/***************************************************/
public static double AreaIntegration(List <IntegrationSlice> slices, double curve, double from, double to, ref double centroid)
{
double result = 0;
double max = System.Math.Max(from, to);
double min = System.Math.Min(from, to);
double sumAreaLength = 0;
for (int i = 0; i < slices.Count; i++)
{
IntegrationSlice slice = slices[i];
if (slice.Centre + slice.Width / 2 > min && slice.Centre - slice.Width / 2 < max)
{
double botSlice = System.Math.Max(min, slice.Centre - slice.Width / 2);
double topSlice = System.Math.Min(max, slice.Centre + slice.Width / 2);
double currentCentre = (topSlice + botSlice) / 2;
double currentValue = curve;
double sliceWidth = (topSlice - botSlice);
result += currentValue * slice.Length * sliceWidth;
sumAreaLength += currentValue * slice.Length * sliceWidth * currentCentre;
}
}
centroid = result != 0 ? sumAreaLength / result : 0;
return(result);
}
public static double WidthAt(this IProfile section, double y)
{
IntegrationSlice slice = Engine.Geometry.Query.SliceAt(section.Edges, y, 1, oM.Geometry.Plane.XZ);
//Slice slice = SliceAt(y, 1, Plane.XZ());// new Plane(Point.Origin, Vector.YAxis()));
return(slice.Length);
}
public static double WidthAt(this IProfile section, double y, ref double[] range)
{
IntegrationSlice slice = Engine.Geometry.Query.SliceAt(section.Edges, y, 1, oM.Geometry.Plane.XZ);
//Slice slice = SliceAt(y, 1, Plane.XZ());
range = slice.Placement;
return(slice.Length);
}
public static double DepthAt(this IProfile section, double x)
{
if (section.IsNull())
{
return(0);
}
IntegrationSlice slice = Engine.Geometry.Query.SliceAt(section.Edges, x, 1, oM.Geometry.Plane.YZ);
//Slice slice = SliceAt(x, 1, Plane.YZ());// new Plane(Point.Origin, Vector.XAxis()));
return(slice.Length);
}
public static double DepthAt(this IProfile section, double x, ref double[] range)
{
if (section.IsNull())
{
return(0);
}
IntegrationSlice slice = Engine.Geometry.Query.SliceAt(section.Edges, x, 1, oM.Geometry.Plane.YZ);
//Slice slice = SliceAt(x, 1, Plane.YZ());
range = slice.Placement;
return(slice.Length);
}
/***************************************************/
public static double AreaIntegration(List <IntegrationSlice> slices, double constant, double xPower, double yPower, double origin = 0)
{
double result = 0;
for (int i = 0; i < slices.Count; i++)
{
IntegrationSlice slice = slices[i];
double dx = slice.Width;
result += constant * System.Math.Pow(slice.Centre - origin, xPower) * System.Math.Pow(slice.Length, yPower) * dx;
}
return(result);
}
/***************************************************/
public static double AreaIntegration(List <IntegrationSlice> slices, Vector direction, ICurve curve, double from, double to, ref double centroid)
{
double result = 0;
double max = System.Math.Max(from, to);
double min = System.Math.Min(from, to);
double sumAreaLength = 0;
Point origin = Point.Origin;
Plane plane = new Plane {
Origin = origin, Normal = direction
};
for (int i = 0; i < slices.Count; i++)
{
IntegrationSlice slice = slices[i];
if (slice.Centre + slice.Width / 2 > min && slice.Centre - slice.Width / 2 < max)
{
double botSlice = System.Math.Max(min, slice.Centre - slice.Width / 2);
double topSlice = System.Math.Min(max, slice.Centre + slice.Width / 2);
double currentCentre = (topSlice + botSlice) / 2;
double sliceWidth = (topSlice - botSlice);
plane.Origin = (origin + plane.Normal * currentCentre);
List <Point> points = curve.IPlaneIntersections(plane, 0.001);
double currentValue = 0;
if (points.Count == 2)
{
currentValue = System.Math.Abs(points[0].Y - points[1].Y);
}
else if (points.Count == 1)
{
currentValue = points[0].Y;
}
result += currentValue * slice.Length * sliceWidth;
sumAreaLength += currentValue * slice.Length * sliceWidth * currentCentre;
}
}
centroid = result != 0 ? sumAreaLength / result : 0;
return(result);
}
/***************************************************/
public static double AreaIntegration(List <IntegrationSlice> slices, double constant, double xPower, double yPower, double from = double.MinValue, double to = double.MaxValue, double origin = 0)
{
double result = 0;
double max = System.Math.Max(from, to);
double min = System.Math.Min(from, to);
for (int i = 0; i < slices.Count; i++)
{
IntegrationSlice slice = slices[i];
if (slice.Centre + slice.Width / 2 > min && slice.Centre - slice.Width / 2 < max)
{
double botSlice = System.Math.Max(min, slice.Centre - slice.Width / 2);
double topSlice = System.Math.Min(max, slice.Centre + slice.Width / 2);
double sliceCentre = (topSlice + botSlice) / 2;
double dx = (topSlice - botSlice);
result += constant * System.Math.Pow(sliceCentre - origin, xPower) * System.Math.Pow(slice.Length, yPower) * dx;
}
}
return(result);
}
public static double PlasticModulus(List <IntegrationSlice> slices, double area, double max, double min)
{
double result = 0;
slices = slices.OrderBy(x => x.Centre).ToList();
double plasticNeutralAxis = 0;
for (int i = 0; i < slices.Count; i++)
{
IntegrationSlice slice = slices[i];
double sliceArea = slice.Length * slice.Width;
if (result + sliceArea < area / 2)
{
result += sliceArea;
}
else
{
plasticNeutralAxis = slices[i - 1].Centre + slices[i - 1].Width / 2;
double diff = area / 2 - result;
double ratio = diff / sliceArea;
plasticNeutralAxis += ratio * slice.Width;
break;
}
}
double centreTop = 0;
double centreBot = 0;
double areaTop = Geometry.Query.AreaIntegration(slices, 1, max, plasticNeutralAxis, ref centreTop);
double areaBot = Geometry.Query.AreaIntegration(slices, 1, min, plasticNeutralAxis, ref centreBot);
return(areaTop * Math.Abs(centreTop - plasticNeutralAxis) + areaBot * Math.Abs(centreBot - plasticNeutralAxis));
}