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feat: add Goldberg polyhedron generation functionality

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master
hoba 10 months ago
parent aa63c7d28e
commit 321d9fbb03
10 changed files with 1255 additions and 49 deletions
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  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
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@ -9,6 +9,8 @@ ScriptedImporter:
assetBundleVariant: assetBundleVariant:
script: {fileID: 11500000, guid: 80f1e0e8eacc4a945b07bba9e3065c99, type: 3} script: {fileID: 11500000, guid: 80f1e0e8eacc4a945b07bba9e3065c99, type: 3}
radius: 1 radius: 1
subdivision: 3 subdivision: 4
m: 1
n: 0
generateLightmapUVs: 0 generateLightmapUVs: 0
readWriteMeshes: 0 readWriteMeshes: 0

21
Assets/Scripts/Editor/GoldbergPolyhedronImporter.cs
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@ -4,6 +4,7 @@ using UnityEditor;
using UnityEditor.AssetImporters; using UnityEditor.AssetImporters;
using UnityEngine; using UnityEngine;
using UnityEngine.Rendering; using UnityEngine.Rendering;
using static Metamesh.GoldbergBuilder;
namespace Metamesh namespace Metamesh
{ {
@ -12,6 +13,9 @@ namespace Metamesh
{ {
[SerializeField] float radius = 1; [SerializeField] float radius = 1;
[SerializeField, Min(2)] uint subdivision = 2; [SerializeField, Min(2)] uint subdivision = 2;
[SerializeField, Min(1)] int m = 1;
[SerializeField, Min(0)] int n = 0;
[SerializeField] bool generateLightmapUVs = false; [SerializeField] bool generateLightmapUVs = false;
[SerializeField] bool readWriteMeshes = false; [SerializeField] bool readWriteMeshes = false;
@ -42,7 +46,7 @@ namespace Metamesh
{ {
var mesh = new Mesh(); var mesh = new Mesh();
mesh.name = "Mesh"; mesh.name = "Mesh";
/*
var builder = new IcosphereBuilder(); var builder = new IcosphereBuilder();
for (var i = 1; i < subdivision; ++i) for (var i = 1; i < subdivision; ++i)
{ {
@ -54,8 +58,19 @@ namespace Metamesh
var indices = builder.Indices.ToList(); var indices = builder.Indices.ToList();
ApplyGoldbergTransformation(vertices, normals, indices); 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.SetVertices(vertices);
mesh.SetNormals(normals); mesh.SetNormals(normals);
mesh.SetIndices(indices, MeshTopology.Triangles, 0); mesh.SetIndices(indices, MeshTopology.Triangles, 0);

987
Assets/Scripts/GeodesicMesh.cs
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@ -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;
}
}
}

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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;
*/
}
}
}

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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);
*/
}
}
}

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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);
}
}
}

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