/// <summary>
/// Creates a manifold, consisting of a topology and vertex positions, in the shape of an icosahedron.
/// </summary>
/// <param name="surface">The spherical surface describing the overall shape of the manifold.</param>
/// <param name="topology">The topology created.</param>
/// <param name="vertexPositions">The vertex positions created.</param>
public static void CreateIcosahedron(SphericalSurface surface, out Topology topology, out Vector3[] vertexPositions)
{
var latitude = Mathf.Atan2(1, 2);
var longitude = Mathf.PI * 0.2f;
var cosLat = Mathf.Cos(latitude);
var scaledCosLat = surface.radius * cosLat;
var x0 = 0.0f;
var x1 = scaledCosLat * Mathf.Sin(longitude);
var x2 = scaledCosLat * Mathf.Sin(longitude * 2.0f);
var y0 = +surface.radius;
var y1 = surface.radius * Mathf.Sin(latitude);
var y2 = -surface.radius;
var z0 = scaledCosLat;
var z1 = scaledCosLat * Mathf.Cos(longitude);
var z2 = scaledCosLat * Mathf.Cos(longitude * 2.0f);
vertexPositions = new Vector3[12];
vertexPositions[0] = new Vector3(x0, y0, 0f);
vertexPositions[1] = new Vector3(x0, +y1, -z0);
vertexPositions[2] = new Vector3(-x2, +y1, -z2);
vertexPositions[3] = new Vector3(-x1, +y1, +z1);
vertexPositions[4] = new Vector3(+x1, +y1, +z1);
vertexPositions[5] = new Vector3(+x2, +y1, -z2);
vertexPositions[6] = new Vector3(x0, -y1, +z0);
vertexPositions[7] = new Vector3(-x2, -y1, +z2);
vertexPositions[8] = new Vector3(-x1, -y1, -z1);
vertexPositions[9] = new Vector3(+x1, -y1, -z1);
vertexPositions[10] = new Vector3(+x2, -y1, +z2);
vertexPositions[11] = new Vector3(x0, y2, 0f);
var orientation = surface.orientation;
for (int i = 0; i < vertexPositions.Length; ++i)
{
vertexPositions[i] = orientation * vertexPositions[i];
}
var indexer = new ManualFaceNeighborIndexer(12, 60, 20);
if (!surface.isInverted)
{
indexer.AddFace(0, 1, 2);
indexer.AddFace(0, 2, 3);
indexer.AddFace(0, 3, 4);
indexer.AddFace(0, 4, 5);
indexer.AddFace(0, 5, 1);
indexer.AddFace(1, 8, 2);
indexer.AddFace(2, 8, 7);
indexer.AddFace(2, 7, 3);
indexer.AddFace(3, 7, 6);
indexer.AddFace(3, 6, 4);
indexer.AddFace(4, 6, 10);
indexer.AddFace(4, 10, 5);
indexer.AddFace(5, 10, 9);
indexer.AddFace(5, 9, 1);
indexer.AddFace(1, 9, 8);
indexer.AddFace(11, 6, 7);
indexer.AddFace(11, 7, 8);
indexer.AddFace(11, 8, 9);
indexer.AddFace(11, 9, 10);
indexer.AddFace(11, 10, 6);
}
else
{
indexer.AddFace(2, 1, 0);
indexer.AddFace(3, 2, 0);
indexer.AddFace(4, 3, 0);
indexer.AddFace(5, 4, 0);
indexer.AddFace(1, 5, 0);
indexer.AddFace(2, 8, 1);
indexer.AddFace(7, 8, 2);
indexer.AddFace(3, 7, 2);
indexer.AddFace(6, 7, 3);
indexer.AddFace(4, 6, 3);
indexer.AddFace(10, 6, 4);
indexer.AddFace(5, 10, 4);
indexer.AddFace(9, 10, 5);
indexer.AddFace(1, 9, 5);
indexer.AddFace(8, 9, 1);
indexer.AddFace(7, 6, 11);
indexer.AddFace(8, 7, 11);
indexer.AddFace(9, 8, 11);
indexer.AddFace(10, 9, 11);
indexer.AddFace(6, 10, 11);
}
topology = TopologyUtility.BuildTopology(indexer);
}
/// <summary>
/// Reverses the roles of vertices and faces, as when taking the dual of a polyhedron.
/// </summary>
/// <param name="surface">The spherical surface describing the overall shape of the manifold.</param>
/// <param name="topology">The topology containing the vertices and faces to swap.</param>
/// <param name="vertexPositions">The positions of the vertices, which will become the new positions after the call is complete, calculated as the face centroids of the original topology.</param>
public static void MakeDual(SphericalSurface surface, Topology topology, ref Vector3[] vertexPositions)
{
ManifoldUtility.MakeDual(topology, FaceAttributeUtility.CalculateSphericalFaceCentroidsFromVertexPositions(topology.faces, surface, vertexPositions.AsVertexAttribute()), out vertexPositions);
}
/// <summary>
/// Creates a manifold, consisting of a topology and vertex positions, in the shape of a dodecahedron.
/// </summary>
/// <param name="surface">The spherical surface describing the overall shape of the manifold.</param>
/// <param name="topology">The topology created.</param>
/// <param name="vertexPositions">The vertex positions created.</param>
public static void CreateDodecahedron(SphericalSurface surface, out Topology topology, out Vector3[] vertexPositions)
{
CreateIcosahedron(surface, out topology, out vertexPositions);
MakeDual(surface, topology, ref vertexPositions);
}
protected override void OnPropertiesGUI()
{
var generator = (PlanarManifoldGenerator)target;
EditorGUILayout.PropertyField(_serializedGenerator.FindProperty("size"), new GUIContent("Size"));
EditorGUILayout.Space();
generator.tileType = (PlanarManifoldGenerator.TileTypes)EditorGUILayout.EnumPopup("Tile Type", generator.tileType);
switch (generator.tileType)
{
case PlanarManifoldGenerator.TileTypes.Quadrilateral:
{
generator.SetQuadTileShape((PlanarManifoldGenerator.QuadTileShapes)EditorGUILayout.EnumPopup("Tile Shape", generator.quadTileShape));
bool canGenerate = generator.canGenerate;
RectangularQuadGrid surface = null;
Topology topology = null;
Vector3[] vertexPositions = null;
if (canGenerate && Event.current.type == EventType.Repaint)
{
surface = generator.ResetSurface(CreateInstance <RectangularQuadGrid>(), Vector3.zero, Quaternion.identity, true, new Numerics.IntVector2(3, 3));
topology = surface.CreateManifold(out vertexPositions);
}
EditorGUILayout.BeginHorizontal();
{
EditorGUILayout.Space();
float previewSize = 128f;
var previewRect = GUILayoutUtility.GetRect(previewSize, previewSize + _previewStyle.margin.top + _previewStyle.margin.bottom, _previewStyle, GUILayout.ExpandWidth(false));
if (canGenerate && Event.current.type == EventType.Repaint)
{
DrawQuadTilePreview(generator, previewRect.min, previewSize);
}
EditorGUILayout.Space();
previewRect = GUILayoutUtility.GetRect(previewSize, previewSize + _previewStyle.margin.top + _previewStyle.margin.bottom, _previewStyle, GUILayout.ExpandWidth(false));
if (canGenerate && Event.current.type == EventType.Repaint)
{
DrawQuadTile3x3Preview(generator, topology, vertexPositions, previewRect.min, previewSize);
}
EditorGUILayout.Space();
}
EditorGUILayout.EndHorizontal();
EditorGUI.BeginChangeCheck();
generator.axis0 = EditorGUILayout.Vector2Field("Axis 0", generator.axis0);
generator.axis1 = EditorGUILayout.Vector2Field("Axis 1", generator.axis1);
if (EditorGUI.EndChangeCheck())
{
generator.SetQuadTileShape(PlanarManifoldGenerator.QuadTileShapes.Custom);
}
break;
}
case PlanarManifoldGenerator.TileTypes.Hexagonal:
{
generator.SetHexTileShape((PlanarManifoldGenerator.HexTileShapes)EditorGUILayout.EnumPopup("Tile Shape", generator.hexTileShape));
bool canGenerate = generator.canGenerate;
RectangularHexGrid surface = null;
Topology topology = null;
Vector3[] vertexPositions = null;
if (canGenerate && Event.current.type == EventType.Repaint)
{
surface = generator.ResetSurface(CreateInstance <RectangularHexGrid>(), Vector3.zero, Quaternion.identity, true, new Numerics.IntVector2(3, 3));
topology = surface.CreateManifold(out vertexPositions);
}
EditorGUILayout.BeginHorizontal();
{
EditorGUILayout.Space();
float previewSize = 128f;
var previewRect = GUILayoutUtility.GetRect(previewSize, previewSize + _previewStyle.margin.top + _previewStyle.margin.bottom, _previewStyle, GUILayout.ExpandWidth(false));
if (canGenerate && Event.current.type == EventType.Repaint)
{
DrawHexTilePreview(generator, surface, topology, vertexPositions, previewRect.min, previewSize);
}
EditorGUILayout.Space();
previewRect = GUILayoutUtility.GetRect(previewSize, previewSize + _previewStyle.margin.top + _previewStyle.margin.bottom, _previewStyle, GUILayout.ExpandWidth(false));
if (canGenerate && Event.current.type == EventType.Repaint)
{
DrawHexTile3x3Preview(generator, surface, topology, vertexPositions, previewRect.min, previewSize);
}
EditorGUILayout.Space();
}
EditorGUILayout.EndHorizontal();
EditorGUI.BeginChangeCheck();
generator.midpoint = EditorGUILayout.Vector2Field("Midpoint", generator.midpoint);
generator.majorCorner = EditorGUILayout.Vector2Field("Major Corner", generator.majorCorner);
generator.minorCorner = EditorGUILayout.Vector2Field("Minor Corner", generator.minorCorner);
generator.hexGridAxisStyle = (HexGridAxisStyles)EditorGUILayout.EnumPopup("Axis Style", generator.hexGridAxisStyle);
generator.swapAxes = EditorGUILayout.Toggle("Swap Axes", generator.swapAxes);
if (EditorGUI.EndChangeCheck())
{
generator.SetHexTileShape(PlanarManifoldGenerator.HexTileShapes.Custom);
}
break;
}
default: throw new System.NotImplementedException();
}
generator.isAxis0Wrapped = EditorGUILayout.Toggle("Axis 0 Wraps", generator.isAxis0Wrapped, GUILayout.ExpandWidth(false));
generator.isAxis1Wrapped = EditorGUILayout.Toggle("Axis 1 Wraps", generator.isAxis1Wrapped, GUILayout.ExpandWidth(false));
EditorGUILayout.Space();
generator.origin = EditorGUILayout.Vector3Field("Origin", generator.origin);
generator.rotation = EditorGUILayout.Vector3Field("Rotation", generator.rotation);
}
private void DrawHexTile3x3Preview(PlanarManifoldGenerator generator, RectangularHexGrid surface, Topology topology, Vector3[] vertexPositions, Vector3 root, float previewSize)
{
var adjustedVertexPositions = new Vector3[vertexPositions.Length].AsVertexAttribute();
Vector3 min = vertexPositions[0];
Vector3 max = vertexPositions[0];
for (int i = 1; i < vertexPositions.Length; ++i)
{
min = Vector3.Min(min, vertexPositions[i]);
max = Vector3.Max(max, vertexPositions[i]);
}
Vector3 range = max - min;
float maxRange = Mathf.Max(range.x, range.y);
Vector3 margin = (new Vector3(maxRange, maxRange, 0f) - range) * 0.5f;
Vector3 offset = margin - min;
float scale = previewSize / maxRange;
for (int i = 0; i < vertexPositions.Length; ++i)
{
adjustedVertexPositions[i] = AdjustPosition(vertexPositions[i], offset, root, maxRange, scale);
}
var faceVertexPositions = new Vector3[6];
Handles.color = fillColor;
foreach (var face in topology.internalFaces)
{
var edge = face.firstEdge;
for (int i = 0; i < 6; ++i)
{
faceVertexPositions[i] = adjustedVertexPositions[edge];
edge = edge.next;
}
Handles.DrawAAConvexPolygon(faceVertexPositions);
}
Handles.color = outlineColor;
foreach (var edge in topology.vertexEdges)
{
if (edge.nearVertex < edge.farVertex)
{
Handles.DrawAAPolyLine(adjustedVertexPositions[edge.nearVertex], adjustedVertexPositions[edge.farVertex]);
}
}
var p0 = adjustedVertexPositions[surface.GetVertexIndex(0, 0)];;
if (!generator.swapAxes)
{
var a01 = adjustedVertexPositions[surface.GetVertexIndex(2, 0)];
var a02 = adjustedVertexPositions[surface.GetVertexIndex(4, 0)];
var a11 = adjustedVertexPositions[surface.GetVertexIndex(0, 1)];
var a12 = adjustedVertexPositions[surface.GetVertexIndex(0, 2)];
Handles.color = Handles.xAxisColor;
Handles.DrawAAPolyLine(p0, a01, a02);
Handles.DrawSolidDisc(a01, Vector3.back, 3f);
Handles.DrawSolidDisc(a02, Vector3.back, 3f);
if (generator.hexGridAxisStyle != HexGridAxisStyles.Straight)
{
Handles.color = ChangeAlpha(Handles.yAxisColor + Color.white * 0.25f, 0.75f);
Handles.DrawAAPolyLine(p0, a12);
}
Handles.color = Handles.yAxisColor;
Handles.DrawAAPolyLine(p0, a11, a12);
Handles.DrawSolidDisc(a11, Vector3.back, 3f);
Handles.DrawSolidDisc(a12, Vector3.back, 3f);
}
else
{
var a01 = adjustedVertexPositions[surface.GetVertexIndex(1, 0)];
var a02 = adjustedVertexPositions[surface.GetVertexIndex(2, 0)];
var a11 = adjustedVertexPositions[surface.GetVertexIndex(0, 2)];
var a12 = adjustedVertexPositions[surface.GetVertexIndex(0, 4)];
if (generator.hexGridAxisStyle != HexGridAxisStyles.Straight)
{
Handles.color = ChangeAlpha(Handles.xAxisColor + Color.white * 0.25f, 0.75f);
Handles.DrawAAPolyLine(p0, a02);
}
Handles.color = Handles.xAxisColor;
Handles.DrawAAPolyLine(p0, a01, a02);
Handles.DrawSolidDisc(a01, Vector3.back, 3f);
Handles.DrawSolidDisc(a02, Vector3.back, 3f);
Handles.color = Handles.yAxisColor;
Handles.DrawAAPolyLine(p0, a11, a12);
Handles.DrawSolidDisc(a11, Vector3.back, 3f);
Handles.DrawSolidDisc(a12, Vector3.back, 3f);
}
}
private void DrawHexTilePreview(PlanarManifoldGenerator generator, RectangularHexGrid surface, Topology topology, Vector3[] vertexPositions, Vector3 root, float previewSize)
{
var face = topology.internalFaces[0];
var adjustedVertexPositions = new Vector3[face.neighborCount].AsVertexAttribute();
var firstEdge = face.firstEdge;
var pos = vertexPositions[firstEdge.vertex.index];
Vector3 min = pos;
Vector3 max = pos;
var edge = firstEdge.next;
while (edge != firstEdge)
{
pos = vertexPositions[edge.vertex.index];
min = Vector3.Min(min, pos);
max = Vector3.Max(max, pos);
edge = edge.next;
}
Vector3 range = max - min;
float maxRange = Mathf.Max(range.x, range.y);
Vector3 margin = (new Vector3(maxRange, maxRange, 0f) - range) * 0.5f;
Vector3 offset = margin - min;
float scale = previewSize / maxRange;
for (int i = 0; i < face.neighborCount; ++i)
{
adjustedVertexPositions[i] = AdjustPosition(vertexPositions[edge.vertex.index], offset, root, maxRange, scale);
edge = edge.next;
}
Handles.color = fillColor;
Handles.DrawAAConvexPolygon(adjustedVertexPositions.array);
Handles.color = outlineColor;
Handles.DrawAAPolyLine(adjustedVertexPositions.array);
Handles.DrawAAPolyLine(adjustedVertexPositions[5], adjustedVertexPositions[0]);
Vector2 pC = (vertexPositions[firstEdge.vertex.index] + vertexPositions[firstEdge.next.next.next.vertex.index]) * 0.5f;
Vector3 vC = AdjustPosition(pC, offset, root, maxRange, scale);
Vector3 v2 = AdjustPosition(pC + generator.majorCorner, offset, root, maxRange, scale);
Vector3 v3 = AdjustPosition(pC + generator.minorCorner, offset, root, maxRange, scale);
Vector3 vM = AdjustPosition(pC + generator.midpoint, offset, root, maxRange, scale);
var midpointColor = generator.swapAxes ? Handles.yAxisColor : Handles.xAxisColor;
Handles.color = midpointColor;
Handles.DrawAAPolyLine(vC, vM);
Handles.color = ChangeAlpha(midpointColor, 0.25f);
Handles.DrawSolidDisc(vM, Vector3.back, 5f);
Handles.color = midpointColor;
Handles.DrawWireDisc(vM, Vector3.back, 5f);
Color majorCornerColor;
if (generator.hexGridAxisStyle == HexGridAxisStyles.Straight)
{
majorCornerColor = Embolden(Average(Handles.xAxisColor, Handles.yAxisColor));
}
else
{
majorCornerColor = generator.swapAxes ? Handles.xAxisColor : Handles.yAxisColor;
}
Handles.color = majorCornerColor;
Handles.DrawAAPolyLine(vC, v2);
Handles.color = ChangeAlpha(majorCornerColor, 0.25f);
Handles.DrawSolidDisc(v2, Vector3.back, 5f);
Handles.color = majorCornerColor;
Handles.DrawWireDisc(v2, Vector3.back, 5f);
Color minorCornerColor = Handles.zAxisColor;
Handles.color = minorCornerColor;
Handles.DrawAAPolyLine(vC, v3);
Handles.color = ChangeAlpha(minorCornerColor, 0.25f);
Handles.DrawSolidDisc(v3, Vector3.back, 5f);
Handles.color = minorCornerColor;
Handles.DrawWireDisc(v3, Vector3.back, 5f);
if (generator.hexGridAxisStyle == HexGridAxisStyles.Straight)
{
Handles.color = generator.swapAxes ? Handles.xAxisColor : Handles.yAxisColor;
Handles.DrawAAPolyLine(vC, (v2 + v3) * 0.5f);
}
}
private void DrawQuadTile3x3Preview(PlanarManifoldGenerator generator, Topology topology, Vector3[] vertexPositions, Vector3 root, float previewSize)
{
var adjustedVertexPositions = new Vector3[vertexPositions.Length].AsVertexAttribute();
Vector3 min = vertexPositions[0];
Vector3 max = vertexPositions[0];
for (int i = 1; i < vertexPositions.Length; ++i)
{
min = Vector3.Min(min, vertexPositions[i]);
max = Vector3.Max(max, vertexPositions[i]);
}
Vector3 range = max - min;
float maxRange = Mathf.Max(range.x, range.y);
Vector3 margin = (new Vector3(maxRange, maxRange, 0f) - range) * 0.5f;
Vector3 offset = margin - min;
float scale = previewSize / maxRange;
for (int i = 0; i < vertexPositions.Length; ++i)
{
adjustedVertexPositions[i] = AdjustPosition(vertexPositions[i], offset, root, maxRange, scale);
}
var faceVertexPositions = new Vector3[4];
Handles.color = fillColor;
foreach (var face in topology.internalFaces)
{
var edge = face.firstEdge;
for (int i = 0; i < 4; ++i)
{
faceVertexPositions[i] = adjustedVertexPositions[edge];
edge = edge.next;
}
Handles.DrawAAConvexPolygon(faceVertexPositions);
}
Handles.color = outlineColor;
foreach (var edge in topology.vertexEdges)
{
if (edge.nearVertex < edge.farVertex)
{
Handles.DrawAAPolyLine(adjustedVertexPositions[edge.nearVertex], adjustedVertexPositions[edge.farVertex]);
}
}
var p0 = AdjustPosition(Vector3.zero, offset, root, maxRange, scale);
var a01 = AdjustPosition(generator.axis0 * 1f, offset, root, maxRange, scale);
var a02 = AdjustPosition(generator.axis0 * 2f, offset, root, maxRange, scale);
var a03 = AdjustPosition(generator.axis0 * 3f, offset, root, maxRange, scale);
var a11 = AdjustPosition(generator.axis1 * 1f, offset, root, maxRange, scale);
var a12 = AdjustPosition(generator.axis1 * 2f, offset, root, maxRange, scale);
var a13 = AdjustPosition(generator.axis1 * 3f, offset, root, maxRange, scale);
Handles.color = Handles.xAxisColor;
Handles.DrawAAPolyLine(p0, a03);
Handles.DrawSolidDisc(a01, Vector3.back, 3f);
Handles.DrawSolidDisc(a02, Vector3.back, 3f);
Handles.DrawSolidDisc(a03, Vector3.back, 3f);
Handles.color = Handles.yAxisColor;
Handles.DrawAAPolyLine(p0, a13);
Handles.DrawSolidDisc(a11, Vector3.back, 3f);
Handles.DrawSolidDisc(a12, Vector3.back, 3f);
Handles.DrawSolidDisc(a13, Vector3.back, 3f);
}