internal void ReplaceFace(Face face)
{
var key = face.Handle;
DictFaces[key] = face;
}
/// <summary>
/// Creates and returns a Pyramid as a DCEL with the specified dimensions centered in the worlds coordinate system.
/// </summary>
/// <param name="dimensionX">Width of the Pyramid in X-dimension</param>
/// <param name="dimensionY">Height of the Pyramid in Y-dimension.</param>
/// <param name="dimensionZ">Depth of the Pyramid in Z-dimension.</param>
/// <returns></returns>
public static Geometry CreatePyramidGeometry(float dimensionX, float dimensionY, float dimensionZ)
{
//check input
if (dimensionX <= 0 || dimensionY <= 0 || dimensionZ <= 0)
{
throw new ArgumentException("The dimension values can not be <= 0");
}
var xPos = dimensionX / 2.0f;
var yPos = dimensionY / 2.0f;
var zPos = dimensionZ / 2.0f;
var pyramid = new Geometry();
var positions = new float3[5];
//stores all Vertices positions
positions[0] = new float3(-xPos, -yPos, -zPos);
positions[1] = new float3(xPos, -yPos, -zPos);
positions[2] = new float3(xPos, -yPos, zPos);
positions[3] = new float3(-xPos, -yPos, zPos);
positions[4] = new float3(0, yPos, 0);
var baseFace = new Face(6)
{
OuterHalfEdge = 4
};
//create nad add vertices
for (var i = 0; i < 5; i++)
{
Vertex current = new Vertex(pyramid.CreateVertHandleId(), positions[i]);
if (i < 4)
{
current.IncidentHalfEdge = i * 4 + 1;
}
if (i == 4)
{
current.IncidentHalfEdge = 3;
}
pyramid.DictVertices.Add(current.Handle, current);
}
//create add Edges and Faces
for (var i = 0; i < 4; i++)
{
var h1 = new HalfEdge(i * 4 + 1);
var h2 = new HalfEdge(i * 4 + 2);
var h3 = new HalfEdge(i * 4 + 3);
var h4 = new HalfEdge(i * 4 + 4);
var sideFace = new Face(i + 2)
{
OuterHalfEdge = h1.Handle
};
h1.IncidentFace = sideFace.Handle;
h2.IncidentFace = sideFace.Handle;
h3.IncidentFace = sideFace.Handle;
h4.IncidentFace = baseFace.Handle;
h1.NextHalfEdge = h2.Handle;
h2.NextHalfEdge = h3.Handle;
h3.NextHalfEdge = h1.Handle;
h1.PrevHalfEdge = h3.Handle;
h2.PrevHalfEdge = h1.Handle;
h3.PrevHalfEdge = h2.Handle;
h3.OriginVertex = pyramid.DictVertices[5].Handle;
h1.TwinHalfEdge = h4.Handle;
h4.TwinHalfEdge = h1.Handle;
if (i < 3)
{
h4.PrevHalfEdge = (i + 1) * 4 + 4;
h2.TwinHalfEdge = (i + 1) * 4 + 3;
h1.OriginVertex = pyramid.DictVertices[i + 1].Handle;
h2.OriginVertex = pyramid.DictVertices[i + 2].Handle;
h4.OriginVertex = pyramid.DictVertices[i + 2].Handle;
}
else
{
h4.PrevHalfEdge = 4;
h2.TwinHalfEdge = 3;
h1.OriginVertex = pyramid.DictVertices[i + 1].Handle;
h2.OriginVertex = pyramid.DictVertices[1].Handle;
h4.OriginVertex = pyramid.DictVertices[1].Handle;
}
if (i > 0)
{
h3.TwinHalfEdge = (i - 1) * 4 + 2;
h4.NextHalfEdge = (i - 1) * 4 + 4;
}
else
{
h3.TwinHalfEdge = 3 * 4 + 2;
h4.NextHalfEdge = 3 * 4 + 4;
}
//add
pyramid.DictHalfEdges.Add(h1.Handle, h1);
pyramid.DictHalfEdges.Add(h2.Handle, h2);
pyramid.DictHalfEdges.Add(h3.Handle, h3);
pyramid.DictHalfEdges.Add(h4.Handle, h4);
pyramid.DictFaces.Add(sideFace.Handle, sideFace);
}
pyramid.DictFaces.Add(baseFace.Handle, baseFace);
pyramid.SetHighestHandles();
var allFaces = pyramid.GetAllFaces().ToList();
foreach (var face in allFaces)
{
var faceVertices = pyramid.GetFaceVertices(face.Handle).ToList();
pyramid.SetFaceNormal(faceVertices, face);
}
return(pyramid);
}
/// <summary>
/// Creates and returns a UV-Sphere as a DCEL with the specified dimensions centered in the worlds coordinate system.
/// </summary>
/// <param name="radius">Radius of the sphere.</param>
/// <param name="horizontalResolution">Lines of latitude, smallest value is 3.</param>
/// <param name="verticalResolution">Lines of longitude, smallest value is 3.</param>
/// <returns>A UV-Sphere centered in the world coordinate system as a DCEL.</returns>
public static Geometry CreateSpehreGeometry(float radius, int horizontalResolution, int verticalResolution)
{
//check input
if (radius <= 0)
{
throw new ArgumentException("Radius can not be <= 0");
}
if (horizontalResolution <= 3)
{
horizontalResolution = 3;
}
if (verticalResolution <= 2)
{
verticalResolution = 2;
}
var sphere = new Geometry();
var northPole = new Vertex(sphere.CreateVertHandleId(), new float3(0, radius, 0));
var southPole = new Vertex(sphere.CreateVertHandleId(), new float3(0, -radius, 0));
var horizontalAngleStep = System.Math.PI * 2 / horizontalResolution; // s
var verrticalAngleStep = System.Math.PI / verticalResolution; // t
var currentLatitudeVerticesHandles = new int[horizontalResolution];
var lastLaitudeVerticesHandles = new int[horizontalResolution]; //stores last vertices to connect them later with the next latidute vertices
for (var i = 1; i < verticalResolution + 1; i++)
{
//create all vertices
if (i < verticalResolution)
{
for (var j = 0; j < horizontalResolution; j++)
{
//create all Vertices of current latitude
var xPos = (float)(radius * System.Math.Sin(horizontalAngleStep * j) * System.Math.Sin(verrticalAngleStep * i));
var yPos = (float)(radius * System.Math.Cos(verrticalAngleStep * (i)));
var zPos = (float)(radius * System.Math.Cos(horizontalAngleStep * j) * System.Math.Sin(verrticalAngleStep * i));
var circleVertex = new Vertex(sphere.CreateVertHandleId(), new float3(xPos, yPos, zPos));
sphere.DictVertices.Add(circleVertex.Handle, circleVertex);
currentLatitudeVerticesHandles[j] = circleVertex.Handle;
}
}
//create faces
var topHeHandles = new int[horizontalResolution];
for (var j = 0; j < horizontalResolution; j++)
{
// bottom triangles of sphere
if (i == verticalResolution)
{
var bottomTriangle = new Face(sphere.CreateFaceHandleId());
var h1 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
var h2 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
var h3 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
topHeHandles[j] = h1.Handle;
h1.NextHalfEdge = h2.Handle;
h2.NextHalfEdge = h3.Handle;
h3.NextHalfEdge = h1.Handle;
h1.PrevHalfEdge = h3.Handle;
h2.PrevHalfEdge = h1.Handle;
h3.PrevHalfEdge = h2.Handle;
h1.IncidentFace = bottomTriangle.Handle;
h2.IncidentFace = bottomTriangle.Handle;
h3.IncidentFace = bottomTriangle.Handle;
h1.OriginVertex = currentLatitudeVerticesHandles[j];
h2.OriginVertex = j == horizontalResolution - 1 ? currentLatitudeVerticesHandles[0] : currentLatitudeVerticesHandles[j + 1];
h3.OriginVertex = southPole.Handle;
bottomTriangle.OuterHalfEdge = h1.Handle;
southPole.IncidentHalfEdge = h3.Handle;
//write changes
sphere.DictHalfEdges.Add(h1.Handle, h1);
sphere.DictHalfEdges.Add(h2.Handle, h2);
sphere.DictHalfEdges.Add(h3.Handle, h3);
sphere.DictFaces.Add(bottomTriangle.Handle, bottomTriangle);
}
// top triangles of sphere
else if (i == 1)
{
var topTriangle = new Face(sphere.CreateFaceHandleId());
var h1 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
var h2 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
var h3 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
topHeHandles[j] = h1.Handle;
h1.NextHalfEdge = h2.Handle;
h2.NextHalfEdge = h3.Handle;
h3.NextHalfEdge = h1.Handle;
h1.PrevHalfEdge = h3.Handle;
h2.PrevHalfEdge = h1.Handle;
h3.PrevHalfEdge = h2.Handle;
h1.IncidentFace = topTriangle.Handle;
h2.IncidentFace = topTriangle.Handle;
h3.IncidentFace = topTriangle.Handle;
h1.OriginVertex = j == horizontalResolution - 1 ? currentLatitudeVerticesHandles[0] : currentLatitudeVerticesHandles[j + 1];
h2.OriginVertex = currentLatitudeVerticesHandles[j];
h3.OriginVertex = northPole.Handle;
topTriangle.OuterHalfEdge = h1.Handle;
var currentVertex = sphere.GetVertexByHandle(currentLatitudeVerticesHandles[j]);
currentVertex.IncidentHalfEdge = h2.Handle;
northPole.IncidentHalfEdge = h3.Handle;
//write changes
sphere.DictHalfEdges.Add(h1.Handle, h1);
sphere.DictHalfEdges.Add(h2.Handle, h2);
sphere.DictHalfEdges.Add(h3.Handle, h3);
sphere.DictFaces.Add(topTriangle.Handle, topTriangle);
sphere.ReplaceVertex(currentVertex);
}
// middle quads of sphere
else
{
var quad = new Face(sphere.CreateFaceHandleId());
var h1 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
var h2 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
var h3 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
var h4 = new HalfEdge(sphere.CreateHalfEdgeHandleId());
topHeHandles[j] = h1.Handle;
h1.NextHalfEdge = h2.Handle;
h2.NextHalfEdge = h3.Handle;
h3.NextHalfEdge = h4.Handle;
h4.NextHalfEdge = h1.Handle;
h1.PrevHalfEdge = h4.Handle;
h2.PrevHalfEdge = h1.Handle;
h3.PrevHalfEdge = h2.Handle;
h4.PrevHalfEdge = h3.Handle;
h1.IncidentFace = quad.Handle;
h2.IncidentFace = quad.Handle;
h3.IncidentFace = quad.Handle;
h4.IncidentFace = quad.Handle;
quad.OuterHalfEdge = h1.Handle;
h4.OriginVertex = currentLatitudeVerticesHandles[j];
h3.OriginVertex = j == horizontalResolution - 1 ? currentLatitudeVerticesHandles[0] : currentLatitudeVerticesHandles[j + 1];
h2.OriginVertex = j == horizontalResolution - 1 ? lastLaitudeVerticesHandles[0] : lastLaitudeVerticesHandles[j + 1];
h1.OriginVertex = lastLaitudeVerticesHandles[j];
var currentVertex = sphere.GetVertexByHandle(currentLatitudeVerticesHandles[j]);
currentVertex.IncidentHalfEdge = h4.Handle;
//write changes
sphere.DictFaces.Add(quad.Handle, quad);
sphere.DictHalfEdges.Add(h1.Handle, h1);
sphere.DictHalfEdges.Add(h2.Handle, h2);
sphere.DictHalfEdges.Add(h3.Handle, h3);
sphere.DictHalfEdges.Add(h4.Handle, h4);
sphere.ReplaceVertex(currentVertex);
}
}
//set twins
for (int j = 0; j < horizontalResolution; j++)
{
//set twins of adjacent triangles bottom
if (i == 1)
{
int nextH1Index;
nextH1Index = j == 0 ? horizontalResolution - 1 : j - 1;
var h1 = sphere.GetHalfEdgeByHandle(topHeHandles[j]);
var h2 = sphere.GetHalfEdgeByHandle(h1.NextHalfEdge);
var nextH1 = sphere.GetHalfEdgeByHandle(topHeHandles[nextH1Index]);
var nextH3 = sphere.GetHalfEdgeByHandle(nextH1.PrevHalfEdge);
nextH3.TwinHalfEdge = h2.Handle;
h2.TwinHalfEdge = nextH3.Handle;
sphere.ReplaceHalfEdge(nextH3);
sphere.ReplaceHalfEdge(h2);
}
else if (i == verticalResolution)
{
int nextH1Index;
nextH1Index = j == 0 ? horizontalResolution - 1 : j - 1;
var h1 = sphere.GetHalfEdgeByHandle(topHeHandles[j]);
var h3 = sphere.GetHalfEdgeByHandle(h1.PrevHalfEdge);
var nextH1 = sphere.GetHalfEdgeByHandle(topHeHandles[nextH1Index]);
var nextH2 = sphere.GetHalfEdgeByHandle(nextH1.NextHalfEdge);
nextH2.TwinHalfEdge = h3.Handle;
h3.TwinHalfEdge = nextH2.Handle;
sphere.ReplaceHalfEdge(nextH2);
sphere.ReplaceHalfEdge(h3);
}
else //set twins of adjacent quads
{
var h1 = sphere.GetHalfEdgeByHandle(topHeHandles[j]);
var h4 = sphere.GetHalfEdgeByHandle(h1.PrevHalfEdge);
int nextH1Index;
nextH1Index = j == 0 ? horizontalResolution - 1 : j - 1;
var nextH1 = sphere.GetHalfEdgeByHandle(topHeHandles[nextH1Index]);
var nextH2 = sphere.GetHalfEdgeByHandle(nextH1.NextHalfEdge);
nextH2.TwinHalfEdge = h4.Handle;
h4.TwinHalfEdge = nextH2.Handle;
sphere.ReplaceHalfEdge(nextH2);
sphere.ReplaceHalfEdge(h4);
}
//set twin of face on top
if (i > 1)
{
var h1 = sphere.GetHalfEdgeByHandle(topHeHandles[j]);
var lastVertex = sphere.GetVertexByHandle(lastLaitudeVerticesHandles[j]);
var topH1 = sphere.GetHalfEdgeByHandle(lastVertex.IncidentHalfEdge);
while (true)
{
if (topH1.TwinHalfEdge == 0)
{
break;
}
topH1 = sphere.GetHalfEdgeByHandle(topH1.NextHalfEdge);
}
topH1.TwinHalfEdge = h1.Handle;
h1.TwinHalfEdge = topH1.Handle;
sphere.ReplaceHalfEdge(h1);
sphere.ReplaceHalfEdge(topH1);
}
}
Array.Copy(currentLatitudeVerticesHandles, lastLaitudeVerticesHandles,
currentLatitudeVerticesHandles.Length);
}
sphere.DictVertices.Add(northPole.Handle, northPole);
sphere.DictVertices.Add(southPole.Handle, southPole);
//calculate normals
var allFaces = sphere.GetAllFaces().ToList();
foreach (var face in allFaces)
{
sphere.SetFaceNormal(sphere.GetFaceVertices(face.Handle).ToList(), face);
}
return(sphere);
}
/// <summary>
/// Creates and returns a cone with the given dimensions.
/// </summary>
/// <param name="baseRadius">The radiaus of the base circle.</param>
/// <param name="dimensionY">The height of the cone.</param>
/// <param name="sliceCount">The horizontal resulotion of the base circle. Min value is 3. For a basic cone 15.</param>
/// <returns></returns>
public static Geometry CreateConeGeometry(float baseRadius, float dimensionY, int sliceCount)
{
//check input
if (sliceCount < 3)
{
sliceCount = 3;
}
if (baseRadius <= 0 || dimensionY <= 0)
{
throw new ArgumentException("You can not input paramaters <= 0");
}
var cone = new Geometry();
var northPole = new Vertex(cone.CreateVertHandleId(), new float3(0, dimensionY / 2, 0));
var southPole = new Vertex(cone.CreateVertHandleId(), new float3(0, -dimensionY / 2, 0));
var angleStep = System.Math.PI * 2 / sliceCount;
var yPos = -dimensionY / 2.0f;
int[] firstHandles = null; //stores the handles of the first slice to connect it later with the last slice
var lastH3 = new HalfEdge();
var lastH2 = new HalfEdge();
var lastVertex = southPole;
for (var i = 1; i < sliceCount + 1; i++)
{
var x = (float)System.Math.Cos(angleStep * i) * baseRadius;
var z = (float)System.Math.Sin(angleStep * i) * baseRadius;
var tempVertex = new Vertex(cone.CreateVertHandleId(), new float3(x, yPos, z));
//south to temp
var h1 = new HalfEdge(cone.CreateHalfEdgeHandleId());
var h2 = new HalfEdge(cone.CreateHalfEdgeHandleId()); //twin of h1
tempVertex.IncidentHalfEdge = h2.Handle;
h1.OriginVertex = southPole.Handle;
h2.OriginVertex = tempVertex.Handle;
h1.TwinHalfEdge = h2.Handle;
h2.TwinHalfEdge = h1.Handle;
//temp to north
var h3 = new HalfEdge(cone.CreateHalfEdgeHandleId());
var h4 = new HalfEdge(cone.CreateHalfEdgeHandleId());
northPole.IncidentHalfEdge = h3.Handle;
southPole.IncidentHalfEdge = h1.Handle;
h3.OriginVertex = northPole.Handle;
h4.OriginVertex = tempVertex.Handle;
h3.TwinHalfEdge = h4.Handle;
h4.TwinHalfEdge = h3.Handle;
if (lastVertex == southPole)
{
firstHandles = new[] { tempVertex.Handle, h1.Handle, h4.Handle };
lastH3 = h3;
lastH2 = h2;
cone.DictVertices.Add(tempVertex.Handle, tempVertex);
cone.DictHalfEdges.Add(h1.Handle, h1);
cone.DictHalfEdges.Add(h2.Handle, h2);
cone.DictHalfEdges.Add(h3.Handle, h3);
cone.DictHalfEdges.Add(h4.Handle, h4);
lastVertex = tempVertex;
continue;
}
//temp to last
var h5 = new HalfEdge(cone.CreateHalfEdgeHandleId());
var h6 = new HalfEdge(cone.CreateHalfEdgeHandleId());
h5.OriginVertex = lastVertex.Handle;
h6.OriginVertex = tempVertex.Handle;
h5.TwinHalfEdge = h6.Handle;
h6.TwinHalfEdge = h5.Handle;
//create top triangles south-temp-last
var triangle1 = new Face(cone.CreateFaceHandleId());
h5.NextHalfEdge = h4.Handle;
triangle1.OuterHalfEdge = h5.Handle;
h4.NextHalfEdge = lastH3.Handle;
lastH3.NextHalfEdge = h5.Handle;
h5.IncidentFace = triangle1.Handle;
h4.IncidentFace = triangle1.Handle;
lastH3.IncidentFace = triangle1.Handle;
h5.PrevHalfEdge = lastH3.Handle;
lastH3.PrevHalfEdge = h4.Handle;
h4.PrevHalfEdge = h5.Handle;
//north-last-temp
var triangle2 = new Face(cone.CreateFaceHandleId());
h6.NextHalfEdge = lastH2.Handle;
triangle2.OuterHalfEdge = h6.Handle;
lastH2.NextHalfEdge = h1.Handle;
h1.NextHalfEdge = h6.Handle;
h6.IncidentFace = triangle2.Handle;
lastH2.IncidentFace = triangle2.Handle;
h1.IncidentFace = triangle2.Handle;
h6.PrevHalfEdge = h1.Handle;
h1.PrevHalfEdge = lastH2.Handle;
lastH2.PrevHalfEdge = h6.Handle;
//write
cone.DictVertices.Add(tempVertex.Handle, tempVertex);
cone.DictHalfEdges.Add(h1.Handle, h1);
cone.DictHalfEdges.Add(h2.Handle, h2);
cone.DictHalfEdges.Add(h3.Handle, h3);
cone.DictHalfEdges.Add(h4.Handle, h4);
cone.DictHalfEdges.Add(h5.Handle, h5);
cone.DictHalfEdges.Add(h6.Handle, h6);
cone.ReplaceHalfEdge(lastH2);
cone.ReplaceHalfEdge(lastH3);
cone.DictFaces.Add(triangle1.Handle, triangle1);
cone.DictFaces.Add(triangle2.Handle, triangle2);
lastH2 = h2;
lastH3 = h3;
lastVertex = tempVertex;
}
//add south and northpole
cone.DictVertices.Add(southPole.Handle, southPole);
cone.DictVertices.Add(northPole.Handle, northPole);
//create last 2 traingles
var firstVertex = cone.GetVertexByHandle(firstHandles[0]);
var firtstH1 = cone.GetHalfEdgeByHandle(firstHandles[1]);
var firstH4 = cone.GetHalfEdgeByHandle(firstHandles[2]);
var lastH5 = new HalfEdge(cone.CreateHalfEdgeHandleId());
var lastH6 = new HalfEdge(cone.CreateHalfEdgeHandleId());
lastH5.OriginVertex = lastVertex.Handle;
lastH6.OriginVertex = firstVertex.Handle;
lastH5.TwinHalfEdge = lastH6.Handle;
lastH6.TwinHalfEdge = lastH5.Handle;
//create to triangles south-temp-last, north-last-temp
var triangleL1 = new Face(cone.CreateFaceHandleId())
{
OuterHalfEdge = lastH5.Handle
};
lastH5.NextHalfEdge = firstH4.Handle;
firstH4.NextHalfEdge = lastH3.Handle;
lastH3.NextHalfEdge = lastH5.Handle;
lastH5.IncidentFace = triangleL1.Handle;
firstH4.IncidentFace = triangleL1.Handle;
lastH3.IncidentFace = triangleL1.Handle;
lastH5.PrevHalfEdge = lastH3.Handle;
lastH3.PrevHalfEdge = firstH4.Handle;
firstH4.PrevHalfEdge = lastH5.Handle;
var triangleL2 = new Face(cone.CreateFaceHandleId())
{
OuterHalfEdge = lastH6.Handle
};
lastH6.NextHalfEdge = lastH2.Handle;
lastH2.NextHalfEdge = firtstH1.Handle;
firtstH1.NextHalfEdge = lastH6.Handle;
lastH6.IncidentFace = triangleL2.Handle;
lastH2.IncidentFace = triangleL2.Handle;
firtstH1.IncidentFace = triangleL2.Handle;
lastH6.PrevHalfEdge = firtstH1.Handle;
firtstH1.PrevHalfEdge = lastH2.Handle;
lastH2.PrevHalfEdge = lastH6.Handle;
//write
cone.ReplaceHalfEdge(firtstH1);
cone.DictHalfEdges.Add(lastH5.Handle, lastH5);
cone.DictHalfEdges.Add(lastH6.Handle, lastH6);
cone.ReplaceHalfEdge(lastH2);
cone.ReplaceHalfEdge(lastH3);
cone.ReplaceHalfEdge(firstH4);
cone.DictFaces.Add(triangleL1.Handle, triangleL1);
cone.DictFaces.Add(triangleL2.Handle, triangleL2);
//face normals
var allFaces = cone.GetAllFaces().ToList();
foreach (var face in allFaces)
{
cone.SetFaceNormal(cone.GetFaceVertices(face.Handle).ToList(), face);
}
return(cone);
}
