uc-hoba
/
Test-Planet
Archived
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

feat: add Goldberg polyhedron generation functionality

Browse Source
master
hoba 10 months ago
parent aa63c7d28e
commit 321d9fbb03
10 changed files with 1255 additions and 49 deletions
Whitespace
Show all changes Ignore whitespace when comparing lines Ignore changes in amount of whitespace Ignore changes in whitespace at EOL
Split View
Diff Options
Show Stats Download Patch File Download Diff File
  1. 4
      Assets/Resources/New GoldbergPolyhedron.gph.meta
  2. 21
      Assets/Scripts/Editor/GoldbergPolyhedronImporter.cs
  3. 987
      Assets/Scripts/GeodesicMesh.cs
  4. 2
      Assets/Scripts/GeodesicMesh.cs.meta
  5. 174
      Assets/Scripts/GoldbergBuilder.cs
  6. 2
      Assets/Scripts/GoldbergBuilder.cs.meta
  7. 43
      Assets/Scripts/GoldbergPolyhedron.cs
  8. 2
      Assets/Scripts/GoldbergPolyhedron.cs.meta
  9. 67
      Assets/Scripts/IsoVector.cs
  10. 2
      Assets/Scripts/IsoVector.cs.meta

4
Assets/Resources/New GoldbergPolyhedron.gph.meta
Unescape View File

@ -9,6 +9,8 @@ ScriptedImporter:
assetBundleVariant:
script: {fileID: 11500000, guid: 80f1e0e8eacc4a945b07bba9e3065c99, type: 3}
radius: 1
subdivision: 3
subdivision: 4
m: 1
n: 0
generateLightmapUVs: 0
readWriteMeshes: 0

21
Assets/Scripts/Editor/GoldbergPolyhedronImporter.cs
Unescape View File

@ -4,6 +4,7 @@ using UnityEditor;
using UnityEditor.AssetImporters;
using UnityEngine;
using UnityEngine.Rendering;
using static Metamesh.GoldbergBuilder;
namespace Metamesh
{
@ -12,6 +13,9 @@ namespace Metamesh
{
[SerializeField] float radius = 1;
[SerializeField, Min(2)] uint subdivision = 2;
[SerializeField, Min(1)] int m = 1;
[SerializeField, Min(0)] int n = 0;
[SerializeField] bool generateLightmapUVs = false;
[SerializeField] bool readWriteMeshes = false;
@ -42,7 +46,7 @@ namespace Metamesh
{
var mesh = new Mesh();
mesh.name = "Mesh";
/*
var builder = new IcosphereBuilder();
for (var i = 1; i < subdivision; ++i)
{
@ -54,8 +58,19 @@ namespace Metamesh
var indices = builder.Indices.ToList();
ApplyGoldbergTransformation(vertices, normals, indices);
if (builder.VertexCount > 65535) mesh.indexFormat = IndexFormat.UInt32;
*/
var builder = new GoldbergBuilder();
var options = new GoldbergCreationOption()
{
m = m,
n = n,
};
var data = builder.CreateGoldberg(options);
var vertices = data.vertices;
var normals = data.normals;
var indices = data.indices;
if (vertices.Count > 65535) mesh.indexFormat = IndexFormat.UInt32;
mesh.SetVertices(vertices);
mesh.SetNormals(normals);
mesh.SetIndices(indices, MeshTopology.Triangles, 0);

987
Assets/Scripts/GeodesicMesh.cs
Unescape View File

@ -0,0 +1,987 @@
using System;
using System.Collections.Generic;
using System.Linq;
using UnityEngine;
namespace Metamesh
{
public class PrimaryIsoTriangle
{
public int m;
public int n;
public List<Vector3> cartesian = new List<Vector3>();
public List<IsoVector> vertices = new List<IsoVector>();
public List<int> max = new List<int>();
public List<int> min = new List<int>();
public Dictionary<string, int> vecToidx = new Dictionary<string, int>();
public Dictionary<string, List<int>> vertByDist = new Dictionary<string, List<int>>();
public List<List<int>> closestTo = new List<List<int>>();
public List<List<string>> innerFacets = new List<List<string>>();
public List<List<IsoVector>> isoVecsABOB = new List<List<IsoVector>>();
public List<List<IsoVector>> isoVecsOBOA = new List<List<IsoVector>>();
public List<List<IsoVector>> isoVecsBAOA = new List<List<IsoVector>>();
public List<List<int>> vertexTypes = new List<List<int>>();
public float coau;
public float cobu;
public float coav;
public float cobv;
//float PHI = (1 + Mathf.Sqrt(5f)) / 2;
const float PHI = 1.618034f;
public PolyhedronData IDATA = new PolyhedronData(
"icosahedron",
"Regular",
new List<Vector3> {
new Vector3(0, PHI, -1),
new Vector3(-PHI, 1, 0),
new Vector3(-1, 0, -PHI),
new Vector3(1, 0, -PHI),
new Vector3(PHI, 1, 0),
new Vector3(0, PHI, 1),
new Vector3(-1, 0, PHI),
new Vector3(-PHI, -1, 0),
new Vector3(0, -PHI, -1),
new Vector3(PHI, -1, 0),
new Vector3(1, 0, PHI),
new Vector3(0, -PHI, 1),
},
new List<List<int>> {
new List<int> {0, 2, 1},
new List<int> {0, 3, 2},
new List<int> {0, 4, 3},
new List<int> {0, 5, 4},
new List<int> {0, 1, 5},
new List<int> {7, 6, 1},
new List<int> {8, 7, 2},
new List<int> {9, 8, 3},
new List<int> {10, 9, 4},
new List<int> {6, 10, 5},
new List<int> {2, 7, 1},
new List<int> {3, 8, 2},
new List<int> {4, 9, 3},
new List<int> {5, 10, 4},
new List<int> {1, 6, 5},
new List<int> {11, 6, 7},
new List<int> {11, 7, 8},
new List<int> {11, 8, 9},
new List<int> {11, 9, 10},
new List<int> {11, 10, 6},
}
);
private int HighestCommonFactor(int a, int b)
{
var r = a % b;
if (r == 0)
{
return b;
}
return HighestCommonFactor(b, r);
}
public void SetIndices()
{
var indexCount = 12; // 12 vertices already assigned
var vecToidx = new Dictionary<string, int>();
var m = this.m;
var n = this.n;
var g = m; // hcf of m, n when n != 0
var m1 = 1;
var n1 = 0;
if (n != 0)
{
g = HighestCommonFactor(m, n);
}
m1 = m / g;
n1 = n / g;
int fr; //face to the right of current face
string rot; //rotation about which vertex for fr
int O;
int A;
int B;
var oVec = IsoVector.Zero();
var aVec = new IsoVector(m, n);
var bVec = new IsoVector(-n, m + n);
var oaVec = IsoVector.Zero();
var abVec = IsoVector.Zero();
var obVec = IsoVector.Zero();
var verts = new List<int>();
string idx;
string idxR;
string isoId;
string isoIdR;
var closestTo = new List<List<int>>();
var vDist = this.vertByDist;
System.Action<int, int, string, string> matchIdx = (f, fr, isoId, isoIdR) =>
{
idx = f + "|" + isoId;
idxR = fr + "|" + isoIdR;
if (!(vecToidx.ContainsKey(idx) || vecToidx.ContainsKey(idxR)))
{
vecToidx[idx] = indexCount;
vecToidx[idxR] = indexCount;
indexCount++;
}
else if (vecToidx.ContainsKey(idx) && !(vecToidx.ContainsKey(idxR)))
{
vecToidx[idxR] = vecToidx[idx];
}
else if (vecToidx.ContainsKey(idxR) && !(vecToidx.ContainsKey(idx)))
{
vecToidx[idx] = vecToidx[idxR];
}
if (vDist[isoId][0] > 2)
{
closestTo[vecToidx[idx]] = new List<int> { -vDist[isoId][0], vDist[isoId][1], vecToidx[idx] };
}
else
{
closestTo[vecToidx[idx]] = new List<int> { verts[vDist[isoId][0]], vDist[isoId][1], vecToidx[idx] };
}
};
this.IDATA.edgematch = new List<(int, string, int, string)> {
(1, "B", 0, ""),
(2, "B", 0, ""),
(3, "B", 0, ""),
(4, "B", 0, ""),
(0, "B", 0, ""),
(10, "O", 14, "A"),
(11, "O", 10, "A"),
(12, "O", 11, "A"),
(13, "O", 12, "A"),
(14, "O", 13, "A"),
(0, "O", 0, ""),
(1, "O", 0, ""),
(2, "O", 0, ""),
(3, "O", 0, ""),
(4, "O", 0, ""),
(19, "B", 5, "A"),
(15, "B", 6, "A"),
(16, "B", 7, "A"),
(17, "B", 8, "A"),
(18, "B", 9, "A"),
};
/***edges AB to OB***** rotation about B*/
for (var f = 0; f < 20; f++)
{
//f current face
verts = this.IDATA.face[f];
O = verts[2];
A = verts[1];
B = verts[0];
isoId = oVec.x + "|" + oVec.y;
idx = f + "|" + isoId;
if (!vecToidx.ContainsKey(idx))
{
vecToidx[idx] = O;
closestTo[O] = new List<int> { verts[vDist[isoId][0]], vDist[isoId][1] };
}
isoId = aVec.x + "|" + aVec.y;
idx = f + "|" + isoId;
if (!vecToidx.ContainsKey(idx))
{
vecToidx[idx] = A;
closestTo[A] = new List<int> { verts[vDist[isoId][0]], vDist[isoId][1] };
}
isoId = bVec.x + "|" + bVec.y;
idx = f + "|" + isoId;
if (!vecToidx.ContainsKey(idx))
{
vecToidx[idx] = B;
closestTo[B] = new List<int> { verts[vDist[isoId][0]], vDist[isoId][1] };
}
//for edge vertices
fr = this.IDATA.edgematch[f].Item1;
rot = this.IDATA.edgematch[f].Item2;
if (rot == "B")
{
for (var i = 1; i < g; i++)
{
abVec.x = m - i * (m1 + n1);
abVec.y = n + i * m1;
obVec.x = -i * n1;
obVec.y = i * (m1 + n1);
isoId = abVec.x + "|" + abVec.y;
isoIdR = obVec.x + "|" + obVec.y;
matchIdx(f, fr, isoId, isoIdR);
}
}
if (rot == "O")
{
for (var i = 1; i < g; i++)
{
obVec.x = -i * n1;
obVec.y = i * (m1 + n1);
oaVec.x = i * m1;
oaVec.y = i * n1;
isoId = obVec.x + "|" + obVec.y;
isoIdR = oaVec.x + "|" + oaVec.y;
matchIdx(f, fr, isoId, isoIdR);
}
}
fr = this.IDATA.edgematch[f].Item3;
rot = this.IDATA.edgematch[f].Item4;
if (rot == "A")
{
for (var i = 1; i < g; i++)
{
oaVec.x = i * m1;
oaVec.y = i * n1;
abVec.x = m - (g - i) * (m1 + n1); //reversed for BA
abVec.y = n + (g - i) * m1; //reversed for BA
isoId = oaVec.x + "|" + oaVec.y;
isoIdR = abVec.x + "|" + abVec.y;
matchIdx(f, fr, isoId, isoIdR);
}
}
for (var i = 0; i < this.vertices.Count; i++)
{
isoId = this.vertices[i].x + "|" + this.vertices[i].y;
idx = f + "|" + isoId;
if (!vecToidx.ContainsKey(idx))
{
vecToidx[idx] = indexCount++;
if (vDist[isoId][0] > 2)
{
closestTo[vecToidx[idx]] = new List<int> { -vDist[isoId][0], vDist[isoId][1], vecToidx[idx] };
}
else
{
closestTo[vecToidx[idx]] = new List<int> { verts[vDist[isoId][0]], vDist[isoId][1], vecToidx[idx] };
}
}
}
}
this.closestTo = closestTo;
this.vecToidx = vecToidx;
}
public void CalcCoeffs()
{
var m = this.m;
var n = this.n;
var thirdR3 = Mathf.Sqrt(3) / 3;
var LSQD = m * m + n * n + m * n;
this.coau = (m + n) / LSQD;
this.cobu = -n / LSQD;
this.coav = (-thirdR3 * (m - n)) / LSQD;
this.cobv = (thirdR3 * (2 * m + n)) / LSQD;
}
public void CreateInnerFacets()
{
var m = this.m;
var n = this.n;
for (var y = 0; y < n + m + 1; y++)
{
for (var x = this.min[y]; x < this.max[y] + 1; x++)
{
if (x < this.max[y] && x < this.max[y + 1] + 1)
{
this.innerFacets.Add(new List<string> { "|" + x + "|" + y, "|" + x + "|" + (y + 1), "|" + (x + 1) + "|" + y });
}
if (y > 0 && x < this.max[y - 1] && x + 1 < this.max[y] + 1)
{
this.innerFacets.Add(new List<string> { "|" + x + "|" + y, "|" + (x + 1) + "|" + y, "|" + (x + 1) + "|" + (y - 1) });
}
}
}
}
public void EdgeVecsABOB()
{
var m = this.m;
var n = this.n;
var B = new IsoVector(-n, m + n);
for (var y = 1; y < m + n; y++)
{
var point = new IsoVector(this.min[y], y);
var prev = new IsoVector(this.min[y - 1], y - 1);
var next = new IsoVector(this.min[y + 1], y + 1);
var pointR = point.Clone();
var prevR = prev.Clone();
var nextR = next.Clone();
pointR.Rotate60About(B);
prevR.Rotate60About(B);
nextR.Rotate60About(B);
var maxPoint = new IsoVector(this.max[pointR.y], pointR.y);
var maxPrev = new IsoVector(this.max[pointR.y - 1], pointR.y - 1);
var maxLeftPrev = new IsoVector(this.max[pointR.y - 1] - 1, pointR.y - 1);
if (pointR.x != maxPoint.x || pointR.y != maxPoint.y)
{
if (pointR.x != maxPrev.x)
{
// type2
//up
this.vertexTypes.Add(new List<int> { 1, 0, 0 });
this.isoVecsABOB.Add(new List<IsoVector> { point, maxPrev, maxLeftPrev });
//down
this.vertexTypes.Add(new List<int> { 1, 0, 0 });
this.isoVecsABOB.Add(new List<IsoVector> { point, maxLeftPrev, maxPoint });
}
else if (pointR.y == nextR.y)
{
// type1
//up
this.vertexTypes.Add(new List<int> { 1, 1, 0 });
this.isoVecsABOB.Add(new List<IsoVector> { point, prev, maxPrev });
//down
this.vertexTypes.Add(new List<int> { 1, 0, 1 });
this.isoVecsABOB.Add(new List<IsoVector> { point, maxPrev, next });
}
else
{
// type 0
//up
this.vertexTypes.Add(new List<int> { 1, 1, 0 });
this.isoVecsABOB.Add(new List<IsoVector> { point, prev, maxPrev });
//down
this.vertexTypes.Add(new List<int> { 1, 0, 0 });
this.isoVecsABOB.Add(new List<IsoVector> { point, maxPrev, maxPoint });
}
}
}
}
public void MapABOBtoOBOA()
{
var point = new IsoVector(0, 0);
for (var i = 0; i < this.isoVecsABOB.Count; i++)
{
var temp = new List<IsoVector>();
for (var j = 0; j < 3; j++)
{
point.x = this.isoVecsABOB[i][j].x;
point.y = this.isoVecsABOB[i][j].y;
if (this.vertexTypes[i][j] == 0)
{
point.RotateNeg120(this.m, this.n);
}
temp.Add(point.Clone());
}
this.isoVecsOBOA.Add(temp);
}
}
public void MapABOBtoBAOA()
{
var point = new IsoVector(0, 0);
for (var i = 0; i < this.isoVecsABOB.Count; i++)
{
var temp = new List<IsoVector>();
for (var j = 0; j < 3; j++)
{
point.x = this.isoVecsABOB[i][j].x;
point.y = this.isoVecsABOB[i][j].y;
if (this.vertexTypes[i][j] == 1)
{
point.Rotate120(this.m, this.n);
}
temp.Add(point.Clone());
}
this.isoVecsBAOA.Add(temp);
}
}
public void MapToFace(int faceNb, PolyhedronData geodesicData)
{
var F = this.IDATA.face[faceNb];
var oidx = F[2];
var aidx = F[1];
var bidx = F[0];
var oidxVec = this.IDATA.vertex[oidx];
var aidxVec = this.IDATA.vertex[aidx];
var bidxVec = this.IDATA.vertex[bidx];
var O = new Vector3(oidxVec[0], oidxVec[1], oidxVec[2]);
var A = new Vector3(aidxVec[0], aidxVec[1], aidxVec[2]);
var B = new Vector3(bidxVec[0], bidxVec[1], bidxVec[2]);
var OA = A - O;
var OB = B - O;
var x = OA * this.coau + OB * this.cobu;
var y = OA * this.coav + OB * this.cobv;
var mapped = new List<List<float>>();
string idx;
for (var i = 0; i < this.cartesian.Count; i++)
{
var tempVec = x * this.cartesian[i].x + y * this.cartesian[i].y + O;
mapped[i] = new List<float> { tempVec.x, tempVec.y, tempVec.z };
idx = faceNb + "|" + this.vertices[i].x + "|" + this.vertices[i].y;
geodesicData.vertex[this.vecToidx[idx]] = tempVec;
}
}
//statics
/**Creates a primary triangle
* @internal
*/
public PrimaryIsoTriangle Build(int m, int n)
{
var vertices = new List<IsoVector>();
var O = IsoVector.Zero();
var A = new IsoVector(m, n);
var B = new IsoVector(-n, m + n);
vertices.AddRange(new IsoVector[] { O, A, B });
//max internal isoceles triangle vertices
for (var iy = n; iy < m + 1; iy++)
{
for (var ix = 0; ix < m + 1 - iy; ix++)
{
vertices.Add(new IsoVector(ix, iy));
}
}
//shared vertices along edges when needed
if (n > 0)
{
var g = HighestCommonFactor(m, n);
var m1 = m / g;
var n1 = n / g;
for (var i = 1; i < g; i++)
{
vertices.Add(new IsoVector(i * m1, i * n1)); //OA
vertices.Add(new IsoVector(-i * n1, i * (m1 + n1))); //OB
vertices.Add(new IsoVector(m - i * (m1 + n1), n + i * m1)); // AB
}
//lower rows vertices and their rotations
var ratio = m / n;
for (var iy = 1; iy < n; iy++)
{
for (var ix = 0; ix < iy * ratio; ix++)
{
vertices.Add(new IsoVector(ix, iy));
vertices.Add(new IsoVector(ix, iy).Rotate120(m, n));
vertices.Add(new IsoVector(ix, iy).RotateNeg120(m, n));
}
}
}
//order vertices by x and then y
vertices.Sort((a, b) =>
{
return a.x - b.x;
});
vertices.Sort((a, b) =>
{
return a.y - b.y;
});
var min = new List<int> { m + n + 1 };
var max = new List<int> { m + n + 1 };
for (var i = 0; i < min.Count; i++)
{
min[i] = int.MaxValue;
max[i] = int.MinValue;
}
var y = 0;
var x = 0;
var len = vertices.Count;
for (var i = 0; i < len; i++)
{
x = vertices[i].x;
y = vertices[i].y;
min[y] = Mathf.Min(x, min[y]);
max[y] = Mathf.Max(x, max[y]);
}
//calculates the distance of a vertex from a given primary vertex
Func<IsoVector, string, int> distFrom = (IsoVector vert, string primVert) =>
{
var v = vert.Clone();
if (primVert == "A")
{
v.RotateNeg120(m, n);
}
if (primVert == "B")
{
v.Rotate120(m, n);
}
if (v.x < 0)
{
return v.y;
}
return v.x + v.y;
};
var cartesian = new List<Vector3>();
var distFromO = new List<int>();
var distFromA = new List<int>();
var distFromB = new List<int>();
var vertByDist = new Dictionary<string, List<int>>();
;
var vertData = new List<List<int>>();
var closest = -1;
var dist = -1;
for (var i = 0; i < len; i++)
{
cartesian[i] = vertices[i].ToCartesianOrigin(new IsoVector(0, 0), 0.5f);
distFromO[i] = distFrom(vertices[i], "O");
distFromA[i] = distFrom(vertices[i], "A");
distFromB[i] = distFrom(vertices[i], "B");
if (distFromO[i] == distFromA[i] && distFromA[i] == distFromB[i])
{
closest = 3;
dist = distFromO[i];
}
else if (distFromO[i] == distFromA[i])
{
closest = 4;
dist = distFromO[i];
}
else if (distFromA[i] == distFromB[i])
{
closest = 5;
dist = distFromA[i];
}
else if (distFromB[i] == distFromO[i])
{
closest = 6;
dist = distFromO[i];
}
if (distFromO[i] < distFromA[i] && distFromO[i] < distFromB[i])
{
closest = 2;
dist = distFromO[i];
}
if (distFromA[i] < distFromO[i] && distFromA[i] < distFromB[i])
{
closest = 1;
dist = distFromA[i];
}
if (distFromB[i] < distFromA[i] && distFromB[i] < distFromO[i])
{
closest = 0;
dist = distFromB[i];
}
vertData.Add(new List<int> { closest, dist, vertices[i].x, vertices[i].y });
}
vertData.Sort((a, b) =>
{
return a[2].CompareTo(b[2]);
});
vertData.Sort((a, b) =>
{
return a[3].CompareTo(b[3]);
});
vertData.Sort((a, b) =>
{
return a[1].CompareTo(b[1]);
});
vertData.Sort((a, b) =>
{
return a[0].CompareTo(b[0]);
});
for (var v = 0; v < vertData.Count; v++)
{
vertByDist[vertData[v][2] + "|" + vertData[v][3]] = new List<int> { vertData[v][0], vertData[v][1], v };
}
this.m = m;
this.n = n;
this.vertices = vertices;
this.vertByDist = vertByDist;
this.cartesian = cartesian;
this.min = min;
this.max = max;
return this;
}
}
public class PolyhedronData
{
public string name;
public string category;
public List<Vector3> vertex;
public List<List<int>> face;
public List<(int, string, int, string)> edgematch;
public PolyhedronData(
string name,
string category,
List<Vector3> vertex,
List<List<int>> face
)
{
this.name = name;
this.category = category;
this.vertex = vertex;
this.face = face;
}
}
public class GeodesicData : PolyhedronData
{
//public override edgematch: (number | string)[][];
public List<List<int>> adjacentFaces;
public int sharedNodes;
public int poleNodes;
public GeodesicData(
string name,
string category,
List<Vector3> vertex,
List<List<int>> face
) : base(name, category, vertex, face)
{
}
public void innerToData(int face, PrimaryIsoTriangle primTri)
{
for (var i = 0; i < primTri.innerFacets.Count; i++)
{
this.face.Add(primTri.innerFacets[i].Select((el) => primTri.vecToidx[face + el]).ToList());
}
}
public void MapABOBtoDATA(int faceNb, PrimaryIsoTriangle primTri)
{
var fr = primTri.IDATA.edgematch[faceNb].Item1;
for (var i = 0; i < primTri.isoVecsABOB.Count; i++)
{
var temp = new List<string>();
for (var j = 0; j < 3; j++)
{
if (primTri.vertexTypes[i][j] == 0)
{
temp.Add(faceNb + "|" + primTri.isoVecsABOB[i][j].x + "|" + primTri.isoVecsABOB[i][j].y);
}
else
{
temp.Add(fr + "|" + primTri.isoVecsABOB[i][j].x + "|" + primTri.isoVecsABOB[i][j].y);
}
}
this.face.Add(new List<int> { primTri.vecToidx[temp[0]], primTri.vecToidx[temp[1]], primTri.vecToidx[temp[2]] });
}
}
/**
* @internal
*/
public void MapOBOAtoDATA(int faceNb, PrimaryIsoTriangle primTri)
{
var fr = primTri.IDATA.edgematch[faceNb].Item1;
for (var i = 0; i < primTri.isoVecsOBOA.Count; i++)
{
var temp = new List<string>();
for (var j = 0; j < 3; j++)
{
if (primTri.vertexTypes[i][j] == 1)
{
temp.Add(faceNb + "|" + primTri.isoVecsOBOA[i][j].x + "|" + primTri.isoVecsOBOA[i][j].y);
}
else
{
temp.Add(fr + "|" + primTri.isoVecsOBOA[i][j].x + "|" + primTri.isoVecsOBOA[i][j].y);
}
}
this.face.Add(new List<int> { primTri.vecToidx[temp[0]], primTri.vecToidx[temp[1]], primTri.vecToidx[temp[2]] });
}
}
/**
* @internal
*/
public void MapBAOAtoDATA(int faceNb, PrimaryIsoTriangle primTri)
{
var fr = primTri.IDATA.edgematch[faceNb].Item3;
for (var i = 0; i < primTri.isoVecsBAOA.Count; i++)
{
var temp = new List<string>();
for (var j = 0; j < 3; j++)
{
if (primTri.vertexTypes[i][j] == 1)
{
temp.Add(faceNb + "|" + primTri.isoVecsBAOA[i][j].x + "|" + primTri.isoVecsBAOA[i][j].y);
}
else
{
temp.Add(fr + "|" + primTri.isoVecsBAOA[i][j].x + "|" + primTri.isoVecsBAOA[i][j].y);
}
}
this.face.Add(new List<int> { primTri.vecToidx[temp[0]], primTri.vecToidx[temp[1]], primTri.vecToidx[temp[2]] });
}
}
/**
* @internal
*/
public void OrderData(PrimaryIsoTriangle primTri)
{
var nearTo = new Dictionary<int, List<List<int>>>();
for (var i = 0; i < 13; i++)
{
nearTo[i] = new List<List<int>>();
}
var close = primTri.closestTo;
for (var i = 0; i < close.Count; i++)
{
if (close[i][0] > -1)
{
if (close[i][1] > 0)
{
nearTo[close[i][0]].Add(new List<int> { i, close[i][1] });
}
}
else
{
nearTo[12].Add(new List<int> { i, close[i][0] });
}
}
/*
var near = new List<int>();
for (var i = 0; i < 12; i++)
{
near[i] = i;
}
*/
var near = Enumerable.Range(0, 12).ToList();
var nearIndex = 12;
for (var i = 0; i < 12; i++)
{
nearTo[i].Sort((a, b) =>
{
return a[1] - b[1];
});
/*
for (var j = 0; j < nearTo[i].Count; j++)
{
near[nearTo[i][j][0]] = nearIndex++;
}
*/
foreach (var item in nearTo[i])
{
near[item[0]] = nearIndex++;
}
}
/*
for (var j = 0; j < nearTo[12].Count; j++)
{
near[nearTo[12][j][0]] = nearIndex++;
}
*/
foreach (var item in nearTo[12])
{
near[item[0]] = nearIndex++;
}
/*
for (var i = 0; i < this.vertex.Count; i++)
{
//FIX
this.vertex[i].Add(near[i]);
}
this.vertex.Sort((a, b) =>
{
return a[3].CompareTo(b[3]);
});
for (var i = 0; i < this.vertex.Count; i++)
{
//FIX
this.vertex[i].RemoveAt(this.vertex[i].Count - 1);
}
*/
this.vertex = this.vertex
.Select((v, index) => (Vertex: v, SortKey: near[index]))
.OrderBy(x => x.SortKey)
.Select(x => x.Vertex)
.ToList();
for (var i = 0; i < this.face.Count; i++)
{
for (var j = 0; j < this.face[i].Count; j++)
{
this.face[i][j] = near[this.face[i][j]];
}
}
this.sharedNodes = nearTo[12].Count;
this.poleNodes = this.vertex.Count - this.sharedNodes;
}
public List<int> SetOrder(int m, List<int> faces)
{
var adjVerts = new List<int>();
var dualFaces = new List<int>();
var face = faces.Last();
faces.RemoveAt(faces.Count - 1);
dualFaces.Add(face);
var index = this.face[face].IndexOf(m);
index = (index + 2) % 3;
var v = this.face[face][index];
adjVerts.Add(v);
var f = 0;
while (faces.Count > 0)
{
face = faces[f];
if (this.face[face].IndexOf(v) > -1)
{
// v is a vertex of face f
index = (this.face[face].IndexOf(v) + 1) % 3;
v = this.face[face][index];
adjVerts.Add(v);
dualFaces.Add(face);
faces.RemoveAt(f);
f = 0;
}
else
{
f++;
}
}
this.adjacentFaces.Add(adjVerts);
return dualFaces;
}
public PolyhedronData ToGoldbergPolyhedronData()
{
var goldbergPolyhedronData = new PolyhedronData("GeoDual", "Goldberg", new List<Vector3>(), new List<List<int>>());
goldbergPolyhedronData.name = "GD dual";
var verticesNb = this.vertex.Count;
var map = new List<int>[verticesNb];
for (var v = 0; v < verticesNb; v++)
{
map[v] = new List<int>();
}
for (var f = 0; f < this.face.Count; f++)
{
for (var i = 0; i < 3; i++)
{
map[this.face[f][i]].Add(f);
}
}
float cx;
float cy;
float cz;
List<int> face;
Vector3 vertex;
this.adjacentFaces = new List<List<int>>();
for (var m = 0; m < map.Length; m++)
{
goldbergPolyhedronData.face[m] = this.SetOrder(m, new List<int>(map[m]));
foreach (var el in map[m])
{
cx = 0;
cy = 0;
cz = 0;
face = this.face[el];
for (var i = 0; i < 3; i++)
{
vertex = this.vertex[face[i]];
cx += vertex[0];
cy += vertex[1];
cz += vertex[2];
}
goldbergPolyhedronData.vertex[el] = new Vector3(cx / 3, cy / 3, cz / 3);
}
;
}
return goldbergPolyhedronData;
}
public static GeodesicData BuildGeodesicData(PrimaryIsoTriangle primTri)
{
float PHI = (1 + Mathf.Sqrt(5f)) / 2;
var geodesicData = new GeodesicData(
"Geodesic-m-n",
"Geodesic",
new List<Vector3>() {
new Vector3(0, PHI, -1),
new Vector3(-PHI, 1, 0),
new Vector3(-1, 0, -PHI),
new Vector3(1, 0, -PHI),
new Vector3(PHI, 1, 0),
new Vector3(0, PHI, 1),
new Vector3(-1, 0, PHI),
new Vector3(-PHI, -1, 0),
new Vector3(0, -PHI, -1),
new Vector3(PHI, -1, 0),
new Vector3(1, 0, PHI),
new Vector3(0, -PHI, 1),
},
new List<List<int>>()
);
primTri.SetIndices();
primTri.CalcCoeffs();
primTri.CreateInnerFacets();
primTri.EdgeVecsABOB();
primTri.MapABOBtoOBOA();
primTri.MapABOBtoBAOA();
for (var f = 0; f < primTri.IDATA.face.Count; f++)
{
primTri.MapToFace(f, geodesicData);
geodesicData.innerToData(f, primTri);
if (primTri.IDATA.edgematch[f].Item2 == "B")
{
geodesicData.MapABOBtoDATA(f, primTri);
}
if (primTri.IDATA.edgematch[f].Item2 == "O")
{
geodesicData.MapOBOAtoDATA(f, primTri);
}
if (primTri.IDATA.edgematch[f].Item4 == "A")
{
geodesicData.MapBAOAtoDATA(f, primTri);
}
}
geodesicData.OrderData(primTri);
var radius = 1f;
geodesicData.vertex = geodesicData.vertex.Select((el) =>
{
var a = el[0];
var b = el[1];
var c = el[2];
var d = Mathf.Sqrt(a * a + b * b + c * c);
el[0] *= radius / d;
el[1] *= radius / d;
el[2] *= radius / d;
return el;
}).ToList();
return geodesicData;
}
}
}

2
Assets/Scripts/GeodesicMesh.cs.meta
Unescape View File

@ -0,0 +1,2 @@
fileFormatVersion: 2
guid: 5ba9950a73f64cb4fa05dd46d677a642

174
Assets/Scripts/GoldbergBuilder.cs
Unescape View File

@ -0,0 +1,174 @@
using System.Collections.Generic;
using UnityEngine;
using UnityEngine.Rendering;
namespace Metamesh
{
public class GoldbergBuilder
{
public class GoldbergVertexDataOption
{
public float size = 1;
public float sizeX = 1;
public float sizeY = 1;
public float sizeZ = 1;
};
public class GoldbergCreationOption : GoldbergVertexDataOption
{
public int m;
public int n;
}
public class VertexData
{
public List<Vector3> vertices;
public List<int> indices;
public List<Vector3> normals;
public List<Vector2> uvs;
}
public VertexData CreateGoldbergVertexData(GoldbergVertexDataOption options, PolyhedronData goldbergData)
{
var size = options.size;
var sizeX = options.sizeX;// || size || 1;
var sizeY = options.sizeY;// || size || 1;
var sizeZ = options.sizeZ;// || size || 1;
var positions = new List<Vector3>();
var indices = new List<int>();
var normals = new List<Vector3>();
var uvs = new List<Vector2>();
var minX = float.MaxValue;
var maxX = float.MinValue;
var minY = float.MaxValue;
var maxY = float.MinValue;
for (var v = 0; v < goldbergData.vertex.Count; v++)
{
minX = Mathf.Min(minX, goldbergData.vertex[v].x * sizeX);
maxX = Mathf.Max(maxX, goldbergData.vertex[v].x * sizeX);
minY = Mathf.Min(minY, goldbergData.vertex[v].y * sizeY);
maxY = Mathf.Max(maxY, goldbergData.vertex[v].y * sizeY);
}
var index = 0;
for (var f = 0; f < goldbergData.face.Count; f++)
{
var verts = goldbergData.face[f];
var a = goldbergData.vertex[verts[0]];
var b = goldbergData.vertex[verts[2]];
var c = goldbergData.vertex[verts[1]];
var ba = b - a;
var ca = c - a;
var norm = Vector3.Cross(ca, ba).normalized;
for (var v = 0; v < verts.Count; v++)
{
normals.Add(norm);
var pdata = goldbergData.vertex[verts[v]];
positions.Add(new Vector3(pdata[0] * sizeX, pdata[1] * sizeY, pdata[2] * sizeZ));
var vCoord = (pdata[1] * sizeY - minY) / (maxY - minY);
uvs.Add(new Vector2((pdata[0] * sizeX - minX) / (maxX - minX), vCoord));
}
for (var v = 0; v < verts.Count - 2; v++)
{
indices.AddRange(new int[] { index, index + v + 2, index + v + 1 });
}
index += verts.Count;
}
/*
VertexData._ComputeSides(sideOrientation, positions, indices, normals, uvs);
const vertexData = new VertexData();
vertexData.positions = positions;
vertexData.indices = indices;
vertexData.normals = normals;
vertexData.uvs = uvs;
return vertexData;
*/
return new VertexData()
{
vertices = positions,
indices = indices,
normals = normals,
uvs = uvs,
};
}
/**
* Creates the Mesh for a Goldberg Polyhedron which is made from 12 pentagonal and the rest hexagonal faces
* @see https://en.wikipedia.org/wiki/Goldberg_polyhedron
* @see https://doc.babylonjs.com/features/featuresDeepDive/mesh/creation/polyhedra/goldberg_poly
* @param name defines the name of the mesh
* @param options an object used to set the following optional parameters for the polyhedron, required but can be empty
* @param scene defines the hosting scene
* @returns Goldberg mesh
*/
public VertexData CreateGoldberg(GoldbergCreationOption options)
{
var size = options.size;
var sizeX = options.sizeX;// || size || 1;
var sizeY = options.sizeY;// || size || 1;
var sizeZ = options.sizeZ;// || size || 1;
var m = options.m;// || 1;
var n = options.n;// || 0;
if (n > m)
{
var temp = n;
n = m;
m = temp;
Debug.LogWarning("n > m therefore m and n swapped");
}
var primTri = new PrimaryIsoTriangle();
primTri.Build(m, n);
var geodesicData = GeodesicData.BuildGeodesicData(primTri);
var goldbergData = geodesicData.ToGoldbergPolyhedronData();
//var goldberg = new Mesh();
//goldberg.name = name;
var vertexData = CreateGoldbergVertexData(options, goldbergData);
return vertexData;
/*
vertexData.applyToMesh(goldberg, options.updatable);
goldberg.goldbergData.nbSharedFaces = geodesicData.sharedNodes;
goldberg.goldbergData.nbUnsharedFaces = geodesicData.poleNodes;
goldberg.goldbergData.adjacentFaces = geodesicData.adjacentFaces;
goldberg.goldbergData.nbFaces = goldberg.goldbergData.nbSharedFaces + goldberg.goldbergData.nbUnsharedFaces;
goldberg.goldbergData.nbFacesAtPole = (goldberg.goldbergData.nbUnsharedFaces - 12) / 12;
for (var f = 0; f < geodesicData.vertex.Count; f++)
{
goldberg.goldbergData.faceCenters.push(Vector3.FromArray(geodesicData.vertex[f]));
goldberg.goldbergData.faceCenters[f].x *= sizeX;
goldberg.goldbergData.faceCenters[f].y *= sizeY;
goldberg.goldbergData.faceCenters[f].z *= sizeZ;
goldberg.goldbergData.faceColors.push(new Color4(1, 1, 1, 1));
}
for (var f = 0; f < goldbergData.face.Count; f++)
{
var verts = goldbergData.face[f];
var a = goldbergData.vertex[verts[0]];
var b = goldbergData.vertex[verts[2]];
var c = goldbergData.vertex[verts[1]];
var ba = b - a;
var ca = c - a;
var norm = Vector3.Cross(ca, ba).normalized;
var z = Vector3.Cross(ca, norm).normalized;
//goldberg.goldbergData.faceXaxis.push(ca.normalize());
//goldberg.goldbergData.faceYaxis.push(norm);
//goldberg.goldbergData.faceZaxis.push(z);
}
return goldberg;
*/
}
}
}

2
Assets/Scripts/GoldbergBuilder.cs.meta
Unescape View File

@ -0,0 +1,2 @@
fileFormatVersion: 2
guid: 7d8371f81baddd64e8c1450945f7f75f

43
Assets/Scripts/GoldbergPolyhedron.cs
Unescape View File

@ -1,43 +0,0 @@
using System.Linq;
using UnityEngine;
using UnityEngine.Rendering;
namespace Metamesh
{
public class GoldbergPolyhedron : MonoBehaviour
{
public float radius = 1;
public uint subdivision = 2;
private void Start()
{
}
private void Update()
{
}
public void Generate()
{
var builder = new IcosphereBuilder();
for (var i = 1; i < subdivision; ++i)
{
builder = new IcosphereBuilder(builder);
}
var vertices = builder.Vertices.Select(v => (Vector3)(v * radius));
var normals = builder.Vertices.Select(v => (Vector3)v);
var indices = builder.Indices;
/*
if (builder.VertexCount > 65535) mesh.indexFormat = IndexFormat.UInt32;
mesh.SetVertices(vtx.ToList());
mesh.SetNormals(nrm.ToList());
mesh.SetIndices(idx.ToList(), MeshTopology.Triangles, 0);
*/
}
}
}

2
Assets/Scripts/GoldbergPolyhedron.cs.meta
Unescape View File

@ -1,2 +0,0 @@
fileFormatVersion: 2
guid: 825ce87dd8b71e444a6c78436e3d9903

67
Assets/Scripts/IsoVector.cs
Unescape View File

@ -0,0 +1,67 @@
using UnityEngine;
namespace Metamesh
{
public class IsoVector
{
public int x;
public int y;
public IsoVector(int x, int y)
{
this.x = x;
this.y = y;
}
public IsoVector Clone()
{
return new IsoVector(x, y);
}
public IsoVector Rotate60About(IsoVector other)
{
var x = this.x;
this.x = other.x + other.y - this.y;
this.y = x + this.y - other.x;
return this;
}
public IsoVector RotateNeg60About(IsoVector other)
{
var x = this.x;
this.x = x + this.y - other.y;
this.y = other.x + other.y - x;
return this;
}
public IsoVector Rotate120(int m, int n)
{
var x = this.x;
this.x = m - x - this.y;
this.y = n + x;
return this;
}
public IsoVector RotateNeg120(int m, int n)
{
var x = this.x;
this.x = this.y - n;
this.y = m + n - x - this.y;
return this;
}
public Vector3 ToCartesianOrigin(IsoVector origin, float isoGridSize)
{
var point = Vector3.zero;
point.x = origin.x + 2 * this.x * isoGridSize + this.y * isoGridSize;
point.y = origin.y + Mathf.Sqrt(3) * this.y * isoGridSize;
return point;
}
public static IsoVector Zero()
{
return new IsoVector(0, 0);
}
}
}

2
Assets/Scripts/IsoVector.cs.meta
Unescape View File

@ -0,0 +1,2 @@
fileFormatVersion: 2
guid: 1b57a079742a0234e892f0128b45703f