/// <summary>
/// Break each arc into lots of short straight lines.
/// If they’re short enough no one will be able to tell the difference.
/// </summary>
/// <param name="center">arc center position</param>
/// <param name="endpoint">arc end position</param>
/// <param name="clockwise">true if clockwise motion</param>
/// <param name="startpoint">arc start position</param>
/// <returns>the arc interpolated as a list of straight lines</returns>
public List <LinePoints> RenderArc(Point3D center, Point3D endpoint, bool clockwise, ref Point3D startpoint)
{
// see also
// https://www.marginallyclever.com/2014/03/how-to-improve-the-2-axis-cnc-gcode-interpreter-to-understand-arcs/
// figure out our deltas
var current = new Point3D(startpoint.X, startpoint.Y, startpoint.Z);
double aX = current.X - center.X;
double aY = current.Y - center.Y;
double bX = endpoint.X - center.X;
double bY = endpoint.Y - center.Y;
// angle variables.
double angleA;
double angleB;
if (clockwise)
{
// Clockwise
angleA = Math.Atan2(bY, bX);
angleB = Math.Atan2(aY, aX);
}
else
{
// Counterclockwise
angleA = Math.Atan2(aY, aX);
angleB = Math.Atan2(bY, bX);
}
// Make sure angleB is always greater than angleA
// and if not add 2PI so that it is (this also takes
// care of the special case of angleA == angleB,
// ie we want a complete circle)
if (angleB <= angleA)
{
angleB += 2 * Math.PI;
}
double angle = angleB - angleA;
// calculate a couple useful things.
double radius = Math.Sqrt(aX * aX + aY * aY);
// get length of arc
// float circumference = PI*2.0*radius;
// float length = angle*circumference/(PI*2.0);
// simplifies to:
double length = radius * angle;
// Maximum of either 2.4 times the angle in radians
// or the length of the curve divided by the curve section constant
int steps = Transformation.CalculateStepsAsInt(angle, radius);
// this is the real draw action.
var newPoint = new Point3D(current.X, current.Y, current.Z);
var lastPoint = new Point3D(current.X, current.Y, current.Z);
var output = new List <LinePoints>();
var p = clockwise ? PenColorList.CWArc : PenColorList.CCWArc;
int step;
double fraction;
double angle3;
for (int s = 1; s <= steps; s++)
{
// Forwards for CCW, backwards for CW
if (!clockwise)
{
step = s;
}
else
{
step = steps - s;
}
// interpolate around the arc
fraction = ((double)step / steps);
angle3 = (angle * fraction) + angleA;
// find the intermediate position
newPoint.X = (float)(center.X + Math.Cos(angle3) * radius);
newPoint.Y = (float)(center.Y + Math.Sin(angle3) * radius);
// store max and min values
maxX = Math.Max(maxX, newPoint.X);
maxY = Math.Max(maxY, newPoint.Y);
minX = Math.Min(minX, newPoint.X);
minY = Math.Min(minY, newPoint.Y);
// and add the new line
output.Add(new LinePoints(startpoint, newPoint, p));
// store the last position
startpoint.X = newPoint.X;
startpoint.Y = newPoint.Y;
}
return(output);
}