surface.normal * 5f - _facePositions[edge.nearFace]).normalized;
vertexAttributes.uv = new Vector2(0.25f, 0.5f);
vertexAttributes.Advance();
},
(Topology.Face face, DynamicMesh.IIndexedVertexAttributes vertexAttributes) =>
{
vertexAttributes.position = _facePositions[face];
vertexAttributes.normal = centerVertexNormal;
vertexAttributes.uv = new Vector2(0.25f, 1f);
vertexAttributes.Advance();
});
_dynamicMesh = DynamicMesh.Create(
_topology.enumerableInternalFaces,
DynamicMesh.VertexAttributes.Position |
DynamicMesh.VertexAttributes.Normal |
DynamicMesh.VertexAttributes.UV,
triangulation);
foreach (var mesh in _dynamicMesh.submeshes)
{
var meshObject = Instantiate(meshFilterRendererPrefab);
meshObject.mesh = mesh;
meshObject.transform.SetParent(gameBoardMeshes);
}
_gameBoardBounds = new Bounds(Vector3.zero, Vector3.zero);
foreach (var vertex in _topology.vertices)
{
_gameBoardBounds.Encapsulate(_vertexPositions[vertex]);
}
AdjustCamera();
var pickerCollider = GetComponent <BoxCollider>();
pickerCollider.center = _gameBoardBounds.center;
pickerCollider.size = _gameBoardBounds.size;
_whiteCount = 0;
_blackCount = 0;
_moveCount = 0;
whiteCountText.text = _whiteCount.ToString();
blackCountText.text = _blackCount.ToString();
_gameActive = true;
_turn = BoardState.Black;
}
/// <summary>
/// Calculates the spherical surface area around each vertex that is closest to that vertex, based on face centroid angles of each edge.
/// </summary>
/// <param name="vertices">The collection of vertices whose areas are to be calculated.</param>
/// <param name="surface">The surface describing the overall shape of the spherical manifold.</param>
/// <param name="faceCentroidAngles">The centroid angles, in radians, of the face edges.</param>
/// <param name="vertexAreas">A pre-allocated collection in which the surrounding surface areas will be stored.</param>
/// <returns>The surrounding spherical surface areas of the vertices.</returns>
/// <seealso cref="O:MakeIt.Tile.EdgeAttributeUtility.CalculateSphericalFaceCentroidAnglesFromFaceCentroids"/>
public static IVertexAttribute <float> CalculateSphericalVertexAreasFromFaceCentroidAngles(Topology.VerticesIndexer vertices, SphericalSurface surface, IEdgeAttribute <float> faceCentroidAngles, IVertexAttribute <float> vertexAreas)
{
var radiusSquared = surface.radius * surface.radius;
foreach (var vertex in vertices)
{
float angleSum = 0f;
foreach (var edge in vertex.edges)
{
angleSum += faceCentroidAngles[edge];
}
vertexAreas[vertex] = (angleSum - Mathf.PI) * radiusSquared;
}
return(vertexAreas);
}
/// <summary>
/// Calculates the spherical surface area around each vertex that is closest to that vertex, based on face centroid angles of each edge.
/// </summary>
/// <param name="vertices">The collection of vertices whose areas are to be calculated.</param>
/// <param name="surface">The surface describing the overall shape of the spherical manifold.</param>
/// <param name="faceCentroidAngles">The centroid angles, in radians, of the face edges.</param>
/// <returns>The surrounding spherical surface areas of the vertices.</returns>
/// <seealso cref="O:MakeIt.Tile.EdgeAttributeUtility.CalculateSphericalFaceCentroidAnglesFromFaceCentroids"/>
public static IVertexAttribute <float> CalculateSphericalVertexAreasFromFaceCentroidAngles(Topology.VerticesIndexer vertices, SphericalSurface surface, IEdgeAttribute <float> faceCentroidAngles)
{
return(CalculateSphericalVertexAreasFromFaceCentroidAngles(vertices, surface, faceCentroidAngles, new float[vertices.Count].AsVertexAttribute()));
}
/// <summary>
/// Attempts to move the positions of vertices such that they have roughly uniform density, with a bias towards also making sure that the surface areas of the faces also become more uniform.
/// </summary>
/// <param name="surface">The spherical surface describing the overall shape of the manifold.</param>
/// <param name="topology">The topology to relax.</param>
/// <param name="vertexPositions">The original positions of the vertices to relax.</param>
/// <param name="lockBoundaryPositions">Indicates that vertices with an external neighboring face should not have their positions altered.</param>
/// <param name="relaxedVertexPositions">A pre-allocated collection in which the relaxed vertex positions will be stored. Should not be the same collection as <paramref name="vertexPositions"/>.</param>
/// <param name="faceCentroids">A pre-allocated collection in which the intermediate face centroid positions will be stored.</param>
/// <param name="vertexAreas">A pre-allocated collection in which the intermediate nearby surface areas of vertices will be stored.</param>
/// <param name="faceCentroidAngles">A pre-allocated collection in which the intermediate face centroid angles will be stored.</param>
/// <returns>The relaxed vertex positions.</returns>
public static IVertexAttribute <Vector3> RelaxVertexPositionsForEqualArea(SphericalSurface surface, Topology topology, IVertexAttribute <Vector3> vertexPositions, bool lockBoundaryPositions, IVertexAttribute <Vector3> relaxedVertexPositions, IFaceAttribute <Vector3> faceCentroids, IEdgeAttribute <float> faceCentroidAngles, IVertexAttribute <float> vertexAreas)
{
var idealArea = surface.radius * surface.radius * 4f * Mathf.PI / topology.vertices.Count;
FaceAttributeUtility.CalculateSphericalFaceCentroidsFromVertexPositions(topology.internalFaces, surface, vertexPositions, faceCentroids);
EdgeAttributeUtility.CalculateSphericalFaceCentroidAnglesFromFaceCentroids(topology.faceEdges, surface, faceCentroids, faceCentroidAngles);
VertexAttributeUtility.CalculateSphericalVertexAreasFromFaceCentroidAngles(topology.vertices, surface, faceCentroidAngles, vertexAreas);
for (int i = 0; i < topology.vertices.Count; ++i)
{
relaxedVertexPositions[i] = new Vector3(0f, 0f, 0f);
}
foreach (var vertex in topology.vertices)
{
var multiplier = Mathf.Sqrt(idealArea / vertexAreas[vertex]);
foreach (var edge in vertex.edges)
{
var neighborVertex = edge.vertex;
var neighborRelativeCenter = vertexPositions[edge.twin];
relaxedVertexPositions[neighborVertex] += (vertexPositions[neighborVertex] - neighborRelativeCenter) * multiplier + neighborRelativeCenter;
}
}
foreach (var vertex in topology.vertices)
{
if (!lockBoundaryPositions || !vertex.hasExternalFaceNeighbor)
{
relaxedVertexPositions[vertex] = relaxedVertexPositions[vertex].WithMagnitude(surface.radius);
}
else
{
relaxedVertexPositions[vertex] = vertexPositions[vertex];
}
}
return(relaxedVertexPositions);
}