/// <summary>
/// Attempts to find the centroid or barycenter point of a mesh
/// by using the average of the center of all triangles divided
/// by their mass for an accurate representation.
/// </summary>
/// <param name="mesh">The mesh to find the barycenter point.</param>
/// <returns>A <see cref="Vector3"/> containing the center.</returns>
private static Vector3 FindBaryCenter(Shapes.IMesh mesh)
{
OpenTK.Vector3d totalSum = new OpenTK.Vector3d();
double totalArea = 0;
foreach (Vector3 face in mesh.Faces)
{
Vector3[] vertices = mesh.GetVerticesFromFace(face);
double area = mesh.GetTriArea(vertices);
if (area == 0)
{
continue;
}
totalSum += OpenTK.Vector3d.Multiply(
(OpenTK.Vector3d)CenterOfTriangle(vertices), area);
totalArea += area;
}
return((Vector3)OpenTK.Vector3d.Divide(totalSum, totalArea));
}
private V3[] getExpDirections()
{
var v1 = new V3(1, 0, 0);
if (radioButton1stY.Checked)
{
v1 = new V3(0, 1, 0);
}
else if (radioButton1stZ.Checked)
{
v1 = new V3(0, 0, 1);
}
var v2 = new V3(1, 0, 0);
if (radioButton2ndY.Checked)
{
v2 = new V3(0, 1, 0);
}
else if (radioButton2ndZ.Checked)
{
v2 = new V3(0, 0, 1);
}
var v3 = new V3(1, 0, 0);
if (radioButton3rdY.Checked)
{
v3 = new V3(0, 1, 0);
}
else if (radioButton3rdZ.Checked)
{
v3 = new V3(0, 0, 1);
}
return(new[] { v1, v2, v3 });
}
public TorusKnot(int pathsteps, int shapevertices, double radius, int p, int q, int TexCount)
: base( )
{
Trace.Assert(pathsteps >= MINPathSteps, "A Path must have at least " + MINPathSteps + " Steps to form a volume.");
Trace.Assert(shapevertices >= MINShapeVertices, "A Shape must contain at least " + MINShapeVertices + " Vertices to be considered valid and create a volume.");
Trace.Assert(TexCount > 1, "at least 1 Texture set is required.");
PrimitiveMode = OpenTK.Graphics.OpenGL.BeginMode.TriangleStrip;
Vector3d[] PathPositions = new Vector3d[pathsteps];
#region Find the center Points for each step on the path
for (int i = 0; i < pathsteps; i++)
{
double Angle = (i / (double)pathsteps) * TwoPi;
double AngleTimesP = Angle * p;
double AngleTimesQ = Angle * q;
double r = (0.5 * (2.0 + System.Math.Sin(AngleTimesQ)));
PathPositions[i] = new Vector3d((r * System.Math.Cos(AngleTimesP)),
(r * System.Math.Cos(AngleTimesQ)),
(r * System.Math.Sin(AngleTimesP)));
}
#endregion Find the center Points for each step on the path
#region Find the Torus length
Vector3d result;
double[] Lengths = new double[pathsteps];
Vector3d.Subtract(ref PathPositions[pathsteps - 1], ref PathPositions[0], out result);
Lengths[0] = result.Length;
double TotalLength = result.Length;
for (int i = 1; i < pathsteps; i++) // skipping
{
Vector3d.Subtract(ref PathPositions[i - 1], ref PathPositions[i], out result);
Lengths[i] = result.Length;
TotalLength += result.Length;
}
Trace.WriteLine("the TorusKnot's length is: " + TotalLength + " ");
#endregion Find the Torus length
VertexArray = new VertexT2dN3dV3d[pathsteps * shapevertices];
#region Loft a circle Shape along the path
double TwoPiThroughVert = TwoPi / shapevertices; // precalc for reuse
for (uint i = 0; i < pathsteps; i++)
{
Vector3d last, next, normal, tangent;
if (i == pathsteps - 1)
{
next = PathPositions[0];
}
else
{
next = PathPositions[i + 1];
}
if (i == 0)
{
last = PathPositions[pathsteps - 1];
}
else
{
last = PathPositions[i - 1];
}
Vector3d.Subtract(ref next, ref last, out tangent); // Guesstimate tangent
tangent.Normalize();
Vector3d.Add(ref next, ref last, out normal); // Approximate N
normal.Normalize();
Vector3d.Multiply(ref normal, radius, out normal); // scale the shape to desired radius
for (uint j = 0; j < shapevertices; j++)
{
uint index = i * (uint)shapevertices + j;
// Create a point on the plane and rotate it
OpenTK.Matrix4d RotationMatrix = OpenTK.Matrix4d.Rotate(tangent, -(j * TwoPiThroughVert));
OpenTK.Vector3d point = OpenTK.Vector3d.TransformVector(normal, RotationMatrix);
OpenTK.Vector3d.Add(ref PathPositions[i], ref point, out VertexArray[index].Position);
// Since the used shape is a circle, the Vertex normal's heading is easy to find
OpenTK.Vector3d.Subtract(ref VertexArray[index].Position, ref PathPositions[i], out VertexArray[index].Normal);
VertexArray[index].Normal.Normalize();
// just generate some semi-useful UVs to fill blanks
VertexArray[index].TexCoord = new OpenTK.Vector2d((double)(i / TotalLength / TexCount), j / (shapevertices - 1.0));
}
}
#endregion Loft a circle Shape along the path
PathPositions = null; // not needed anymore
uint currentindex = 0;
#region Build a Triangle strip from the Vertices
IndexArray = new uint[pathsteps * (shapevertices * 2 + 2)]; // 2 triangles per vertex, +2 due to added degenerate triangles
for (uint i = 0; i < pathsteps; i++)
{
uint RowCurrent = i * (uint)shapevertices;
uint RowBelow;
if (i == pathsteps - 1)
{
RowBelow = 0; // for the last row, the first row is the following
}
else
{
RowBelow = (i + 1) * (uint)shapevertices;
}
// new ring begins here
for (uint j = 0; j < shapevertices; j++)
{
IndexArray[currentindex++] = RowCurrent + j;
IndexArray[currentindex++] = RowBelow + j;
}
// ring ends here, repeat first 2 vertices to insert 2 degenerate triangles to reach following ring
IndexArray[currentindex++] = RowCurrent;
IndexArray[currentindex++] = RowBelow;
}
#endregion Build a Triangle strip from the Vertices
}
public VertexT2dN3dV3d(OpenTK.Vector2d texcoord, Vector3d normal, Vector3d position)
{
TexCoord = texcoord;
Normal = normal;
Position = position;
}
/// <summary>
/// ゴニオオブジェクトを生成
/// </summary>
/// <param name="gl"></param>
/// <param name="dir"></param>
/// <param name="angle"></param>
private void setGonio(GLControlAlpha gl, V3[] dir, double[] angle)
{
gl.DeleteAllObjects();
var r = 0.05;
var obj = new List <GLObject>();
var rot = dir.Select((d, i) => Matrix3D.Rot(d, angle[i])).ToArray();
//1st
var mat = new Material(new C4(0.8f, 0.8f, 0f, 1f));
obj.Add(new Cone(dir[0] * 2.1, dir[0] * -0.2, r * 2, mat, DrawingMode.Surfaces));//矢
obj.Add(new TextObject(gl.Name.Contains("ReciPro") ? "Φ" : "1st", 12, dir[0] * 2.1 + dir[0].Normalized() * 0.01, 0.05, true, mat));
if (!checkBoxEnable2nd.Checked) //2ndが存在しない時
{
obj.Add(new Cylinder(dir[0] * -1.9, dir[0] * 3.8, r, mat, DrawingMode.Surfaces)); //軸
obj.Add(new Torus(new V3(0, 0, 0), rot[0] * V3.Cross(dir[0], new V3(dir[0].Z, dir[0].X, dir[0].Y)), 1.6, r * 1.5, mat, DrawingMode.Surfaces)); //トーラス
}
else //2ndが存在する時
{
obj.Add(new Cylinder(dir[0] * -1.9, dir[0] * 0.3, r, mat, DrawingMode.Surfaces)); //軸
obj.Add(new Cylinder(dir[0] * 1.6, dir[0] * 0.3, r, mat, DrawingMode.Surfaces)); //軸
//1stトーラスの法線は、1st軸と2nd軸が直交する方向
obj.Add(new Torus(new V3(0, 0, 0), rot[0] * V3.Cross(dir[0], dir[1]), 1.6, r * 1.5, mat, DrawingMode.Surfaces)); //トーラス
//以下2nd
var rot01 = rot[0] * rot[1];
mat = new Material(new C4(0f, 0.8f, 0.8f, 1f));
var n = rot[0] * dir[1];
obj.Add(new Cone(n * 2.0, -n * 0.2, r * 2, mat, DrawingMode.Surfaces));//矢
obj.Add(new TextObject(gl.Name.Contains("ReciPro") ? "Θ" : "2nd", 12, n * 2.0 + n.Normalized() * 0.01, 0.05, true, mat));
if (!checkBoxEnable3rd.Checked)
{
obj.Add(new Cylinder(n * 1.9, -n * 3.8, r, mat, DrawingMode.Surfaces)); //軸
obj.Add(new Torus(new V3(0, 0, 0), rot01 * V3.Cross(dir[1], new V3(dir[1].Z, dir[1].X, dir[1].Y)), 1.1, r * 1.5, mat, DrawingMode.Surfaces)); //トーラス
}
else
{
obj.Add(new Cylinder(n * 1.9, -n * 0.8, r, mat, DrawingMode.Surfaces)); //軸
obj.Add(new Cylinder(-n * 1.9, n * 0.8, r, mat, DrawingMode.Surfaces)); //軸
//2ndトーラスの法線は、2nd軸と3rd軸が直交する方向
obj.Add(new Torus(new V3(0, 0, 0), rot01 * V3.Cross(dir[1], dir[2]), 1.1, r * 1.5, mat, DrawingMode.Surfaces)); //トーラス
//以下、3rd
mat = new Material(new C4(0.8f, 0f, 0.8f, 1f));
var rot012 = rot[0] * rot[1] * rot[2];
n = rot[0] * rot[1] * dir[2];
obj.Add(new Cylinder(n * 1.3, -n * 2.6, r, mat, DrawingMode.Surfaces)); //軸
obj.Add(new Cone(n * 1.45, -n * 0.2, r * 2, mat, DrawingMode.Surfaces)); //矢
obj.Add(new TextObject(gl.Name.Contains("ReciPro") ? "Ψ" : "3rd", 12, n * 1.45 + n.Normalized() * 0.01, 0.05, true, mat));
if (dir[2].Z == 0)
{
obj.Add(new Torus(new V3(0, 0, 0), rot012 * new V3(0, 0, 1), 0.6, r * 1.5, mat, DrawingMode.Surfaces));//トーラス
}
else
{
obj.Add(new Torus(new V3(0, 0, 0), rot012 * new V3(0, 1, 0), 0.6, r * 1.5, mat, DrawingMode.Surfaces));//トーラス
}
}
}
//中央の球
obj.AddRange(createObject(gl, dir, angle));
gl.AddObjects(obj);
gl.Refresh();
}
public VertexT2dN3dV3d(OpenTK.Vector2d texcoord, Vector3d normal, Vector3d position)
{
TexCoord = texcoord;
Normal = normal;
Position = position;
}
