private void RenderGUI()
{
//============================================================================
// Render a visual marker to highlight the node that is being manipulated
//============================================================================
if (solver.HandleNodeIndex != -1 || solver.NearestNodeIndex != -1)
{
CameraData camera = DynaShapeViewExtension.CameraData;
Triple camOrigin = new Triple(camera.EyePosition.X, -camera.EyePosition.Z, camera.EyePosition.Y);
Triple camZ = new Triple(camera.LookDirection.X, -camera.LookDirection.Z, camera.LookDirection.Y).Normalise();
Triple camY = new Triple(camera.UpDirection.X, -camera.UpDirection.Z, camera.UpDirection.Y).Normalise();
Triple camX = camZ.Cross(camY);
int nodeIndex = solver.HandleNodeIndex != -1 ? solver.HandleNodeIndex : solver.NearestNodeIndex;
Triple v = solver.Nodes[nodeIndex].Position - camOrigin;
float screenDistance = (float)camera.NearPlaneDistance + 0.1f;
v = camOrigin + v * screenDistance / v.Dot(camZ);
float markerSize = 0.025f * screenDistance;
Triple v1 = v + camX * markerSize;
Triple v2 = v - camY * markerSize;
Triple v3 = v - camX * markerSize;
Triple v4 = v + camY * markerSize;
lineGeometry.Positions.Add(v1.ToVector3());
lineGeometry.Positions.Add(v3.ToVector3());
lineGeometry.Positions.Add(v2.ToVector3());
lineGeometry.Positions.Add(v4.ToVector3());
markerSize *= 0.5f;
v1 = v + camX * markerSize;
v2 = v - camY * markerSize;
v3 = v - camX * markerSize;
v4 = v + camY * markerSize;
lineGeometry.Positions.Add(v1.ToVector3());
lineGeometry.Positions.Add(v2.ToVector3());
lineGeometry.Positions.Add(v2.ToVector3());
lineGeometry.Positions.Add(v3.ToVector3());
lineGeometry.Positions.Add(v3.ToVector3());
lineGeometry.Positions.Add(v4.ToVector3());
lineGeometry.Positions.Add(v4.ToVector3());
lineGeometry.Positions.Add(v1.ToVector3());
int temp = lineGeometry.Indices.Count;
for (int i = 0; i < 12; i++)
{
lineGeometry.Indices.Add(temp + i);
lineGeometry.Colors.Add(Color.OrangeRed);
}
}
}
/// <summary>
/// Compute the plane that best fit a set of input points (least squared orthogonal distance)
/// </summary>
/// <param name="points">The input points</param>
/// <param name="planeOrigin">The output plane origin</param>
/// <param name="planeNormal">The output plane normal vector</param>
/// <returns>0 if the input points are identical, 1 if the input points are colinear, 2 if the input points are coplanar (already on a plane), 3 otherwise</returns>
public static int ComputeBestFitPlane(List <Triple> points, out Triple planeOrigin, out Triple planeNormal)
{
Triple centroid = Triple.Zero;
for (int i = 0; i < points.Count; i++)
{
centroid += points[i];
}
centroid /= points.Count;
float[,] P = new float[points.Count, 3];
for (int i = 0; i < points.Count; i++)
{
P[i, 0] = points[i].X - centroid.X;
P[i, 1] = points[i].Y - centroid.Y;
P[i, 2] = points[i].Z - centroid.Z;
}
Matrix <float> covariance = Matrix <float> .Build.Dense(3, 3);
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
for (int k = 0; k < points.Count; k++)
{
covariance[i, j] += P[k, i] * P[k, j];
}
}
}
Evd <float> evd = covariance.Evd();
planeOrigin = centroid;
if (evd.Rank == 0) // The input points are idendtical, so we just pick an arbitrary normal vector
{
planeNormal = Triple.BasisZ;
}
else if (evd.Rank == 1
) // The input points are colinear, so we just pick an arbitrary vector perpendicular to the only eigen vector
{
planeNormal = new Triple(evd.EigenVectors[0, 1], evd.EigenVectors[1, 1], evd.EigenVectors[2, 1])
.GeneratePerpendicular();
}
else // The normal is perpendicular to the two dominant eigen vectors
{
Triple e1 = new Triple(evd.EigenVectors[0, 1], evd.EigenVectors[1, 1], evd.EigenVectors[2, 1]);
Triple e2 = new Triple(evd.EigenVectors[0, 2], evd.EigenVectors[1, 2], evd.EigenVectors[2, 2]);
planeNormal = e2.Cross(e1).Normalise();
}
return(evd.Rank);
}
public void Tessellate(IRenderPackage package, TessellationParameters parameters)
{
for (int i = 0; i < solver.Nodes.Count; i++)
{
GeometryRender.DrawPoint(package, solver.Nodes[i].Position);
}
for (int i = 0; i < solver.GeometryBinders.Count; i++)
{
solver.GeometryBinders[i].DrawGraphics(package, parameters, solver.Nodes);
}
//=======================================================================================
// Draw a cursor to highlight the node that is being manipulated by the mouse
// ... the curor is 2D, so we need to draw it in the camera coordinate system, manually
//=======================================================================================
CameraData camera = ((HelixWatch3DViewModel)Solver.Viewport).Camera.Dispatcher.Invoke(() => Solver.Viewport.GetCameraInformation());
Triple camOrigin = new Triple(camera.EyePosition.X, -camera.EyePosition.Z, camera.EyePosition.Y);
Triple camZ = new Triple(camera.LookDirection.X, -camera.LookDirection.Z, camera.LookDirection.Y).Normalise();
Triple camY = new Triple(camera.UpDirection.X, -camera.UpDirection.Z, camera.UpDirection.Y).Normalise();
Triple camX = camZ.Cross(camY);
if (solver.HandleNodeIndex != -1 || solver.NearestNodeIndex != -1)
{
int i = solver.HandleNodeIndex != -1 ? solver.HandleNodeIndex : solver.NearestNodeIndex;
Color handleColor = solver.HandleNodeIndex != -1 ? Color.OrangeRed : Color.Black;
Triple v = solver.Nodes[i].Position - camOrigin;
v = camOrigin + ((float)camera.NearPlaneDistance + 0.5f) * v / v.Dot(camZ);
float handleSize = 0.008f;
Triple v1 = v + camX * handleSize;
Triple v2 = v - camY * handleSize;
Triple v3 = v - camX * handleSize;
Triple v4 = v + camY * handleSize;
GeometryRender.DrawPolyline(package, new List <Triple> {
v1, v2, v3, v4, v1
}, handleColor);
handleSize = 0.015f;
v1 = v + camX * handleSize;
v2 = v - camY * handleSize;
v3 = v - camX * handleSize;
v4 = v + camY * handleSize;
GeometryRender.DrawLine(package, v1, v3, handleColor);
GeometryRender.DrawLine(package, v2, v4, handleColor);
}
}
/// <summary>
/// Compute the plane that best fit a set of input points (least squared orthogonal distance)
/// </summary>
/// <param name="points">The input points</param>
/// <param name="planeOrigin">The output plane origin</param>
/// <param name="planeNormal">The output plane normal vector</param>
/// <returns>0 if the input points are identical, 1 if the input points are colinear, 2 if the input points are coplanar (already on a plane), 3 otherwise</returns>
//public static int ComputeBestFitPlane(List<Triple> points, out Triple planeOrigin, out Triple planeNormal)
//{
// Triple centroid = Triple.Zero;
// for (int i = 0; i < points.Count; i++) centroid += points[i];
// centroid /= points.Count;
// float[,] P = new float[points.Count, 3];
// for (int i = 0; i < points.Count; i++)
// {
// P[i, 0] = points[i].X - centroid.X;
// P[i, 1] = points[i].Y - centroid.Y;
// P[i, 2] = points[i].Z - centroid.Z;
// }
// Matrix<float> covariance = Matrix<float>.Build.Dense(3, 3);
// for (int i = 0; i < 3; i++)
// for (int j = 0; j < 3; j++)
// for (int k = 0; k < points.Count; k++)
// covariance[i, j] += P[k, i] * P[k, j];
// Evd<float> evd = covariance.Evd();
// planeOrigin = centroid;
// if (evd.Rank == 0) // The input points are idendtical, so we just pick an arbitrary normal vector
// planeNormal = Triple.BasisZ;
// else if (evd.Rank == 1
// ) // The input points are colinear, so we just pick an arbitrary vector perpendicular to the only eigen vector
// planeNormal = new Triple(evd.EigenVectors[0, 1], evd.EigenVectors[1, 1], evd.EigenVectors[2, 1])
// .GeneratePerpendicular();
// else // The normal is perpendicular to the two dominant eigen vectors
// {
// Triple e1 = new Triple(evd.EigenVectors[0, 1], evd.EigenVectors[1, 1], evd.EigenVectors[2, 1]);
// Triple e2 = new Triple(evd.EigenVectors[0, 2], evd.EigenVectors[1, 2], evd.EigenVectors[2, 2]);
// planeNormal = e2.Cross(e1).Normalise();
// }
// return evd.Rank;
//}
public static int ComputeBestFitPlane(List <Triple> points, out Triple planeOrigin, out Triple planeNormal)
{
Triple centroid = Triple.Zero;
for (int i = 0; i < points.Count; i++)
{
centroid += points[i];
}
centroid /= points.Count;
float[,] P = new float[points.Count, 3];
for (int i = 0; i < points.Count; i++)
{
P[i, 0] = points[i].X - centroid.X;
P[i, 1] = points[i].Y - centroid.Y;
P[i, 2] = points[i].Z - centroid.Z;
}
Matrix3x3 covariance = new Matrix3x3();
for (int k = 0; k < points.Count; k++)
{
covariance.V00 += P[k, 0] * P[k, 0];
covariance.V01 += P[k, 0] * P[k, 1];
covariance.V02 += P[k, 0] * P[k, 2];
covariance.V10 += P[k, 1] * P[k, 0];
covariance.V11 += P[k, 1] * P[k, 1];
covariance.V12 += P[k, 1] * P[k, 2];
covariance.V20 += P[k, 2] * P[k, 0];
covariance.V21 += P[k, 2] * P[k, 1];
covariance.V22 += P[k, 2] * P[k, 2];
}
Matrix3x3 u, v;
AForge.Math.Vector3 e;
covariance.SVD(out u, out e, out v);
planeOrigin = centroid;
Triple e1 = new Triple(u.V00, u.V10, u.V20);
Triple e2 = new Triple(u.V01, u.V11, u.V21);
planeNormal = e2.Cross(e1).Normalise();
return(3);
}
internal int FindNearestNodeIndex(float range = 0.03f)
{
CameraData cameraData = DynaShapeViewExtension.CameraData;
Triple camZ = new Triple(
cameraData.LookDirection.X,
-cameraData.LookDirection.Z,
cameraData.LookDirection.Y).Normalise();
Triple camY = new Triple(
cameraData.UpDirection.X,
-cameraData.UpDirection.Z,
cameraData.UpDirection.Y).Normalise();
Triple camX = camY.Cross(camZ).Normalise();
Triple mousePosition2D = new Triple(
DynaShapeViewExtension.MouseRayDirection.Dot(camX),
DynaShapeViewExtension.MouseRayDirection.Dot(camY),
DynaShapeViewExtension.MouseRayDirection.Dot(camZ));
mousePosition2D /= mousePosition2D.Z;
int nearestNodeIndex = -1;
float minDistSquared = range * range;
for (int i = 0; i < Nodes.Count; i++)
{
Triple v = Nodes[i].Position - DynaShapeViewExtension.MouseRayOrigin;
v = new Triple(v.Dot(camX), v.Dot(camY), v.Dot(camZ));
Triple nodePosition2D = v / v.Z;
float distSquared = (mousePosition2D - nodePosition2D).LengthSquared;
if (distSquared < minDistSquared)
{
minDistSquared = distSquared;
nearestNodeIndex = i;
}
}
return(nearestNodeIndex);
}
public Triple Rotate(Triple origin, Triple Axis, float angle)
{
Triple z = Axis.Normalise();
Triple x = z.GeneratePerpendicular().Normalise();
Triple y = z.Cross(x).Normalise();
Triple v = this - origin;
float vx = x.Dot(v);
float vy = y.Dot(v);
float vz = z.Dot(v);
float sin = (float)Math.Sin(angle);
float cos = (float)Math.Cos(angle);
float vx_ = cos * vx - sin * vy;
float vy_ = sin * vx + cos * vy;
return(origin + x * vx_ + y * vy_ + z * vz);
}
internal int FindNearestNodeIndex(IRay clickRay, float range = 0.03f)
{
CameraData cameraData = Viewport.GetCameraInformation();
Triple camZ = new Triple(cameraData.LookDirection.X, -cameraData.LookDirection.Z,
cameraData.LookDirection.Y).Normalise();
Triple camY = new Triple(cameraData.UpDirection.X, -cameraData.UpDirection.Z, cameraData.UpDirection.Y)
.Normalise();
Triple camX = camY.Cross(camZ).Normalise();
Triple clickRayOrigin = new Triple(clickRay.Origin.X, clickRay.Origin.Y, clickRay.Origin.Z);
Triple clickRayDirection = new Triple(clickRay.Direction.X, clickRay.Direction.Y, clickRay.Direction.Z);
Triple mousePosition2D = new Triple(clickRayDirection.Dot(camX), clickRayDirection.Dot(camY),
clickRayDirection.Dot(camZ));
mousePosition2D /= mousePosition2D.Z;
int nearestNodeIndex = -1;
float minDistSquared = range * range;
for (int i = 0; i < Nodes.Count; i++)
{
Triple v = Nodes[i].Position - clickRayOrigin;
v = new Triple(v.Dot(camX), v.Dot(camY), v.Dot(camZ));
Triple nodePosition2D = v / v.Z;
float distSquared = (mousePosition2D - nodePosition2D).LengthSquared;
if (distSquared < minDistSquared)
{
minDistSquared = distSquared;
nearestNodeIndex = i;
}
}
return(nearestNodeIndex);
}