/// <summary>
/// Gets an array of rectangles used in a Riemman sum approximation.
/// </summary>
/// <param name="upperboundCurve">The curve to be approximated.</param>
/// <param name="lowerbound">The line defining the range under the upperbound curve.</param>
/// <param name="riemmanSumRule">The approximation rule.</param>
/// <param name="intervals">The number of intervals, or rectangles, to use.</param>
/// <param name="intervalWidth"></param>
/// <param name="offset">The height by which to offset the rectangles above the upperbound curve.</param>
/// <returns></returns>
public static Rectangle3d[] RiemmanSumRectangles(this Curve upperboundCurve, Line lowerbound,
RiemmanSumRule riemmanSumRule, int intervals, double intervalWidth, double offset)
{
Curve upperCurve;
if (Math.Abs(offset) > .000000)
{
var transformation = Point3d.Origin.GetVectorTo(new Point3d(0, offset, 0));
upperCurve = (Curve)upperboundCurve.GetTransformedCopy(Matrix3d.Displacement(transformation));
}
else
{
upperCurve = upperboundCurve;
}
return(upperCurve.RiemmanSumRectangles(lowerbound, riemmanSumRule, intervals, intervalWidth));
}
/// <summary>
/// Gets an array of rectangles used in a Riemman sum approximation.
/// </summary>
/// <param name="upperboundCurve">The curve to be approximated.</param>
/// <param name="lowerbound">The line defining the range under the upperbound curve.</param>
/// <param name="riemmanSumRule">The approximation rule.</param>
/// <param name="intervals">The number of intervals, or rectangles, to use. </param>
/// <param name="width">The width of the intervals. </param>
/// <returns></returns>
public static Rectangle3d[] RiemmanSumRectangles(this Curve upperboundCurve, Line lowerbound, RiemmanSumRule riemmanSumRule, int intervals, double width)
{
try
{
var trueIntervals = intervals == 0 ? Math.Floor(lowerbound.Length / width) : intervals;
var rectangles = new Rectangle3d[Convert.ToInt32(trueIntervals)];
double x = intervals == 0 ? width : lowerbound.Length / intervals;
for (var k = 0; k < trueIntervals; k++)
{
// p2 p3
// p1 p4
var p1 = new Point3d(
x: lowerbound.StartPoint.X + (x * k),
y: lowerbound.StartPoint.Y,
z: lowerbound.StartPoint.Z);
var p4 = new Point3d(
x: lowerbound.StartPoint.X + (x * (k + 1)),
y: lowerbound.StartPoint.Y,
z: lowerbound.StartPoint.Z);
var p2Intersect = new Line(p1,
new Point3d(p1.X, upperboundCurve.GeometricExtents.MaxPoint.Y + 1, p1.Z));
var p3Intersect = new Line(p4,
new Point3d(p4.X, upperboundCurve.GeometricExtents.MaxPoint.Y + 1, p4.Z));
var p2Intersection = upperboundCurve.Intersect(p2Intersect,
Autodesk.AutoCAD.DatabaseServices.Intersect.ExtendArgument)?[0]; // y = f(x0)
var p3Intersection = upperboundCurve.Intersect(p3Intersect,
Autodesk.AutoCAD.DatabaseServices.Intersect.ExtendArgument)?[0]; // y = f(x1)
var p2 = p2Intersection ?? throw new ArgumentOutOfRangeException();
var p3 = p3Intersection ?? throw new ArgumentOutOfRangeException();
switch (riemmanSumRule)
{
case RiemmanSumRule.Left:
{
p3 = new Point3d(p3.X, p2.Y, p3.Z);
break;
}
case RiemmanSumRule.Right:
{
p2 = new Point3d(p2.X, p3.Y, p2.Z);
break;
}
case RiemmanSumRule.Middle:
{
var midx = (p4.X - p1.X) / 2;
var midLine = new Line(new Point3d(p1.X + midx, p1.Y, p1.Z),
new Point3d(p1.X + midx, upperboundCurve.GeometricExtents.MaxPoint.Y + 1, p1.Z));
var midIntersection = upperboundCurve.Intersect(midLine,
Autodesk.AutoCAD.DatabaseServices.Intersect.ExtendArgument)?[0];
var intersect = midIntersection ?? throw new ArgumentOutOfRangeException();
p2 = new Point3d(p1.X, intersect.Y, p1.Z);
p3 = new Point3d(p4.X, intersect.Y, p4.Z);
break;
}
default:
throw new ArgumentOutOfRangeException(nameof(riemmanSumRule), riemmanSumRule, null);
}
var rectangle = new Rectangle3d(p2, p3, p1, p4);
rectangles[k] = rectangle;
}
return(rectangles.ToArray());
}
catch (Autodesk.AutoCAD.Runtime.Exception ex)
{
Interaction.WriteLine($"An error occured.\n{ex.Message}");
throw;
}
}
