public virtual void Draw(Vector3d location, Quaterniond rotation)
{
Matrix4d trans;
Matrix4d rot;
Matrix4d sca;
Matrix4d temp;
Vector3d axis;
double angle;
//Console.WriteLine("DDDDrawing at {0},{1},{2}", location.X, location.Y, location.Z);
// Translate and rotate stuff.
trans = Matrix4d.CreateTranslation(location);
rotation.ToAxisAngle(out axis, out angle);
Matrix4d.CreateFromAxisAngle(axis, angle, out rot);
sca = Matrix4d.Scale(scale.X, 1, scale.Y);
temp = Matrix4d.Mult(Graphics.Modelview, trans);
temp = Matrix4d.Mult(sca, Matrix4d.Mult(rot, temp));
//Console.WriteLine("MMMMatrix:\n{0}", temp);
GL.PushMatrix();
GL.LoadMatrix(ref temp);
//Console.WriteLine("Matrix'd");
// Do drawing stuff.
GL.ActiveTexture(TextureUnit.Texture0);
GL.BindTexture(TextureTarget.Texture2D, frames[animFrame]);
geometry.Draw();
GL.PopMatrix();
}
public virtual void Draw(Vector3d location, Quaterniond rotation)
{
Matrix4d trans;
Matrix4d rot;
Matrix4d sca;
Matrix4d temp;
Vector3d axis;
double angle;
// Translate and rotate stuff.
trans = Matrix4d.CreateTranslation(location);
rotation.ToAxisAngle(out axis, out angle);
Matrix4d.CreateFromAxisAngle(axis, angle, out rot);
sca = Matrix4d.Scale(scale.X, 1, scale.Y);
temp = Matrix4d.Mult(Graphics.Modelview, trans);
temp = Matrix4d.Mult(sca, Matrix4d.Mult(rot, temp));
GL.PushMatrix();
GL.LoadMatrix(ref temp);
//Console.WriteLine("Matrix'd");
// Do drawing stuff.
//GL.ClientActiveTexture(TextureUnit.Texture0);
//GL.ActiveTexture(TextureUnit.Texture1);
//GL.BindTexture(TextureTarget.Texture2D, tex);
//int loc = GL.GetUniformLocation(Graphics.CurrentShader, "tex1");
//GL.Uniform1(loc, 1);
//Console.WriteLine("Texture'd {0}", tex);
material.Draw();
geometry.Draw();
GL.PopMatrix();
}
public InputManager(KeyboardDevice keyboard)
{
_config = new CameraConfig(new Vector3d(10, 0, 0), new Vector3d(-1, 0, 0), new Vector3d(0, 1, 0), 1, 0, 1);
_keyboard = keyboard;
_bindings = new Dictionary <Key, Action <float> >
{
{ Key.W, dt => _config.Position += _config.Lookat * dt * _config.MoveSpeed },
{ Key.S, dt => _config.Position -= _config.Lookat * dt * _config.MoveSpeed },
{ Key.A, dt => _config.Position += Vector3d.Cross(_config.Up, _config.Lookat) * dt * _config.MoveSpeed },
{ Key.D, dt => _config.Position -= Vector3d.Cross(_config.Up, _config.Lookat) * dt * _config.MoveSpeed },
{ Key.ShiftLeft, dt => _config.Position += _config.Up * dt * _config.MoveSpeed },
{ Key.Space, dt => _config.Position -= _config.Up * dt * _config.MoveSpeed },
{ Key.Q, dt => _config.Up = Vector3d.Transform(_config.Up, Matrix4d.CreateFromAxisAngle(_config.Lookat, TurnSpeed * dt)) },
{ Key.E, dt => _config.Up = Vector3d.Transform(_config.Up, Matrix4d.CreateFromAxisAngle(_config.Lookat, -TurnSpeed * dt)) },
{ Key.Left, dt => _config.Lookat = Vector3d.Transform(_config.Lookat, Matrix4d.CreateFromAxisAngle(_config.Up, TurnSpeed * dt * _config.Fov)) },
{ Key.Right, dt => _config.Lookat = Vector3d.Transform(_config.Lookat, Matrix4d.CreateFromAxisAngle(_config.Up, -TurnSpeed * dt * _config.Fov)) },
{ Key.Up, dt => _config.Lookat = Vector3d.Transform(_config.Lookat, Matrix4d.CreateFromAxisAngle(Vector3d.Cross(_config.Up, _config.Lookat), TurnSpeed * dt * _config.Fov)) },
{ Key.Down, dt => _config.Lookat = Vector3d.Transform(_config.Lookat, Matrix4d.CreateFromAxisAngle(Vector3d.Cross(_config.Up, _config.Lookat), -TurnSpeed * dt * _config.Fov)) },
{ Key.R, dt => _config.MoveSpeed *= 1 + dt },
{ Key.F, dt => _config.MoveSpeed *= 1 - dt },
{ Key.N, dt => _config.Fov *= 1 + dt },
{ Key.M, dt => _config.Fov *= 1 - dt }
};
_keyboard.KeyDown += KeyboardOnKeyDown;
}
public void Update(double elapsedTime, EntityManager entityManager)
{
var speedExponent = Math.Max(0.5, Math.Log10(Math.Abs(_camera.Position.Y)));
var delta = (elapsedTime - _lastUpdate) * Math.Pow(10, speedExponent);
var up = Vector3d.Cross(_camera.Right, _camera.Forward).Normalized();
var direction = new Vector3d(0, 0, 0);
bool keyDown = false;
if (_keyboardInputProcessor.IsButtonDown(Key.W))
{
direction += _camera.Forward;
keyDown = true;
}
if (_keyboardInputProcessor.IsButtonDown(Key.S))
{
direction += -_camera.Forward;
keyDown = true;
}
if (_keyboardInputProcessor.IsButtonDown(Key.D))
{
direction += _camera.Right;
keyDown = true;
}
if (_keyboardInputProcessor.IsButtonDown(Key.A))
{
direction += -_camera.Right;
keyDown = true;
}
if (_keyboardInputProcessor.IsButtonDown(Key.LShift))
{
direction += up;
keyDown = true;
}
if (_keyboardInputProcessor.IsButtonDown(Key.LControl))
{
direction += -up;
keyDown = true;
}
if (keyDown)
{
var result = Vector3d.Multiply(direction.Normalized(), delta);
_camera.Target += result;
_camera.Position += result;
}
var relativeMousePositionDelta = _mouseInputProcessor.GetMousePositionDelta();
var rotation = Matrix4d.CreateFromAxisAngle(up, -relativeMousePositionDelta.X / 500.0) * Matrix4d.CreateFromAxisAngle(_camera.Right, -relativeMousePositionDelta.Y / 500.0);
var rotated = Vector3d.Transform(_camera.Forward, rotation);
_camera.Target = _camera.Position + rotated;
_lastUpdate = elapsedTime;
}
public static Location RotateAround(this ILocatable loc, ILocatable axis, float degs)
{
var a = degs * Math.PI / 180;
var p = loc.ToPositionAboveSeaLeveld(0);
var o = axis.ToPositionAboveSeaLeveld(0);
o.Normalize();
var m = Matrix4d.CreateFromAxisAngle(o, a);
var r = m.Tx(p);
return(r.ToLocation());
}
Vector3d point(double ang)
{
var maxr = Math.Max(MajorRadius, MinorRadius);
var minr = Math.Min(MajorRadius, MinorRadius);
MajorRadius = maxr;
MinorRadius = minr;
var mtr4 = Matrix4d.CreateFromAxisAngle(Normal, ang);
var res = Vector4d.Transform(new Vector4d(norm), mtr4);
var realAng = Vector3d.CalculateAngle(res.Xyz, RefDir);
var rad = MajorRadius * MinorRadius / (Math.Sqrt(Math.Pow(MajorRadius * Math.Sin(realAng), 2) + Math.Pow(MinorRadius * Math.Cos(realAng), 2)));
res *= rad;
return(Location + res.Xyz);
}
public void Orbit(double aYaw, double aPitch)
{
Matrix4d m1 = Matrix4d.CreateFromAxisAngle(mUp, aYaw);
Matrix4d m2 = Matrix4d.CreateFromAxisAngle(mRight, aPitch);
Matrix4d m = m1 * m2;
Matrix4d mI = Matrix4d.Transpose(m);
Vector3d tmp = mEye - mCenter;
double dst = tmp.Length;
tmp.Normalize();
mUp = Vector3d.Transform(mUp, mI);
mUp.Normalize();
tmp = Vector3d.Transform(tmp, mI);
tmp.Normalize();
mRight = Vector3d.Cross(mUp, tmp);
mEye = tmp * dst + mCenter;
}
internal Vector3d CalcConjugateNormal()
{
var nm = tring1.GetPlane().Normal.Normalized();
var point0 = AuxPoint0;
var point1 = AuxPoint1;
var neg = -nm;
var axis = (edge.End - edge.Start).Normalized();
PlaneSurface pp = new PlaneSurface()
{
Position = edge.Start, Normal = axis
};
var prj0 = pp.ProjPoint(point0) - edge.Start;
var prj1 = pp.ProjPoint(point1) - edge.Start;
var crs1 = Vector3d.Cross(prj0, prj1) / prj0.Length / prj1.Length;
var ang2 = Vector3d.CalculateAngle(prj0, prj1);
if (crs1.Length > 1e-8)
{
axis = -crs1.Normalized();
}
var mtr = Matrix4d.CreateFromAxisAngle(axis, ang2);
var mtr2 = Matrix4d.CreateFromAxisAngle(axis, -ang2);
var trans = Vector3d.Transform(neg, mtr2);
var check = Vector3d.Transform(prj0.Normalized(), mtr);
var check2 = Vector3d.Transform(prj1.Normalized(), mtr);
if (!(Vector3d.Cross(tring2.GetPlane().Normal, trans).Length < 1e-8 || Vector3d.Cross(tring2.GetPlane().Normal, -trans).Length < 1e-8))
{
DebugHelper.Error?.Invoke("inconsistent normal was calculated");
}
normal1 = trans;
return(trans);
}
public override void Drag(OpenGLControlWrapper w, MouseEventArgs e)
{
if (_dragging == DragState.Idle)
{
return;
}
Lookat = Target.Position;
switch (_dragging)
{
case DragState.ArcBalling: // moving
{
var relativePosition = _eye - _lookat;
var lookToward = new Vector3d(-relativePosition);
lookToward.Normalize();
var right = Vector3d.Cross(lookToward, Up);
var yaw = YawGain * (e.Location.X - _lastLocation.X);
var yawMatrix = Matrix4d.CreateFromAxisAngle(Up, yaw);
var pitch = PitchGain * (e.Location.Y - _lastLocation.Y);
var pitchMatrix = Matrix4d.CreateFromAxisAngle(right, pitch);
var distance = relativePosition.Length;
relativePosition = Vector3d.TransformVector(relativePosition, yawMatrix * pitchMatrix);
relativePosition.Normalize();
relativePosition = relativePosition * distance;
_eye = _lookat + relativePosition;
relativePosition.Normalize();
Up = Vector3d.Cross(relativePosition, right);
Up.Normalize();
_lastLocation = e.Location;
}
break;
case DragState.Scaling: // scaling
{
var d = ZoomGain * (e.Location.Y - _lastLocation.Y);
var zoom = Math.Exp(d);
var rp = _startPosition * (ZoomFactor * zoom);
_eye = _lookat + rp;
}
break;
case DragState.RotatingUp:
{
var centerX = w.Width / 2;
var centerY = w.Height / 2;
var v1 = new Vector3d(_lastLocation.X - centerX, _lastLocation.Y - centerY, 0d);
var v2 = new Vector3d(e.Location.X - centerX, e.Location.Y - centerY, 0d);
var v3 = Vector3d.Cross(v1, v2);
var v3Mag = v3[2];
var angDeg = Math.Asin(v3Mag / (v1.Length * v2.Length)); //*180d/Math.PI
var axis = _lookat - _eye;
axis.Normalize();
var mat = Matrix4d.CreateFromAxisAngle(axis, -angDeg);
Up = Vector3d.TransformVector(Up, mat); // was _startUp
Up.Normalize();
_lastLocation = e.Location; // not sure about this
}
break;
}
Dirty = true;
w.Invalidate();
}
public override void UpdateMesh(ProjectPolygon[] p)
{
ProjectPolygons = p;
PlaneSurface ps = new PlaneSurface()
{
Position = Location, Normal = Axis
};
var bs = ps.GetBasis();
var vec0 = bs[0] * Radius;
//stage1
//check nesting
List <ProjectPolygon> tops = new List <ProjectPolygon>();
foreach (var item in ProjectPolygons)
{
bool good = true;
foreach (var item2 in ProjectPolygons)
{
if (item == item2)
{
continue;
}
var pnts2 = item2.Points.ToArray();
if (GeometryUtils.pnpoly(pnts2, item.Points[0].X, item.Points[0].Y))
{
good = false; break;
}
}
if (good)
{
tops.Add(item);
}
}
List <Vector2d[]> triangls = new List <Vector2d[]>();
double step = AngleStep / 180f * Math.PI;
//extract 3d contours
Contours.Clear();
foreach (var item in tops)
{
var cc = new Contour3d();
Contours.Add(cc);
var maxy = item.Points.Max(z => z.Y) + 1;
var miny = item.Points.Min(z => z.Y) - 1;
for (int i = 0; i < item.Points.Count; i++)
{
var p0 = item.Points[i];
var p1 = item.Points[(i + 1) % item.Points.Count];
double last = 0;
List <Vector2d> cutPoints = new List <Vector2d>();
List <Vector2d> tempPoints = new List <Vector2d>();
cutPoints.Add(p0);
while (true)
{
var p00 = last;
var p11 = p00 + step;
last += step;
p00 = Math.Min(p00, 10 * Math.PI * 2);
p11 = Math.Min(p11, 10 * Math.PI * 2);
if (Math.Abs(p00 - p11) < 1e-8)
{
break;
}
Vector2d ret1 = Vector2d.Zero;
if (GeometryUtils.IntersectSegments(p0, p1, new Vector2d(p11, miny), new Vector2d(p11, maxy), ref ret1))
{
tempPoints.Add(ret1);
}
}
tempPoints.Add(p1);
while (tempPoints.Any())
{
var fr = tempPoints.OrderBy(z => (z - cutPoints.Last()).Length).First();
cutPoints.Add(fr);
tempPoints.Remove(fr);
}
for (int j = 0; j < cutPoints.Count; j++)
{
var ang = cutPoints[j].X;
var mtr = Matrix4d.CreateFromAxisAngle(Axis, -ang);
var rot0 = Vector3d.Transform(vec0 + Axis * cutPoints[j].Y * Lenght, mtr);
cc.Points.Add(Location + rot0);
}
}
}
foreach (var item in tops)
{
List <ProjectPolygon> holes = new List <ProjectPolygon>();
var pnts2 = item.Points.ToArray();
foreach (var xitem in ProjectPolygons.Except(tops))
{
if (GeometryUtils.pnpoly(pnts2, xitem.Points[0].X, xitem.Points[0].Y))
{
holes.Add(xitem);
}
}
PolyBoolCS.PolyBool pb = new PolyBoolCS.PolyBool();
PolyBoolCS.Polygon p1 = new PolyBoolCS.Polygon();
var pl1 = new PolyBoolCS.PointList();
p1.regions = new List <PolyBoolCS.PointList>();
pl1.AddRange(item.Points.Select(z => new PolyBoolCS.Point(z.X, z.Y)).ToArray());
p1.regions.Add(pl1);
var maxy = pl1.Max(z => z.y) + 1;
var miny = pl1.Min(z => z.y) - 1;
double last = 0;
while (true)
//for (double i = step; i < (Math.PI * 2); i += step)
{
var p0 = last;
var p11 = p0 + step;
last += step;
p0 = Math.Min(p0, 10 * Math.PI * 2);
p11 = Math.Min(p11, 10 * Math.PI * 2);
if (Math.Abs(p0 - p11) < 1e-8)
{
break;
}
PolyBoolCS.Polygon p2 = new PolyBoolCS.Polygon();
p2.regions = new List <PolyBoolCS.PointList>();
var pl2 = new PolyBoolCS.PointList();
pl2.Add(new PolyBoolCS.Point(p0, miny));
pl2.Add(new PolyBoolCS.Point(p0, maxy));
pl2.Add(new PolyBoolCS.Point(p11, maxy));
pl2.Add(new PolyBoolCS.Point(p11, miny));
p2.regions.Add(pl2);
if (holes.Any(z => GeometryUtils.AlmostEqual(z.Area(), 0)))
{
throw new GeomPadException("zero area contour detected");
}
var res = pb.intersect(p1, p2);
if (res.regions.Any())
{
foreach (var region in res.regions)
{
var triangls2 = GeometryUtils.TriangulateWithHoles(
new[] { region.Select(z => new Vector2d(z.x, z.y)).ToArray() }
,
holes.Select(z => z.Points.ToArray()).ToArray(), true);
triangls.AddRange(triangls2);
}
}
}
}
//stage2
List <TriangleInfo> tt = new List <TriangleInfo>();
foreach (var item in triangls)
{
TriangleInfo tin = new TriangleInfo();
List <VertexInfo> v = new List <VertexInfo>();
foreach (var d in item)
{
var ang = d.X;
var mtr = Matrix4d.CreateFromAxisAngle(Axis, -ang);
var rot0 = Vector3d.Transform(vec0 + Axis * d.Y * Lenght, mtr);
v.Add(new VertexInfo()
{
Position = Location + rot0
});
}
var v01 = v[1].Position - v[0].Position;
var v11 = v[2].Position - v[0].Position;
var crs = Vector3d.Cross(v01, v11).Normalized();
if (double.IsNaN(crs.X))
{
throw new GeomPadException("normal is NaN");
}
foreach (var item0 in v)
{
item0.Normal = crs;
}
tin.Vertices = v.ToArray();
tt.Add(tin);
}
Mesh = new Mesh()
{
Triangles = tt
};
}
public override void Draw(IDrawingContext gr)
{
if (!Visible)
{
return;
}
GL.Color3(Color.Blue);
if (Selected)
{
GL.Color3(Color.Red);
}
if (ShowGismos)
{
DrawHelpers.DrawCross(Location, DrawSize);
PlaneSurface ps = new PlaneSurface()
{
Position = Location, Normal = Axis
};
var bs = ps.GetBasis();
var dir = bs[0] * Radius;
List <Vector3d> pnts = new List <Vector3d>();
var step = Math.PI * AngleStep / 180f;
for (double i = 0; i <= Math.PI * 2; i += step)
{
var mtr4 = Matrix4d.CreateFromAxisAngle(Axis, i);
var res = Vector4d.Transform(new Vector4d(dir), mtr4);
pnts.Add(Location + res.Xyz);
}
GL.Begin(PrimitiveType.LineStrip);
for (int i = 0; i < pnts.Count; i++)
{
GL.Vertex3(pnts[i]);
}
GL.End();
pnts.Clear();
for (double i = 0; i <= Math.PI * 2; i += step)
{
var mtr4 = Matrix4d.CreateFromAxisAngle(Axis, i);
var res = Vector4d.Transform(new Vector4d(dir), mtr4);
pnts.Add(Location + res.Xyz + Axis * Lenght);
}
GL.Begin(PrimitiveType.LineStrip);
for (int i = 0; i < pnts.Count; i++)
{
GL.Vertex3(pnts[i]);
}
GL.End();
GL.Begin(PrimitiveType.Lines);
GL.Vertex3(Location);
GL.Vertex3(Location + Axis * Lenght);
GL.End();
}
if (ShowMesh)
{
drawMesh();
}
drawContours();
}
public void RotateAxis(Vector3d axis, double angle)
{
matrix = Matrix4d.CreateFromAxisAngle(axis, angle) * matrix;
inverse_matrix *= Matrix4d.CreateFromAxisAngle(axis, -angle);
}
public LensRayTransferFunction.Parameters ConvertSurfaceRayToParameters(
Ray ray,
Vector3d canonicalNormal, double surfaceSinTheta,
Sphere sphericalSurface, ElementSurface surface)
{
//Console.WriteLine("ray->parameters");
// - convert origin
// *- transform to hemispherical coordinates
// - find out if it is on the surface
// *- scale with respect to the spherical cap
// *- normalize
Vector3d unitSpherePos = (ray.Origin - sphericalSurface.Center) * sphericalSurface.RadiusInv;
unitSpherePos.Z *= canonicalNormal.Z;
//Console.WriteLine("unit sphere position: {0}", unitSpherePos);
Vector2d originParametric = Sampler.SampleSphereWithUniformSpacingInverse(
unitSpherePos, surfaceSinTheta, 1);
// - convert direction
// *- transform from camera space to local frame
// *- compute normal at origin
//Console.WriteLine("ray origin: {0}", ray.Origin);
Vector3d normalLocal = surface.SurfaceNormalField.GetNormal(ray.Origin);
normalLocal.Normalize(); // TODO: check if it is unnecessary
//Console.WriteLine("local normal: {0}", normalLocal);
// *- create rotation quaternion from canonical normal to local
// normal
Vector3d direction = ray.Direction;
//Console.WriteLine("local direction: {0}", direction);
if (surface.Convex)
{
direction = -direction;
}
Vector3d rotationAxis = Vector3d.Cross(canonicalNormal, normalLocal);
//Console.WriteLine("rotation axis: {0}", rotationAxis);
if (rotationAxis.Length > 0)
{
double angle = Math.Acos(Vector3d.Dot(normalLocal, canonicalNormal));
//Console.WriteLine("angle: {0}", angle);
double positionPhi = originParametric.Y;
// first transformed to the frame of the local normal
//Console.WriteLine("position phi: {0}", positionPhi);
Matrix4d rotMatrix = Matrix4d.CreateFromAxisAngle(rotationAxis, -angle);
// then rotate the local direction around Z using the position phi
rotMatrix = rotMatrix * Matrix4d.CreateRotationZ(2 * Math.PI * -positionPhi);
direction = Vector3d.Transform(direction, rotMatrix);
}
//Console.WriteLine("abs. direction: {0}", direction);
// *- transform to hemispherical coordinates
// - find out if it is within the local hemisphere
double sinTheta = direction.Z / canonicalNormal.Z;
double dirTheta = Math.Asin(sinTheta);
double cosTheta = Math.Sqrt(1 - sinTheta * sinTheta);
double dirPhi = Math.Atan2(direction.Y, direction.X);
if (dirPhi < 0)
{
// map [-PI; PI] to [0; 2*PI]
dirPhi += 2 * Math.PI;
}
// *- normalize
Vector2d directionParametric = new Vector2d(
dirTheta / (0.5 * Math.PI),
dirPhi / (2 * Math.PI));
//Console.WriteLine("position parameters: {0}", new Vector2d(
// originParametric.X, originParametric.Y));
return(new LensRayTransferFunction.Parameters(
originParametric.X, originParametric.Y,
directionParametric.X, directionParametric.Y));
}
/// <summary>
/// Convert a ray with origin at the back or front lens surface from
/// its parametric representation.
/// </summary>
/// <param name="position">Position on lens surface in parameteric
/// representation (normalized hemispherical coordinates).</param>
/// <param name="direction">Direction of the ray with respect to the
/// local frame in parameteric representation (normalized hemispherical
/// coordinates).
/// </param>
/// <param name="canonicalNormal">Normal of the lens surface
/// hemisphere (typically (0,0,1) for the back surface or (0,0,-1) for
/// the front surface).</param>
/// <param name="surfaceSinTheta">Sine of the surface spherical cap
/// theta angle.</param>
/// <param name="sphericalSurface">Lens surface represented as a
/// sphere.</param>
/// <param name="surface">Lens surface with its normal field.</param>
/// <returns>Ray corresponding to its parametric representation.
/// </returns>
public Ray ConvertParametersToSurfaceRay(
LensRayTransferFunction.Parameters parameters,
Vector3d canonicalNormal, double surfaceSinTheta,
Sphere sphericalSurface, ElementSurface surface)
{
//Console.WriteLine("parameters->ray");
//Console.WriteLine("position parameters: {0}", parameters.Position);
// uniform spacing sampling for LRTF sampling
Vector3d unitSpherePos = Sampler.SampleSphereWithUniformSpacing(
parameters.Position, surfaceSinTheta, 1);
//Console.WriteLine("unit sphere position: {0}", unitSpherePos);
unitSpherePos.Z *= canonicalNormal.Z;
Vector3d lensPos = sphericalSurface.Center + sphericalSurface.Radius * unitSpherePos;
//Console.WriteLine("ray origin: {0}", lensPos);
// - get normal N at P
Vector3d normalLocal = surface.SurfaceNormalField.GetNormal(lensPos);
// - compute direction D from spherical coordinates (wrt normal Z = (0,0,+/-1))
double theta = 0.5 * Math.PI * parameters.DirectionTheta;
double phi = 2 * Math.PI * parameters.DirectionPhi;
double cosTheta = Math.Cos(theta);
Vector3d directionZ = new Vector3d(
Math.Cos(phi) * cosTheta,
Math.Sin(phi) * cosTheta,
Math.Sin(theta) * canonicalNormal.Z);
// - rotate D from Z to N frame
// - using a (normalized) quaternion Q
// - N and Z should be assumed to be already normalized
// - more efficient method: Efficiently building a matrix to
// rotate one vector to another [moller1999]
normalLocal.Normalize(); // TODO: check if it is unnecessary
//Console.WriteLine("abs. direction: {0}", directionZ);
//Console.WriteLine("local normal: {0}", normalLocal);
Vector3d rotationAxis = Vector3d.Cross(canonicalNormal, normalLocal);
//Console.WriteLine("rotation axis: {0}", rotationAxis);
Vector3d rotatedDir = directionZ;
if (rotationAxis.Length > 0)
{
double angle = Math.Acos(Vector3d.Dot(canonicalNormal, normalLocal));
//Console.WriteLine("angle: {0}", angle);
// first the local direction must be rotated around using the position phi!
//Console.WriteLine("position phi: {0}", parameters.PositionPhi);
Matrix4d rotMatrix = Matrix4d.CreateRotationZ(2 * Math.PI * parameters.PositionPhi);
// only then can be transformed to the frame of the local normal
rotMatrix = rotMatrix * Matrix4d.CreateFromAxisAngle(rotationAxis, angle);
rotatedDir = Vector3d.Transform(directionZ, rotMatrix);
}
if (surface.Convex)
{
rotatedDir = -rotatedDir;
}
//Console.WriteLine("local direction: {0}", rotatedDir);
Ray result = new Ray(lensPos, rotatedDir);
return(result);
}
