private int FindHelper(kdnode node, Point3D pt)
{
if (node == null)
{
return -1;
}
else if (Math.Abs(pt.X - node.Pt.X) < mEpsilon &&
Math.Abs(pt.Y - node.Pt.Y) < mEpsilon &&
Math.Abs(pt.Z - node.Pt.Z) < mEpsilon)
{
return node.Idx;
}
else if (pt.X < node.Pt.X - mEpsilon)
{
return FindHelper(node.Left, new Point3D(pt.Y, pt.Z, pt.X));
}
else if (pt.X > node.Pt.X + mEpsilon)
{
return FindHelper(node.Right, new Point3D(pt.Y, pt.Z, pt.X));
}
else
{
int leftresult = FindHelper(node.Left, new Point3D(pt.Y, pt.Z, pt.X));
if (leftresult != -1)
return leftresult;
return FindHelper(node.Right, new Point3D(pt.Y, pt.Z, pt.X));
}
}
public static void ConvexHull(ref Surface surf)
{
if (surf.NumPoints < 4)
return;
//add the middle point to make a tetrahedron for some numerical stability
Point3D Middle = new Point3D();
for (int i = 0; i < surf.NumPoints; i++)
{
Middle += surf.Point(i);
}
Middle /= surf.NumPoints;
int mid = surf.AddPoint(Middle);
//clean out the faces, and add faces of a tetrahedron using the first 3 pts and the middle.
Point3D inside = (surf.Point(0) + surf.Point(1) + surf.Point(2) + surf.Point(mid)) / 4.0;
while (surf.NumFaces > 0)
surf.RemoveFace(0);
surf.AddFace(0, 1, 2, inside);
surf.AddFace(0, 1, mid, inside);
surf.AddFace(0, 2, mid, inside);
surf.AddFace(1, 2, mid, inside);
// add in points one at a time, remove and replace faces as necessary
for (int i = 3; i < surf.NumPoints; i++)
{
List<Edge> Edges = new List<Edge>();
//for the ith point...
//go through the each existing face,
for (int j = surf.NumFaces - 1; j >= 0; j--)
{
//if a triangle is facing our new point, remove the face, add its edges to a list.
double tmp = Point3D.Dot(surf.FaceNormal(j), surf.Point(i) - surf.Point(surf.Face(j).I));
if (Point3D.Dot(surf.FaceNormal(j), (surf.Point(i) - surf.Point(surf.Face(j).I)).Normalized) > -DMS.EPSILON)
{
Edges.Add(new Edge(surf.Face(j).I, surf.Face(j).J));
Edges.Add(new Edge(surf.Face(j).J, surf.Face(j).K));
Edges.Add(new Edge(surf.Face(j).K, surf.Face(j).I));
surf.RemoveFace(j);
}
}
//now add a triangle using any non duplicated edges together with our new point.
Edges.Sort(Edge.Comparison);
for (int j = 0; j < Edges.Count(); j++)
{
if (j != Edges.Count() - 1 && Edges[j] == Edges[j + 1])
{
//this edge is a duplicate, do nothing.
j++; //we'll skip the next one which is a duplicate too.
continue;
}
surf.AddFace(Edges[j].I, Edges[j].J, i, inside);
}
}
}
public Rotation(double Angle, Point3D Axis)
{
Axis.Normalize();
mQ0 = Math.Cos(Angle / 2.0);
Axis.Scale(Math.Sin(Angle / 2.0));
mQX = Axis.X;
mQY = Axis.Y;
mQZ = Axis.Z;
Normalize();
}
public Color GetSpherePixel(Point3D point)
{
//look up theta and phi "directly" from X, Y.
double X = point.Theta / DMS.TAU;
double Y = point.Phi / DMS.HALFTAU; //but really 0 is at the north pole.
if (X < 0.0) X += 1.0;
return GetPixel( (int)(X * m_Size.Width), (int)(Y * m_Size.Height) );
}
//constructors;
public OctahedronUnit(Size size, DMSImage Source, Point3D center, Point3D topRight)
: base(size, Source)
{
O = center.Normalized;
F = Point3D.Cross(center, topRight).Normalized;
A = Point3D.Cross(F, O);
H = -A;
C = -F;
B = (O + A + C).ScaledTo(2.0 / Math.Sqrt(3.0));
E = (O + C + H).ScaledTo(2.0 / Math.Sqrt(3.0));
G = (O + F + H).ScaledTo(2.0 / Math.Sqrt(3.0));
D = (O + F + A).ScaledTo(2.0 / Math.Sqrt(3.0));
}
public Cylinder(Point3D Center, Point3D Direction, double Height, double Radius, int nPoints)
{
//create cylinder centered at 0, along z axis, with given length and radius.
for (int i = 0; i < nPoints; i++)
{
AddPoint(Point3D.FromCylindricalCoords(Radius, Height / 2.0, Math.PI * 2.0 * ((double)i / nPoints)));
AddPoint(Point3D.FromCylindricalCoords(Radius, -Height / 2.0, Math.PI * 2.0 * ((double)i / nPoints)));
}
AddPoint(new Point3D(0, 0, Height / 2.0));
AddPoint(new Point3D(0, 0, -Height / 2.0));
//add faces
for (int i = 0; i < nPoints; i++)
{
int next = (i + 1) % nPoints;
AddFace(nPoints, i * 2, next * 2, Point3D.Origin);
AddFace(nPoints + 1, i * 2 + 1, next * 2 + 1, Point3D.Origin);
AddFace(next * 2, i * 2 + 1, i * 2, Point3D.Origin);
AddFace(next * 2, i * 2 + 1, next * 2 + 1, Point3D.Origin);
}
if (Radius < 0)
{
foreach (Triangle tri in mFaces)
tri.Reverse();
}
//transform points
if (Direction.R > DMS.EPSILON && Direction.Phi > DMS.EPSILON)
{
Rotation rot = new Rotation(Direction.Normalized.Phi,
new Point3D(-Direction.Y, Direction.X, 0));
for (int i = 0; i < mPts.Count(); i++)
{
mPts[i] = rot.Rotate(mPts[i]);
}
}
//add offset
for (int i = 0; i < mPts.Count(); i++)
{
mPts[i] += Center;
}
}
public override Color GetPixel(int x, int y)
{
Point3D Q;
if (m_bOrthographic)
{
//if outside circle
if ((new Point2D(x, y) - m_center).R > m_radius)
{
return m_Blank;
}
double u = (double)(x - m_radius) / m_radius;
double v = (double)(y - m_radius) / m_radius;
double w = Math.Sqrt(Math.Max(1.0 - u * u - v * v, 0.0));
Q = new Point3D(u, v, w);
Q = m_sphereRot.Rotate(Q);
}
else
{
double u = (double)(x) / (double)(m_Size.Width) * DMS.TAU;
double v = (double)(y) / (double)(m_Size.Height) * DMS.HALFTAU;
Q = Point3D.FromSphericalCoords(1.0, v, u);
}
if( m_Source != null )
{
return m_Source.GetPixel( new Point2D( DMS.FixAnglePositive(-Q.Theta) / DMS.TAU,
Q.Phi / DMS.HALFTAU) );
}
RelativePosition RP = m_Skeleton.NearestSegmentOnSphere( Q );
Segment S = RP.Segment;
int nIdx = m_Skeleton.IndexOf(S);
//draw skeleton line
if( RP.Distance < 0.4 * DMS.TAU/360.0 )
return Color.Black;
return Globemaker.colorFromRandomIndex(nIdx);
}
public override Color GetPixel(int x, int y)
{
//convert x,y to 0 to 1
double remapX = (double)x / (double)Size.Width;
double remapY = (double)y / (double)Size.Width;
if (remapX + remapY > 1.5 ||
remapX + remapY < 0.5 ||
remapX - remapY < -0.5 ||
remapX - remapY > 0.5)
{
return m_Blank;
}
Point3D O = new Point3D(2, 1, 0);
Point3D U = new Point3D(-2, 0, 2);
Point3D V = new Point3D(-2, 0, -2);
Point3D src = O + remapX*U + remapY*V;
return m_Source.GetSpherePixel(src);
}
private bool InsertHelper(ref kdnode node, Point3D pt, int idx)
{
if (node == null)
{
node = new kdnode(pt, idx);
return true;
}
else if( Math.Abs(pt.X - node.Pt.X) < mEpsilon &&
Math.Abs(pt.Y - node.Pt.Y) < mEpsilon &&
Math.Abs(pt.Z - node.Pt.Z) < mEpsilon )
{
return false;
}
else
{
if (pt.X < node.Pt.X)
return InsertHelper(ref node.Left, new Point3D(pt.Y, pt.Z, pt.X), idx);
else
return InsertHelper(ref node.Right, new Point3D(pt.Y, pt.Z, pt.X), idx);
}
}
private Segment m_Segment; //which segment we're talking about
#endregion Fields
#region Constructors
//point on sphere
public RelativePosition( Point3D p, Segment seg )
{
m_Segment = seg;
Point3D PosOnSphere = m_Segment.Arot.Inverse.Rotate( p ); //we think of our segment starting at z and rotating towards x;
double fAngle = DMS.FixAnglePositive(Math.Atan2(PosOnSphere.X, PosOnSphere.Z));
//test if closest orthoganally
if( fAngle < m_Segment.Length )
{
m_fTheta = PosOnSphere.Y > 0 ? DMS.QUARTERTAU : -DMS.QUARTERTAU;
m_fClosestPt = fAngle;
m_fDistance = Math.Abs(Math.Asin( PosOnSphere.Y ));
} /* if */
//angle to A (z-axis) is TWO_PI-fAngle, angle to B (end of rot.) is fAngle-length
// test if point on sphere is closer to z axis then to end of rot.
else if( (DMS.TAU - fAngle) < (fAngle - m_Segment.Length) )
{
m_fTheta = PosOnSphere.Theta;
m_fClosestPt = 0.0;
m_fDistance = PosOnSphere.Phi;
} /* else if */
// otherwise point on sphere is closer to end of rotation then to z axis
else
{
//rotate posonsphere about y (from x to z) by grSegments[dtCurrent.nIdx].length
PosOnSphere = new Point3D(
Math.Sin(Math.Atan2(PosOnSphere.X, PosOnSphere.Z)-m_Segment.Length) * Math.Sqrt(1.0-PosOnSphere.Y*PosOnSphere.Y),
PosOnSphere.Y,
Math.Cos(Math.Atan2(PosOnSphere.X, PosOnSphere.Z)-m_Segment.Length) * Math.Sqrt(1.0-PosOnSphere.Y*PosOnSphere.Y) );
//now it's same as before except for fClosestPt
m_fTheta = PosOnSphere.Theta;
m_fClosestPt = m_Segment.Length;
m_fDistance = PosOnSphere.Phi;
} /* else if */
}
private void AddCity()
{
Point3D city;
double greyval;
while(true)
{
city = new Point3D( m_rand.NextDouble()-0.5,
m_rand.NextDouble() - 0.5,
m_rand.NextDouble() - 0.5);
if( city.R > 0.5 ) continue; //go from uniform random cube to uniform random random sphere.
greyval = GetGreyValue(city);
m_totalareacount++;
if( greyval < 0.0 ) //don't add cities to empty spaces
{
m_emptyareacount++;
continue;
}
if( m_rand.NextDouble() * greyval * greyval > 0.01 )
continue;
break;
}
m_SumGreyValues += greyval;
city.Normalize();
m_Cities.Add(city);
}
public RelativePosition NearestSegmentOnSphere(Point3D pos)
{
RelativePosition result = null;
foreach( Segment seg in m_Segments )
{
RelativePosition current = new RelativePosition(pos, seg);
if( result == null ||
current.Distance * current.Segment.Strength + DMS.EPSILON <
result.Distance * result.Segment.Strength )
{
result = current;
} /* if */
} /* foreach */
return result;
}
private Point2D coordsInFundDomain(Point3D p)
{
//want baricentric coords (u,v) st. B + u*(A-B) + v*(C-B) = p'
//where p' is p projected to X=1.0 plane.
p.Scale(1.0 / p.X);
Point3D A = domainCorner(0);
Point3D B = domainCorner(1);
Point3D C = domainCorner(2);
Point2D v0 = new Point2D(A.Y - B.Y, A.Z - B.Z);
Point2D v1 = new Point2D(C.Y - B.Y, C.Z - B.Z);
Point2D v2 = new Point2D(p.Y - B.Y, p.Z - B.Z);
double dot00 = Point2D.Dot(v0, v0);
double dot01 = Point2D.Dot(v0, v1);
double dot02 = Point2D.Dot(v0, v2);
double dot11 = Point2D.Dot(v1, v1);
double dot12 = Point2D.Dot(v1, v2);
double invDenom = 1.0 / (dot00 * dot11 - dot01 * dot01);
return new Point2D( (dot11 * dot02 - dot01 * dot12) * invDenom,
(dot00 * dot12 - dot01 * dot02) * invDenom);
}
public PixelInfo(int u, int v, Point3D color)
{
_U = u;
_V = v;
_color = color;
Up = Down = Left = Right = 0;
}
private double MinWeightedDist(Point3D a, Point3D b)
{
double greyvalueA = GetGreyValue(a);
double greyvalueB = GetGreyValue(b);
double result = Math.Acos(Point3D.Dot(a, b));
result -= m_GlobalRadius * GetGreyValue(a);
result -= m_GlobalRadius * GetGreyValue(b);
return result / Math.Max(greyvalueA, greyvalueB);
}
private bool IsInThirt(Point3D pt)
{
Point3D[] thirt = new Point3D[]
{ new Point3D(-3.662782754263035300e-01, 7.559006998770361200e-01, 5.426364868640331000e-01),
new Point3D(-9.408369689587646700e-01, 3.266601753606225300e-01, -9.010509238579085500e-02),
new Point3D(2.949031158172585300e-01, -6.086014011689210300e-01, -7.366386405670685100e-01),
new Point3D(-7.408675404485654300e-20, 1.131011890285944400e-19, 1.000000000000000000e+00),
new Point3D(-7.559006998770361200e-01, -3.662782754263035300e-01, 5.426364868640331000e-01),
new Point3D(-3.266601753606225300e-01, -9.408369689587646700e-01, -9.010509238579085500e-02),
new Point3D(6.086014011689210300e-01, 2.949031158172585300e-01, -7.366386405670685100e-01),
new Point3D(3.662782754263035300e-01, -7.559006998770361200e-01, 5.426364868640331000e-01),
new Point3D(9.408369689587646700e-01, -3.266601753606225300e-01, -9.010509238579085500e-02),
new Point3D(-2.949031158172585300e-01, 6.086014011689210300e-01, -7.366386405670685100e-01),
new Point3D(7.559006998770361200e-01, 3.662782754263035300e-01, 5.426364868640331000e-01),
new Point3D(3.266601753606225300e-01, 9.408369689587646700e-01, -9.010509238579085500e-02),
new Point3D(-6.086014011689210300e-01, -2.949031158172585300e-01, -7.366386405670685100e-01) };
for (int i = 0; i < 13; i++)
{
if (Math.Acos(Point3D.Dot(thirt[i], pt.Normalized)) < 57.1367031 / 2.0 * Math.PI / 180.0)
{
return true;
}
}
return false;
}
private List<Point3D> Interpolate(int idx, int pieces, bool bSpline)
{
List<Point3D> result = new List<Point3D>();
if (!bSpline)
{
//line segment
Point3D dir = (m_Cities[(idx + 1) % m_Cities.Count] - m_Cities[idx]) / (double)pieces;
for (int i = 0; i <= pieces; i++)
{
result.Add(m_Cities[idx] + dir * i);
}
}
else
{
//spline
Point3D p4 = m_Cities[idx];
Point3D p3 = m_Cities[(idx - 1 + m_Cities.Count) % m_Cities.Count];
Point3D p2 = m_Cities[(idx - 2 + m_Cities.Count) % m_Cities.Count];
Point3D p1 = m_Cities[(idx - 3 + m_Cities.Count) % m_Cities.Count];
double[] a = new double[5];
double[] b = new double[5];
Point3D[] A = new Point3D[5];
A[0] = (-p1 + 3.0 * p2 - 3.0 * p3 + p4) / 6.0;
A[1] = (3.0 * p1 - 6.0 * p2 + 3.0 * p3) / 6.0;
A[2] = (-3.0 * p1 + 3.0 * p3) / 6.0;
A[3] = (p1 + 4 * p2 + p3) / 6.0;
for (int i = 0; i <= pieces; i++)
{
float t = (float)i / pieces;
result.Add((A[2] + t * (A[1] + t * A[0])) * t + A[3]);
}
}
return result;
}
private double Dist( Point3D a, Point3D b )
{
double result = Math.Acos(Point3D.Dot(a, b));
result -= m_GlobalRadius * GetGreyValue(a);
result -= m_GlobalRadius * GetGreyValue(b);
return result;
}
private double GetGreyValue(Point3D pt)
{
if (m_Source == null)
{
#if false
if( IsInThirt( pt ) )
return 0.1; //dark
else
return -1.0; //so light it's not there.
#elif true
if( IsInCox53( pt ) )
return 0.1; //dark
else
return -1.0; //so light it's not there.
#else
return 1.0;
#endif
}
double result;
lock (m_Source)
{
result = m_Source.GetSpherePixel(pt).GetBrightness();
}
if (result == 1.0)
return -1.0;
return (0.1 + 0.9 * result);
}
public static Point3D Cross( Point3D A, Point3D B )
{
return new Point3D( A.Y*B.Z - A.Z*B.Y,
A.Z*B.X - A.X*B.Z,
A.X*B.Y - A.Y*B.X );
}
private bool IsInCox53(Point3D pt)
{
bool result = true;
Point3D[] planenorms = new Point3D[]
{ new Point3D(0,0,1),
new Point3D(0,1,0),
new Point3D(0.309016994,-0.809016994,-0.5),
new Point3D(0.309016994,-0.809016994,0.5),
new Point3D(0.309016994,0.809016994,-0.5),
new Point3D(0.309016994,0.809016994,0.5),
new Point3D(0.5,-0.309016994,-0.809016994),
new Point3D(0.5,-0.309016994,0.809016994),
new Point3D(0.5,0.309016994,-0.809016994),
new Point3D(0.5,0.309016994,0.809016994),
new Point3D(0.809016994,-0.5,-0.309016994),
new Point3D(0.809016994,-0.5,0.309016994),
new Point3D(0.809016994,0.5,-0.309016994),
new Point3D(0.809016994,0.5,0.309016994),
new Point3D(1,0,0) };
for (int i = 0; i < 15; i++)
{
if (Point3D.Dot(planenorms[i], pt.Normalized) < 0.0)
{
result = !result;
}
}
return result;
}
/// <summary>
/// returns the angle between
/// the plane containing points ABO and
/// the plane containing points CBO
/// where O is the origin
/// </summary>
/// <param name="A"></param>
/// <param name="B"></param>
/// <param name="C"></param>
/// <returns></returns>
public static double DihedralAngle(Point3D A, Point3D B, Point3D C)
{
double result = -1.0;
try
{
Point3D normal1 = Point3D.Cross(A - B, B );
Point3D normal2 = Point3D.Cross(C - B, B);
result = Point3D.Angle(normal1, Point3D.Origin, normal2);
}
catch {}
return result;
}
private Point3D JitterPt(Point3D pt)
{
double oneminuscosjitterradius = 1.0 - Math.Cos(m_JitterRadius * GetGreyValue(pt));
//First we get a random point within spherical cap centered at (0,0,1) with a radius of max
Point3D jitteredpt = Point3D.FromSphericalCoords(1.0,
Math.Acos(1.0 - m_rand.NextDouble() * oneminuscosjitterradius),
m_rand.NextDouble() * 2.0 * Math.PI );
Rotation ToPt = new Rotation(pt.Theta, pt.Phi, 0);
return ToPt.Rotate( jitteredpt );
}
public static double Dot(Point3D A, Point3D B)
{
return A.X*B.X + A.Y*B.Y + A.Z*B.Z;
}
private double SetAvgColour(PixelInfo pixel)
{
Point3D NewColor = new Point3D();
Point3D tmp;
int count = 0;
pixel.SetNeighbors(m_Source, m_resolution);
if (pixel.Up != 0)
{
tmp = GetPixelHelper(pixel.U, pixel.V - pixel.Up);
if (tmp != null)
{
NewColor += tmp;
count++;
}
}
if (pixel.Down != 0)
{
tmp = GetPixelHelper(pixel.U, pixel.V + pixel.Down);
if (tmp != null)
{
NewColor += tmp;
count++;
}
}
if (pixel.Left != 0)
{
tmp = GetPixelHelper(pixel.U - pixel.Left, pixel.V);
if (tmp != null)
{
NewColor += tmp;
count++;
}
}
if (pixel.Up != 0)
{
tmp = GetPixelHelper(pixel.U + pixel.Right, pixel.V);
if (tmp != null)
{
NewColor += tmp;
count++;
}
}
if (count == 0)
NewColor = new Point3D(128, 128, 128);
else
NewColor /= (double)count;
double Result = (pixel.color - NewColor).R;
pixel.color = NewColor;
return Result;
}
public Point3D(Point3D A)
: this(A.X, A.Y, A.Z)
{
}
public override Color GetPixel(int x, int y)
{
Point3D result = GetPixelHelper(x, y);
if (result == null)
{
int u = x - (x % m_resolution);
int v = y - (y % m_resolution);
Point3D A = GetPixelHelper(u, v);
Point3D B = GetPixelHelper(u, v + m_resolution);
Point3D C = GetPixelHelper(u + m_resolution, v);
Point3D D = GetPixelHelper(u + m_resolution, v + m_resolution);
double U = (double)(x - u) / m_resolution;
double V = (double)(y - v) / m_resolution;
result = new Point3D();
double count = 0.0;
if (A != null) { result += (1.0 - U) * (1.0 - V) * A; count += (1.0 - U) * (1.0 - V); }
if (B != null) { result += (1.0 - U) * V * B; count += (1.0 - U) * V; }
if (C != null) { result += U * (1.0 - V) * C; count += U * (1.0 - V); }
if (D != null) { result += U * V * D; count += U * V; }
if (count == 0.0)
result = new Point3D(128, 128, 128);
else
result /= count;
}
if (result.X < 0.0) result.X = 0.0;
if (result.Y < 0.0) result.Y = 0.0;
if (result.Z < 0.0) result.Z = 0.0;
if (result.X > 255.0) result.X = 255.0;
if (result.Y > 255.0) result.Y = 255.0;
if (result.Z > 255.0) result.Z = 255.0;
// we add a dither
return Color.FromArgb(Dither(result.X),
Dither(result.Y),
Dither(result.Z));
}
public Point3D ScaledTo(double newLength )
{
Point3D result = new Point3D(this);
result.R = newLength;
return result;
}
public Color GetSpherePixel(Point3D point)
{
if (mSourceType == DMSImageType.Equirectangular)
{
//latitude and longitude are pulled straight from spherical coordinates of the 3d pooint
double longitude = point.Theta / DMS.TAU;
double latitude = point.Phi / DMS.HALFTAU; //but really 0 is at the north pole.
if (longitude < 0.0 ) longitude += 1.0;
Point2D EquirectangularLocation = new Point2D( longitude, latitude );
return GetPixel(EquirectangularLocation);
}
else
{
// we can get the location on a mirror ball image from the spherical coordinates by taking the sin of phi.
Point2D MirrorBallLocation = Point2D.FromPolar(Math.Sin(point.Phi/2.0), point.Theta);
//the coordinates are from -1 to 1, we need to convert them to 0 to 1
MirrorBallLocation += new Point2D(1, 1);
MirrorBallLocation.Scale(0.5);
return GetPixel(MirrorBallLocation);
}
}
public bool bNearerSegmentOnSphereExists( Point3D pos, double fCriteria )
{
if( m_LastCloserSegment != null &&
RelativePosition.IsNearerOnSphere( pos, m_LastCloserSegment, fCriteria ) )
{
return true;
}
foreach( Segment seg in m_Segments )
{
if (RelativePosition.IsNearerOnSphere(pos, seg, fCriteria))
{
m_LastCloserSegment = seg;
return true;
}
}
return false;
}