/// <summary>Expects CCW triangle order as input, emits 4 new CCW triangles.</summary>
/// <param name="first">1st output Triangle</param>
/// <param name="second">2nd output Triangle</param>
/// <param name="third">3rd output Triangle</param>
/// <param name="fourth">4th output Triangle</param>
public void SubdivideSierpinski(out TetrahedronFace first, out TetrahedronFace second, out TetrahedronFace third, out TetrahedronFace fourth)
{
Vector3d temp;
// find the 3 points AB, BC, CA
Vector3d CenterAB;
Vector3d.Add(ref this.APosition, ref this.BPosition, out temp);
Vector3d.Multiply(ref temp, 0.5f, out CenterAB);
Vector3d CenterBC;
Vector3d.Add(ref this.BPosition, ref this.CPosition, out temp);
Vector3d.Multiply(ref temp, 0.5f, out CenterBC);
Vector3d CenterCA;
Vector3d.Add(ref this.CPosition, ref this.APosition, out temp);
Vector3d.Multiply(ref temp, 0.5f, out CenterCA);
// find the 3 points AD, BD, CD
Vector3d CenterAD;
Vector3d.Lerp(ref this.APosition, ref this.DPosition, 0.5, out CenterAD);
Vector3d CenterBD;
Vector3d.Lerp(ref this.BPosition, ref this.DPosition, 0.5, out CenterBD);
Vector3d CenterCD;
Vector3d.Lerp(ref this.CPosition, ref this.DPosition, 0.5, out CenterCD);
// emit 4 new CCW triangles
first = new TetrahedronFace(ref this.APosition, ref this.ATexCoord,
ref CenterAB, ref this.BTexCoord,
ref CenterCA, ref this.CTexCoord,
ref CenterAD,
ref this.Normal);
second = new TetrahedronFace(ref CenterAB, ref this.ATexCoord,
ref this.BPosition, ref this.BTexCoord,
ref CenterBC, ref this.CTexCoord,
ref CenterBD,
ref this.Normal);
third = new TetrahedronFace(ref CenterCA, ref this.ATexCoord,
ref CenterBC, ref this.BTexCoord,
ref this.CPosition, ref this.CTexCoord,
ref CenterCD,
ref this.Normal);
fourth = new TetrahedronFace(ref CenterAD, ref this.ATexCoord,
ref CenterBD, ref this.BTexCoord,
ref CenterCD, ref this.CTexCoord,
ref this.DPosition,
ref this.Normal);
}
internal static void GetVertexArray( ref TetrahedronFace[] input, out VertexT2dN3dV3d[] output )
{
output = new VertexT2dN3dV3d[input.Length * 3];
int counter = 0;
for ( int i = 0; i < input.Length; i++ )
{
input[i].GetVertices( out output[counter + 0], out output[counter + 1], out output[counter + 2] );
counter += 3;
}
}
/// <summary>Subdivides each triangle into 4 new ones.</summary>
private void SubdivideTetrahedron(ref TetrahedronFace[] source, out TetrahedronFace[] output)
{
output = new TetrahedronFace[source.Length * 4];
int counter = 0;
for (int i = 0; i < source.Length; i++)
{
source[i].SubdivideSierpinski(out output[counter + 0], out output[counter + 1], out output[counter + 2], out output[counter + 3]);
counter += 4; // every source triangle emits 4 new triangles
}
}
private void SubdivideKoch(double height, ref TetrahedronFace[] input, out TetrahedronFace[] output)
{
output = new TetrahedronFace[input.Length * 6];
int counter = 0;
for (int i = 0; i < input.Length; i++)
{
input[i].SubdivideKoch(height, out output[counter + 0], out output[counter + 1], out output[counter + 2], out output[counter + 3], out output[counter + 4], out output[counter + 5]);
counter += 6; // every source triangle emits 6 new triangles
}
}
private void SubdivideKoch( double height, ref TetrahedronFace[] input, out TetrahedronFace[] output )
{
output = new TetrahedronFace[input.Length * 6];
int counter = 0;
for ( int i = 0; i < input.Length; i++ )
{
input[i].SubdivideKoch(height, out output[counter + 0], out output[counter + 1], out output[counter + 2], out output[counter + 3], out output[counter + 4], out output[counter + 5] );
counter += 6; // every source triangle emits 6 new triangles
}
}
/// <summary>Expects CCW triangle order as input, emits 4 new CCW triangles.</summary>
/// <param name="first">1st output Triangle</param>
/// <param name="second">2nd output Triangle</param>
/// <param name="third">3rd output Triangle</param>
/// <param name="fourth">4th output Triangle</param>
public void SubdivideSierpinski( out TetrahedronFace first, out TetrahedronFace second, out TetrahedronFace third, out TetrahedronFace fourth )
{
Vector3d temp;
// find the 3 points AB, BC, CA
Vector3d CenterAB;
Vector3d.Add( ref this.APosition, ref this.BPosition, out temp );
Vector3d.Multiply( ref temp, 0.5f, out CenterAB );
Vector3d CenterBC;
Vector3d.Add( ref this.BPosition, ref this.CPosition, out temp );
Vector3d.Multiply( ref temp, 0.5f, out CenterBC );
Vector3d CenterCA;
Vector3d.Add( ref this.CPosition, ref this.APosition, out temp );
Vector3d.Multiply( ref temp, 0.5f, out CenterCA );
// find the 3 points AD, BD, CD
Vector3d CenterAD;
Vector3d.Lerp( ref this.APosition, ref this.DPosition, 0.5, out CenterAD );
Vector3d CenterBD;
Vector3d.Lerp( ref this.BPosition, ref this.DPosition, 0.5, out CenterBD );
Vector3d CenterCD;
Vector3d.Lerp( ref this.CPosition, ref this.DPosition, 0.5, out CenterCD );
// emit 4 new CCW triangles
first = new TetrahedronFace( ref this.APosition, ref this.ATexCoord,
ref CenterAB, ref this.BTexCoord,
ref CenterCA, ref this.CTexCoord,
ref CenterAD,
ref this.Normal );
second = new TetrahedronFace( ref CenterAB, ref this.ATexCoord,
ref this.BPosition, ref this.BTexCoord,
ref CenterBC, ref this.CTexCoord,
ref CenterBD,
ref this.Normal );
third = new TetrahedronFace( ref CenterCA, ref this.ATexCoord,
ref CenterBC, ref this.BTexCoord,
ref this.CPosition, ref this.CTexCoord,
ref CenterCD,
ref this.Normal );
fourth = new TetrahedronFace( ref CenterAD, ref this.ATexCoord,
ref CenterBD, ref this.BTexCoord,
ref CenterCD, ref this.CTexCoord,
ref this.DPosition,
ref this.Normal );
}
/// <summary>Generates the lowest subdivision mesh, which consists of 4 Triangles.</summary>
internal static void CreateDefaultTetrahedron(double scale, out TetrahedronFace[] array)
{
Vector3d[] Points = new Vector3d[4];
Points[0] = new Vector3d(0.0 * scale, 0.0 * scale, 1.0 * scale);
Points[1] = new Vector3d(-0.816 * scale, 0.471 * scale, -0.333 * scale);
Points[2] = new Vector3d(0.816 * scale, 0.471 * scale, -0.333 * scale);
Points[3] = new Vector3d(0.0 * scale, -0.943 * scale, -0.333 * scale);
Vector2d[] TexCoords = new Vector2d[4];
TexCoords[0] = new Vector2d(0.0, 0.0);
TexCoords[1] = new Vector2d(1.0, 0.0);
TexCoords[2] = new Vector2d(0.0, 1.0);
TexCoords[3] = new Vector2d(1.0, 1.0);
Vector3d Normal;
array = new TetrahedronFace[4];
FindNormal(ref Points[0], ref Points[2], ref Points[1], ref Points[3], out Normal);
array[0] = new TetrahedronFace(ref Points[0], ref TexCoords[2],
ref Points[2], ref TexCoords[0],
ref Points[1], ref TexCoords[1],
ref Points[3],
ref Normal);
FindNormal(ref Points[0], ref Points[3], ref Points[2], ref Points[1], out Normal);
array[1] = new TetrahedronFace(ref Points[0], ref TexCoords[0],
ref Points[3], ref TexCoords[1],
ref Points[2], ref TexCoords[2],
ref Points[1],
ref Normal);
FindNormal(ref Points[0], ref Points[1], ref Points[3], ref Points[2], out Normal);
array[2] = new TetrahedronFace(ref Points[0], ref TexCoords[2],
ref Points[1], ref TexCoords[1],
ref Points[3], ref TexCoords[3],
ref Points[2],
ref Normal);
FindNormal(ref Points[1], ref Points[2], ref Points[3], ref Points[0], out Normal);
array[3] = new TetrahedronFace(ref Points[1], ref TexCoords[3],
ref Points[2], ref TexCoords[2],
ref Points[3], ref TexCoords[1],
ref Points[0],
ref Normal);
}
/// <summary>Generates the lowest subdivision mesh, which consists of 4 Triangles.</summary>
internal static void CreateDefaultTetrahedron( double scale, out TetrahedronFace[] array )
{
Vector3d[] Points = new Vector3d[4];
Points[0] = new Vector3d( 0.0 * scale, 0.0 * scale, 1.0 * scale );
Points[1] = new Vector3d( -0.816 * scale, 0.471 * scale, -0.333 * scale );
Points[2] = new Vector3d( 0.816 * scale, 0.471 * scale, -0.333 * scale );
Points[3] = new Vector3d( 0.0 * scale, -0.943 * scale, -0.333 * scale );
Vector2d[] TexCoords = new Vector2d[4];
TexCoords[0] = new Vector2d( 0.0, 0.0 );
TexCoords[1] = new Vector2d( 1.0, 0.0 );
TexCoords[2] = new Vector2d( 0.0, 1.0 );
TexCoords[3] = new Vector2d( 1.0, 1.0 );
Vector3d Normal;
array = new TetrahedronFace[4];
FindNormal( ref Points[0], ref Points[2], ref Points[1], ref Points[3], out Normal );
array[0] = new TetrahedronFace( ref Points[0], ref TexCoords[2],
ref Points[2], ref TexCoords[0],
ref Points[1], ref TexCoords[1],
ref Points[3],
ref Normal );
FindNormal( ref Points[0], ref Points[3], ref Points[2], ref Points[1], out Normal );
array[1] = new TetrahedronFace( ref Points[0], ref TexCoords[0],
ref Points[3], ref TexCoords[1],
ref Points[2], ref TexCoords[2],
ref Points[1],
ref Normal );
FindNormal( ref Points[0], ref Points[1], ref Points[3], ref Points[2], out Normal );
array[2] = new TetrahedronFace( ref Points[0], ref TexCoords[2],
ref Points[1], ref TexCoords[1],
ref Points[3], ref TexCoords[3],
ref Points[2],
ref Normal );
FindNormal( ref Points[1], ref Points[2], ref Points[3], ref Points[0], out Normal );
array[3] = new TetrahedronFace( ref Points[1], ref TexCoords[3],
ref Points[2], ref TexCoords[2],
ref Points[3], ref TexCoords[1],
ref Points[0],
ref Normal );
}
internal void SubdivideKoch( double height, out TetrahedronFace first, out TetrahedronFace second, out TetrahedronFace third, out TetrahedronFace fourth, out TetrahedronFace fifth, out TetrahedronFace sixth )
{
Vector3d CenterAB, CenterBC, CenterCA, CenterD;
Vector2d TexCoordAB, TexCoordBC, TexCoordCA, TexCoordD;
Vector3d.Lerp( ref this.APosition, ref this.BPosition, 0.5, out CenterAB );
Vector3d.Lerp( ref this.BPosition, ref this.CPosition, 0.5, out CenterBC );
Vector3d.Lerp( ref this.CPosition, ref this.APosition, 0.5, out CenterCA );
CenterD = CenterAB;
Vector3d.Add(ref CenterD, ref CenterBC, out CenterD);
Vector3d.Add(ref CenterD, ref CenterCA, out CenterD);
CenterD /= 3.0;
Vector3d E = CenterD + ( this.Normal * 0.5 );
Vector3d temp = this.Normal;
temp *= height;
Vector3d.Add(ref CenterD, ref temp, out CenterD);
Vector2d.Lerp( ref this.ATexCoord, ref this.BTexCoord, 0.5, out TexCoordAB );
Vector2d.Lerp( ref this.BTexCoord, ref this.CTexCoord, 0.5, out TexCoordBC );
Vector2d.Lerp( ref this.CTexCoord, ref this.ATexCoord, 0.5, out TexCoordCA );
TexCoordD = TexCoordAB;
Vector2d.Add(ref TexCoordD, ref TexCoordBC, out TexCoordD);
Vector2d.Add(ref TexCoordD, ref TexCoordCA, out TexCoordD);
TexCoordD /= 3.0;
#region 1
first.APosition = this.APosition;
first.ATexCoord = this.ATexCoord;
first.BPosition = CenterAB;
first.BTexCoord = TexCoordAB;
first.CPosition = CenterCA;
first.CTexCoord = TexCoordCA;
first.Normal = this.Normal;
temp = ( this.APosition + CenterAB + CenterCA );
temp /= 3.0;
temp += this.Normal * -1.0;
first.DPosition = temp;
#endregion 1
#region 2
second.APosition = CenterAB;
second.ATexCoord = TexCoordAB;
second.BPosition = this.BPosition;
second.BTexCoord = this.BTexCoord;
second.CPosition = CenterBC;
second.CTexCoord = TexCoordBC;
second.Normal = this.Normal;
temp = CenterAB + this.BPosition + CenterBC;
temp /= 3.0;
temp += this.Normal * -1.0;
second.DPosition = temp;
#endregion 2
#region 3
third.APosition = CenterBC;
third.ATexCoord = TexCoordBC;
third.BPosition = this.CPosition;
third.BTexCoord = this.CTexCoord;
third.CPosition = CenterCA;
third.CTexCoord = TexCoordCA;
third.Normal = this.Normal;
temp = CenterBC + this.CPosition + CenterCA;
temp /= 3.0;
temp += this.Normal * -1.0;
third.DPosition = temp;
#endregion 3
#region 4
fourth.APosition = CenterAB;
fourth.ATexCoord = TexCoordAB;
fourth.BPosition = CenterD;
fourth.BTexCoord = TexCoordD;
fourth.CPosition = CenterCA;
fourth.CTexCoord = TexCoordCA;
SierpinskiTetrahedron.FindNormal( ref CenterAB, ref CenterD, ref CenterCA, out fourth.Normal );
fourth.DPosition = E;
#endregion 4
#region 5
fifth.APosition = CenterAB;
fifth.ATexCoord = TexCoordAB;
fifth.BPosition = CenterBC;
fifth.BTexCoord = TexCoordBC;
fifth.CPosition = CenterD;
fifth.CTexCoord = TexCoordD;
SierpinskiTetrahedron.FindNormal( ref CenterAB, ref CenterBC, ref CenterD, out fifth.Normal );
fifth.DPosition = E;
#endregion 5
#region 6
sixth.APosition = CenterBC;
sixth.ATexCoord = TexCoordBC;
sixth.BPosition = CenterCA;
sixth.BTexCoord = TexCoordCA;
sixth.CPosition = CenterD;
sixth.CTexCoord = TexCoordD;
SierpinskiTetrahedron.FindNormal( ref CenterBC, ref CenterCA, ref CenterD, out sixth.Normal );
sixth.DPosition = E;
#endregion 6
}
internal void SubdivideKoch(double height, out TetrahedronFace first, out TetrahedronFace second, out TetrahedronFace third, out TetrahedronFace fourth, out TetrahedronFace fifth, out TetrahedronFace sixth)
{
Vector3d CenterAB, CenterBC, CenterCA, CenterD;
Vector2d TexCoordAB, TexCoordBC, TexCoordCA, TexCoordD;
Vector3d.Lerp(ref this.APosition, ref this.BPosition, 0.5, out CenterAB);
Vector3d.Lerp(ref this.BPosition, ref this.CPosition, 0.5, out CenterBC);
Vector3d.Lerp(ref this.CPosition, ref this.APosition, 0.5, out CenterCA);
CenterD = CenterAB;
Vector3d.Add(ref CenterD, ref CenterBC, out CenterD);
Vector3d.Add(ref CenterD, ref CenterCA, out CenterD);
CenterD /= 3.0;
Vector3d E = CenterD + (this.Normal * 0.5);
Vector3d temp = this.Normal;
temp *= height;
Vector3d.Add(ref CenterD, ref temp, out CenterD);
Vector2d.Lerp(ref this.ATexCoord, ref this.BTexCoord, 0.5, out TexCoordAB);
Vector2d.Lerp(ref this.BTexCoord, ref this.CTexCoord, 0.5, out TexCoordBC);
Vector2d.Lerp(ref this.CTexCoord, ref this.ATexCoord, 0.5, out TexCoordCA);
TexCoordD = TexCoordAB;
Vector2d.Add(ref TexCoordD, ref TexCoordBC, out TexCoordD);
Vector2d.Add(ref TexCoordD, ref TexCoordCA, out TexCoordD);
TexCoordD /= 3.0;
#region 1
first.APosition = this.APosition;
first.ATexCoord = this.ATexCoord;
first.BPosition = CenterAB;
first.BTexCoord = TexCoordAB;
first.CPosition = CenterCA;
first.CTexCoord = TexCoordCA;
first.Normal = this.Normal;
temp = (this.APosition + CenterAB + CenterCA);
temp /= 3.0;
temp += this.Normal * -1.0;
first.DPosition = temp;
#endregion 1
#region 2
second.APosition = CenterAB;
second.ATexCoord = TexCoordAB;
second.BPosition = this.BPosition;
second.BTexCoord = this.BTexCoord;
second.CPosition = CenterBC;
second.CTexCoord = TexCoordBC;
second.Normal = this.Normal;
temp = CenterAB + this.BPosition + CenterBC;
temp /= 3.0;
temp += this.Normal * -1.0;
second.DPosition = temp;
#endregion 2
#region 3
third.APosition = CenterBC;
third.ATexCoord = TexCoordBC;
third.BPosition = this.CPosition;
third.BTexCoord = this.CTexCoord;
third.CPosition = CenterCA;
third.CTexCoord = TexCoordCA;
third.Normal = this.Normal;
temp = CenterBC + this.CPosition + CenterCA;
temp /= 3.0;
temp += this.Normal * -1.0;
third.DPosition = temp;
#endregion 3
#region 4
fourth.APosition = CenterAB;
fourth.ATexCoord = TexCoordAB;
fourth.BPosition = CenterD;
fourth.BTexCoord = TexCoordD;
fourth.CPosition = CenterCA;
fourth.CTexCoord = TexCoordCA;
SierpinskiTetrahedron.FindNormal(ref CenterAB, ref CenterD, ref CenterCA, out fourth.Normal);
fourth.DPosition = E;
#endregion 4
#region 5
fifth.APosition = CenterAB;
fifth.ATexCoord = TexCoordAB;
fifth.BPosition = CenterBC;
fifth.BTexCoord = TexCoordBC;
fifth.CPosition = CenterD;
fifth.CTexCoord = TexCoordD;
SierpinskiTetrahedron.FindNormal(ref CenterAB, ref CenterBC, ref CenterD, out fifth.Normal);
fifth.DPosition = E;
#endregion 5
#region 6
sixth.APosition = CenterBC;
sixth.ATexCoord = TexCoordBC;
sixth.BPosition = CenterCA;
sixth.BTexCoord = TexCoordCA;
sixth.CPosition = CenterD;
sixth.CTexCoord = TexCoordD;
SierpinskiTetrahedron.FindNormal(ref CenterBC, ref CenterCA, ref CenterD, out sixth.Normal);
sixth.DPosition = E;
#endregion 6
}
/// <summary>Subdivides each triangle into 4 new ones.</summary>
private void SubdivideTetrahedron( ref TetrahedronFace[] source, out TetrahedronFace[] output )
{
output = new TetrahedronFace[source.Length * 4];
int counter = 0;
for ( int i = 0; i < source.Length; i++ )
{
source[i].SubdivideSierpinski( out output[counter + 0], out output[counter + 1], out output[counter + 2], out output[counter + 3] );
counter += 4; // every source triangle emits 4 new triangles
}
}