private static IEnumerable <Line> CreateCylinderStartLines2(double alpha, int zLimit, int yLimit)
{
var b = Sqrt(8) / 2;
var alpha2 = 90 - alpha;
var beta = 180 - 45 - alpha2;
var a = 2 - Sin(alpha2.ToRadian()) / Sin(beta.ToRadian()) * b;
var r = CausticCylinder.R;
var verticalLine = new Line((0, 0, -r), (-r, 0, 0));
var distance = Vector3D.AbsoluteValue(verticalLine.SecondPoint - verticalLine.BasePoint);
var midpoint = verticalLine.GetPointOnLine(distance / 2);
var(xDir, yDir, zDir) = (-1, 0, -1 + a) - midpoint;
var zRange = Numpy.LinSpace(0, distance, zLimit).ToList();
var yRange = Numpy.LinSpace(0, CausticCylinder.L, yLimit).ToList();
foreach (var z in zRange)
{
foreach (var y in yRange)
{
var(x, y2, z2) = verticalLine.GetPointOnLine(z);
yield return(Line.FromPointAndDirection((x, y, z2), (xDir, yDir, zDir)));
}
}
}
private static IEnumerable <Line> OctoSphereStartOLD(double alpha, int xLimit, int yLimit)
{
var origin = new Vector3D(0, 0, 0);
var planePoint = new Vector3D(1, 1, 0);
var pointA = new Vector3D(2, 0, 0);
var pointB = new Vector3D(0, 2, 0);
var distanceFromOriginAtTheBase = Vector3D.AbsoluteValue(planePoint - origin);
var distanceFromOriginAtTheBaseOnTheXAxis = distanceFromOriginAtTheBase / Sin(45.0.ToRadian());
var pointOnXAxisOnTheBase = new Vector3D(distanceFromOriginAtTheBaseOnTheXAxis, 0.0, 0.0);
var horizontalDistanceAtTop = Sqrt(8);
var halfDistanceAtTop = horizontalDistanceAtTop / 2;
var horizontalDirection = (planePoint - pointOnXAxisOnTheBase).Normalize();
var halfPoint = (0, 0, 2);
var verticalDistance = Vector3D.AbsoluteValue(planePoint - halfPoint);
var verticalDirection = (planePoint - halfPoint).Normalize();
var horizontalJumps = Numpy.LinSpace(0, horizontalDistanceAtTop, xLimit).ToList();
var verticalJumps = Numpy.LinSpace(0, verticalDistance, yLimit).ToList();
var midPoint = (pointA + (horizontalJumps[xLimit / 2] * horizontalDirection)) + (verticalJumps[yLimit / 2] * verticalDirection);
var mainDirection = origin - midPoint;
foreach (var horizontalJump in horizontalJumps)
{
var point = pointA + (horizontalJump * horizontalDirection);
foreach (var verticalJump in verticalJumps)
{
var finalPoint = point + (verticalJump * verticalDirection);
var direction = RotateVector3D(mainDirection.X, mainDirection.Y, mainDirection.Z, alpha.ToRadian());
yield return(Line.FromPointAndDirection(finalPoint, direction));
}
}
}
private static IEnumerable <Line> OctoSphereStart(double alpha, int xLimit, int yLimit)
{
var xPoint = new Vector3D(2, 0, 0);
var yPoint = new Vector3D(0, 2, 0);
var topPoint = new Vector3D(0, 0, 2);
var distance = Vector3D.AbsoluteValue(yPoint - xPoint);
var bottomLine = new Line(xPoint, yPoint);
var bottomPoint = bottomLine.GetPointOnLine(distance / 2);
var verticalDistance = Vector3D.AbsoluteValue(bottomPoint - topPoint);
var horizontalDirection = (yPoint - xPoint).Normalize();
var verticalDirection = (topPoint - bottomPoint).Normalize();
var mainDirection = -1 * (new Plane(xPoint, yPoint, topPoint).NormalVector);
var horizontalJumps = Numpy.LinSpace(0, distance, xLimit);
var verticalJumps = Numpy.LinSpace(0, verticalDistance, yLimit);
foreach (var horizontalJump in horizontalJumps)
{
var horiPoint = xPoint + (horizontalJump * horizontalDirection);
foreach (var verticalJump in verticalJumps)
{
var finalPoint = horiPoint + (verticalJump * verticalDirection);
var direction = RotateVector3D(mainDirection.X, mainDirection.Y, mainDirection.Z, alpha.ToRadian());
yield return(Line.FromPointAndDirection(finalPoint, direction));
}
}
}
private static IEnumerable <Line> OctoSphereTri()
{
const double alpha = 0.0;
var xPoint = new Vector3D(2, 0, 0);
var yPoint = new Vector3D(0, 2, 0);
var topPoint = new Vector3D(0, 0, 2);
var side1 = Vector3D.AbsoluteValue(yPoint - xPoint);
var side2 = Vector3D.AbsoluteValue(topPoint - xPoint);
var side3 = Vector3D.AbsoluteValue(topPoint - yPoint);
var bigT = Heron(side1, side2, side3);
var distance = Vector3D.AbsoluteValue(yPoint - xPoint);
var bottomLine = new Line(xPoint, yPoint);
var bottomPoint = bottomLine.GetPointOnLine(distance / 2);
var verticalDistance = Vector3D.AbsoluteValue(bottomPoint - topPoint);
var horizontalDirection = (yPoint - xPoint).Normalize();
var verticalDirection = (topPoint - bottomPoint).Normalize();
var mainDirection = -1 * (new Plane(xPoint, yPoint, topPoint).NormalVector);
var horizontalJumps = Numpy.LinSpace(0, distance, 500);
var verticalJumps = Numpy.LinSpace(0, verticalDistance, 500);
foreach (var horizontalJump in horizontalJumps)
{
var horiPoint = xPoint + (horizontalJump * horizontalDirection);
foreach (var verticalJump in verticalJumps)
{
var finalPoint = horiPoint + (verticalJump * verticalDirection);
var dist1 = Vector3D.AbsoluteValue(finalPoint - xPoint);
var dist2 = Vector3D.AbsoluteValue(finalPoint - yPoint);
var dist3 = Vector3D.AbsoluteValue(finalPoint - topPoint);
var T1 = Heron(side1, dist1, dist2);
var T2 = Heron(side2, dist1, dist3);
var T3 = Heron(side3, dist2, dist3);
var T = T1 + T2 + T3;
var difference = Abs(bigT - T);
if (difference >= 0e-5)
{
yield return(Line.GetInvalid());
}
else
{
var direction = RotateVector3D(mainDirection.X, mainDirection.Y, mainDirection.Z, alpha.ToRadian());
yield return(Line.FromPointAndDirection(finalPoint, direction));
}
}
}
}
private static IEnumerable <Line> CreateCylinderStartLines(double alpha, int zLimit, int yLimit, double quarter)
{
var inRadian = alpha.ToRadian();
var dz = Tan(inRadian);
var r = Sqrt(Pow(CausticCylinder.R, 2) - Pow(CausticCylinder.R / quarter, 2));
var zRange = Numpy.LinSpace(-r, r, zLimit).ToList();
var yRange = Numpy.LinSpace(0, CausticCylinder.L, yLimit).ToList();
foreach (var z in zRange)
{
foreach (var y in yRange)
{
if (Abs(Abs(z) - Abs(r)) <= 5e-5 || Abs(y) <= 5e-5 || Abs(y - CausticCylinder.L) <= 5e-5)
{
continue;
}
yield return(Line.FromPointAndDirection((-CausticCylinder.R / quarter, y, z), (-1, 0, dz)));
}
}
}
private static IEnumerable <Line> SphereStart(double alpha, int xLimit, int yLimit)
{
var inRadian = alpha.ToRadian();
var dx = Tan(inRadian);
var xRange = Numpy.LinSpace(-1, 1, xLimit).ToList();
var yRange = Numpy.LinSpace(-1, 1, yLimit).ToList();
foreach (var x in xRange)
{
foreach (var y in yRange)
{
if (x * x + y * y >= 1)
{
continue;
}
yield return(Line.FromPointAndDirection((x - dx, y, 2), (dx, 0, -1)));
}
}
}