// compute the releft point of p according to the Canvas3 (Canvas3_normal, Canvas3_center)
public static MyVector3 Reflect(MyVector3 p, MyVector3 Canvas3_normal, MyVector3 Canvas3_center)
{
MyVector3 u = p - Canvas3_center;
// create a coord system (x,y,z), project to that sys, reflect and project back
MyVector3 x = Canvas3_normal;
MyVector3 y;
if (x.x == 0 && x.y == 0)
{
y = new MyVector3(0, -x.z, x.y);
}
else
{
y = new MyVector3(x.y, -x.x, 0);
}
MyVector3 z = x.Cross(y);
MyMatrix3d R = new MyMatrix3d(x, y, z);
MyMatrix3d InvR = R.InverseSVD();
MyMatrix4d U = new MyMatrix4d(R);
MyMatrix4d V = new MyMatrix4d(InvR);
MyMatrix4d I = MyMatrix4d.IdentityMatrix();
I[0, 0] = -1; // reflect matrix along yz Canvas3
MyMatrix4d T = V * I * U; // the reflection matrix
// reflect
MyVector4 r = new MyVector4(u, 0);
MyVector3 q = Canvas3_center + (T * r).XYZ();
return(q);
}
public static MyMatrix4d RotationMatrixU2V(MyVector3 u, MyVector3 v)
{
// find the rotational matrix which rotate u to v
// one should be extremely careful here, very small viboration
// will make a lot of difference
// e.g., u = (0.5*e-10, 0.1*e-10, 1), v = (0,0,-1), will make
// an fliping around axie (1, 5, 0) with angele Pi
MyMatrix4d R = MyMatrix4d.IdentityMatrix();
double cos = u.Normalize().Dot(v.Normalize());
if (Math.Abs(Math.Abs(cos) - 1.0f) < 1e-5) // coincident, do nothing
{
return(R);
}
MyVector3 axis = u.Cross(v).Normalize();
if (!double.IsNaN(axis.x))
{
if (cos < -1)
{
cos = -1;
}
if (cos > 1)
{
cos = 1;
}
double angle = Math.Acos(cos);
R = MyMatrix4d.RotationMatrix(axis, angle);
}
return(R);
}
public void ComputeBoundQuad()
{
MyVector3 normal = Normal();
MyVector3 xaxis = new MyVector3(1, 0, 0);
MyVector3 yaxis = new MyVector3(0, 1, 0);
MyVector3 zaxis = new MyVector3(0, 0, 1);
MyVector3 rotAxis = zaxis.Cross(normal).Normalize();
double cos = zaxis.Dot(normal);
if (cos > 1)
{
cos = 1;
}
if (cos < -1)
{
cos = -1;
}
double rotAngle = Math.Acos(cos);
MyMatrix4d R = MyMatrix4d.RotationMatrix(rotAxis, rotAngle);
MyVector3 new_xaxis = (R * new MyVector4(xaxis)).XYZ().Normalize();
MyVector3 new_yaxis = (R * new MyVector4(yaxis)).XYZ().Normalize();
CoordinateFrame frame = new CoordinateFrame(this.planeCenter, new_xaxis, new_yaxis, normal);
double xmin = double.MaxValue; double ymin = double.MaxValue;
double xmax = double.MinValue; double ymax = double.MinValue;
foreach (MyVector3 v in this.planeVertices)
{
MyVector3 u = frame.GetPointLocalCoord(v);
xmin = Math.Min(u.x, xmin);
xmax = Math.Max(u.x, xmax);
ymin = Math.Min(u.y, ymin);
ymax = Math.Max(u.y, ymax);
}
MyVector3 v1 = new MyVector3(xmin, ymin, 0);
MyVector3 v2 = new MyVector3(xmax, ymin, 0);
MyVector3 v3 = new MyVector3(xmax, ymax, 0);
MyVector3 v4 = new MyVector3(xmin, ymax, 0);
SmartCanvas.Point3[] pts3 =
new SmartCanvas.Point3[4] {
new SmartCanvas.Point3(frame.GetPointSpaceCoord(v1)),
new SmartCanvas.Point3(frame.GetPointSpaceCoord(v2)),
new SmartCanvas.Point3(frame.GetPointSpaceCoord(v3)),
new SmartCanvas.Point3(frame.GetPointSpaceCoord(v4))
};
this.boundQuad = new Quad3D(pts3);
}
public void Project3dToBelongPlane()
{
// prepare 2d coordinate
MyVector3 circle_norm = this.belongPlane.Normal();
MyVector3 X = new MyVector3(1, 0, 0);
MyVector3 Y = new MyVector3(0, 1, 0);
MyVector3 Z = new MyVector3(0, 0, 1);
MyVector3 rotAxis = Z.Cross(circle_norm).Normalize();
double angle_cos = Z.Dot(circle_norm);
if (angle_cos > 1)
{
angle_cos = 1;
}
if (angle_cos < -1)
{
angle_cos = -1;
}
double rotAngle = Math.Acos(angle_cos);
MyMatrix4d Mat = MyMatrix4d.RotationMatrix(rotAxis, rotAngle);
MyVector3 X_new = (Mat * new MyVector4(X)).XYZ().Normalize();
MyVector3 Y_new = (Mat * new MyVector4(Y)).XYZ().Normalize();
CoordinateFrame frame = new CoordinateFrame(this.belongPlane.planeCenter, X_new, Y_new, circle_norm);
// projection and denoise(leave out far away points)
MyVector3 tmpc = frame.GetPointLocalCoord(this.center);
this.center2d = new MyVector2(tmpc.x, tmpc.y);
for (int i = 0; i < this.circleSlice3d.Count; i++)
{
MyVector3 vert = this.circleSlice3d[i];
MyVector3 tmp = frame.GetPointLocalCoord(vert);
MyVector2 tmp2 = new MyVector2(tmp.x, tmp.y);
double dist = Math.Abs((tmp2 - this.center2d).Length() - this.radius);
if (dist > 0.5 * this.radius && dist < 0.75 * this.radius)
{
this.circleSlice3d.RemoveAt(i);
i--;
}
else
{
this.circleSlice2d.Add(tmp2);
}
}
}
private void SampleCirclePoints3d(MyVector3 center, MyVector3 normal, double radius, int sample)
{
MyPlane circleplane = new MyPlane(center, normal);
//MyVector3 pointonplane = circleplane.ProjectPoint(center - new MyVector3(0.01, 0.01, 0.01));
//MyVector3 u = pointonplane - center;
MyVector3 pointonplane = circleplane.ProjectPoint(center + new MyVector3(-0.1, 0, 0));
MyVector3 u = pointonplane - center;
MyVector3 v = u.Cross(normal);
u = u.Normalize();
v = v.Normalize();
int num = sample;
double theta = 2.0 * Math.PI / (num - 1);
for (int j = 0; j < num; j++)
{
double x = center.x + radius * (u.x * Math.Cos(j * theta) + v.x * Math.Sin(j * theta));
double y = center.y + radius * (u.y * Math.Cos(j * theta) + v.y * Math.Sin(j * theta));
double z = center.z + radius * (u.z * Math.Cos(j * theta) + v.z * Math.Sin(j * theta));
this.circlePoints3d.Add(new MyVector3(x, y, z));
}
}
public MyPlane(MyVector3 point, MyVector3 normal)
{
double d = -point.Dot(normal);
planeEquation = new Plane((float)normal.x, (float)normal.y, (float)normal.z, (float)d);
planeCenter = point;
planeColor = Color.FromArgb(150, 255, 255, 0);
// add three plane points
MyVector3 x = new MyVector3(normal.y, -normal.x, 0);
if (x.x == 0 && x.y == 0)
{
x = new MyVector3(1, 0, 0);
}
MyVector3 y = normal.Cross(x).Normalize();
CoordinateFrame frame = new CoordinateFrame(point, x, y, normal);
double s = 0.8;
MyVector3 v1 = frame.GetPointLocalCoord(new MyVector3(s, s, 0));
MyVector3 v2 = frame.GetPointLocalCoord(new MyVector3(-s, s, 0));
MyVector3 v3 = frame.GetPointLocalCoord(new MyVector3(-s, -s, 0));
MyVector3 v4 = frame.GetPointLocalCoord(new MyVector3(s, -s, 0));
planeVertices.Add(v1);
planeVertices.Add(v2);
planeVertices.Add(v3);
planeVertices.Add(v4);
planePoints.Add(v1);
planePoints.Add(v2);
planePoints.Add(v3);
planePoints.Add(v4);
this.ComputeVertices();
this.ComputeBoundQuad();
this.ComputeCenter();
}
public void BuildLocalFrame()
{
MyVector3 X = new MyVector3(1, 0, 0);
MyVector3 Y = new MyVector3(0, 1, 0);
MyVector3 Z = new MyVector3(0, 0, 1);
MyVector3 rotAxis = Z.Cross(normal).Normalize();
double angle_cos = Z.Dot(normal);
if (angle_cos < -1)
{
angle_cos = -1;
}
if (angle_cos > 1)
{
angle_cos = 1;
}
double rotAngle = Math.Acos(angle_cos);
MyMatrix4d Mat = MyMatrix4d.RotationMatrix(rotAxis, rotAngle);
MyVector3 X_new = (Mat * new MyVector4(X)).XYZ().Normalize();
MyVector3 Y_new = (Mat * new MyVector4(Y)).XYZ().Normalize();
frame = new CoordinateFrame(center, X_new, Y_new, normal);
}
public void Drag(MyVector2 pt)
{
edPt = pt;
edVec = MapToSphere(pt);
//angle = Math.Acos(stVec.Dot(edVec));
double epsilon = 1.0e-5;
MyVector3 prep = stVec.Cross(edVec);
if (prep.Length() > epsilon)
{
quat = new MyVector4();
quat.x = prep.x;
quat.y = prep.y;
quat.z = prep.z;
quat.w = stVec.x + edVec.x + stVec.y + edVec.y + stVec.z + edVec.z;
}
else
{
quat = new MyVector4();
}
//if (prep.Length() > epsilon)
//{
// quat = new MyVector3();
// quat.x = prep.x;
// quat.y = prep.y;
// quat.z = prep.z;
//}
//else
// quat = new MyVector3();
//angle = Math.PI / 2.0 * prep.Length();
}
public MyVector3 Rotate(MyVector3 axis, double cos, double sin)
{
return(this * cos + (axis.Cross(this)) * sin +
axis * ((1.0 - cos) * (axis.Dot(this))));
}
