/// <summary>
/// Compares two <see cref="Element3D"/>s to determine which one lies on top of the other when viewed with the current camera.
/// </summary>
/// <param name="element1">The first element. If this element is in front, the function returns 1.</param>
/// <param name="element2">The second element. If this element is in front, the function returns -1.</param>
/// <returns>1 if <paramref name="element1"/> is in front of <paramref name="element2"/>; -1 if <paramref name="element2"/> is in front of <paramref name="element1"/>; 0 if the two elements do not overlap, intersect or if the order could not be determined for other reasons. </returns>
public virtual int Compare(Element3D element1, Element3D element2)
{
if (element1.ZIndex != element2.ZIndex)
{
return(element1.ZIndex - element2.ZIndex);
}
if (element1 is Point3DElement pt1)
{
Point proj1 = this.Project(pt1[0]);
if (element2 is Point3DElement pt2)
{
Point proj2 = this.Project(pt2[0]);
if ((proj1.X - proj2.X) * (proj1.X - proj2.X) + (proj1.Y - proj2.Y) * (proj1.Y - proj2.Y) < (pt1.Diameter * 0.5 + pt2.Diameter * 0.5) * (pt1.Diameter * 0.5 + pt2.Diameter * 0.5))
{
double dist1 = this.ZDepth(pt1[0]);
double dist2 = this.ZDepth(pt2[0]);
if (Math.Abs(dist1 - dist2) < Camera.Tolerance)
{
return(0);
}
return(-Math.Sign(dist1 - dist2));
}
else
{
return(0);
}
}
else if (element2 is Line3DElement line)
{
Point p0 = proj1;
Point p1 = this.Project(line[0]);
Point p2 = this.Project(line[1]);
double distSq = ((p2.Y - p1.Y) * p0.X - (p2.X - p1.X) * p0.Y + p2.X * p1.Y - p2.Y * p1.X) * ((p2.Y - p1.Y) * p0.X - (p2.X - p1.X) * p0.Y + p2.X * p1.Y - p2.Y * p1.X) / ((p2.X - p1.X) * (p2.X - p1.X) + (p2.Y - p1.Y) * (p2.Y - p1.Y));
double maxDistSq = (pt1.Diameter * 0.5 + line.Thickness * 0.5) * (pt1.Diameter * 0.5 + line.Thickness * 0.5);
Point v1 = new Point(p0.X - p1.X, p0.Y - p1.Y);
Point v2 = new Point(p2.X - p1.X, p2.Y - p1.Y);
double v2Length = v2.Modulus();
Point e2 = new Point(v2.X / v2Length, v2.Y / v2Length);
double dotProd = v1.X * e2.X + v1.Y * e2.Y;
if (dotProd >= -Math.Sqrt(maxDistSq) && dotProd <= v2Length + Math.Sqrt(maxDistSq) && distSq < maxDistSq)
{
Point pointOnLine = new Point(p1.X + dotProd * e2.X, p1.Y + dotProd * e2.Y);
try
{
Point3D pt = this.Deproject(pointOnLine, line);
double dist1 = this.ZDepth(pt1[0]);
double dist2 = this.ZDepth(pt);
if (Math.Abs(dist1 - dist2) < Camera.Tolerance)
{
return(0);
}
return(-Math.Sign(dist1 - dist2));
}
catch
{
return(0);
}
}
else
{
return(0);
}
}
else if (element2 is Triangle3DElement triangle)
{
Point p0 = proj1;
Point p1 = this.Project(triangle[0]);
Point p2 = this.Project(triangle[1]);
Point p3 = this.Project(triangle[2]);
double area = 0.5 * (-p2.Y * p3.X + p1.Y * (-p2.X + p3.X) + p1.X * (p2.Y - p3.Y) + p2.X * p3.Y);
double s = 1 / (2 * area) * (p1.Y * p3.X - p1.X * p3.Y + (p3.Y - p1.Y) * p0.X + (p1.X - p3.X) * p0.Y);
double t = 1 / (2 * area) * (p1.X * p2.Y - p1.Y * p2.X + (p1.Y - p2.Y) * p0.X + (p2.X - p1.X) * p0.Y);
if (s >= 0 && t >= 0 && 1 - s - t >= 0)
{
Point3D pt = this.Deproject(p0, triangle);
double dist1 = this.ZDepth(pt1[0]);
double dist2 = this.ZDepth(pt);
if (Math.Abs(dist1 - dist2) < Camera.Tolerance)
{
return(0);
}
return(-Math.Sign(dist1 - dist2));
}
else
{
return(0);
}
}
else
{
throw new NotImplementedException();
}
}
else if (element1 is Line3DElement line1)
{
if (element2 is Point3DElement)
{
return(-Compare(element2, element1));
}
else if (element2 is Line3DElement line2)
{
Point l11 = this.Project(line1[0]);
Point l12 = this.Project(line1[1]);
Point l21 = this.Project(line2[0]);
Point l22 = this.Project(line2[1]);
(Point inters, double t, double s)? intersection = Intersections2D.Intersect(l11, l12, l21, l22);
if (intersection != null)
{
double vLength = new Point(l12.X - l11.X, l12.Y - l11.Y).Modulus();
double lLength = new Point(l22.X - l21.X, l22.Y - l21.Y).Modulus();
if (intersection?.t >= -line1.Thickness && intersection?.t <= vLength + line1.Thickness && intersection?.s >= -line1.Thickness && intersection?.s <= lLength + line1.Thickness)
{
try
{
Point3D point1 = this.Deproject(intersection.Value.inters, line1);
Point3D point2 = this.Deproject(intersection.Value.inters, line2);
double dist1 = this.ZDepth(point1);
double dist2 = this.ZDepth(point2);
if (Math.Abs(dist1 - dist2) < Camera.Tolerance)
{
return(0);
}
return(-Math.Sign(dist1 - dist2));
}
catch
{
return(0);
}
}
else
{
return(0);
}
}
else
{
return(0);
}
}
else if (element2 is Triangle3DElement triangle)
{
Point l11 = this.Project(line1[0]);
Point l12 = this.Project(line1[1]);
Point lineDirPerp = new Point(l12.Y - l11.Y, l11.X - l12.X);
lineDirPerp = new Point(lineDirPerp.X / lineDirPerp.Modulus(), lineDirPerp.Y / lineDirPerp.Modulus());
Point l21 = new Point(l11.X + lineDirPerp.X * line1.Thickness * 0.5, l11.Y + lineDirPerp.Y * line1.Thickness * 0.5);
Point l22 = new Point(l12.X + lineDirPerp.X * line1.Thickness * 0.5, l12.Y + lineDirPerp.Y * line1.Thickness * 0.5);
Point l31 = new Point(l11.X - lineDirPerp.X * line1.Thickness * 0.5, l11.Y - lineDirPerp.Y * line1.Thickness * 0.5);
Point l32 = new Point(l12.X - lineDirPerp.X * line1.Thickness * 0.5, l12.Y - lineDirPerp.Y * line1.Thickness * 0.5);
Point A = this.Project(triangle[0]);
Point B = this.Project(triangle[1]);
Point C = this.Project(triangle[2]);
List <Point> interss1 = Intersections2D.Intersect(l11, l12, A, B, C, line1.Thickness, Camera.Tolerance);
List <Point> interss2 = Intersections2D.Intersect(l21, l22, A, B, C, Camera.Tolerance);
List <Point> interss3 = Intersections2D.Intersect(l31, l32, A, B, C, Camera.Tolerance);
List <Point> interss = new List <Point>();
if (interss1 != null && interss1.Count > 0)
{
interss.AddRange(interss1);
}
if (interss2 != null && interss2.Count > 0)
{
interss.AddRange(from el in interss2 select Intersections2D.ProjectOnLine(el, l11, l12));
}
if (interss3 != null && interss3.Count > 0)
{
interss.AddRange(from el in interss3 select Intersections2D.ProjectOnLine(el, l11, l12));
}
if (interss != null && interss.Count > 0)
{
int sign = 0;
foreach (Point pt in interss)
{
try
{
Point3D pt3D1 = this.Deproject(pt, line1);
Point3D pt3D2 = this.Deproject(pt, triangle);
double dist1 = this.ZDepth(pt3D1);
double dist2 = this.ZDepth(pt3D2);
int currSign = -Math.Sign(dist1 - dist2);
if (Math.Abs(dist1 - dist2) < Camera.Tolerance)
{
currSign = 0;
}
if (sign == 0 || currSign == sign || currSign == 0)
{
sign = currSign;
}
else
{
//Line intersects with triangle
return(0);
}
}
catch { }
}
return(sign);
}
else
{
return(0);
}
}
else
{
throw new NotImplementedException();
}
}
else if (element1 is Triangle3DElement triangle1)
{
if (element2 is Point3DElement || element2 is Line3DElement)
{
return(-Compare(element2, element1));
}
else if (element2 is Triangle3DElement triangle2)
{
Point[] triangle1Projection = triangle1.GetProjection();
Point[] triangle2Projection = triangle2.GetProjection();
Point A1 = triangle1Projection[0];
Point B1 = triangle1Projection[1];
Point C1 = triangle1Projection[2];
Point A2 = triangle2Projection[0];
Point B2 = triangle2Projection[1];
Point C2 = triangle2Projection[2];
List <Point> intersections = Intersections2D.IntersectTriangles(A1, B1, C1, A2, B2, C2, Camera.Tolerance);
if (intersections.Count >= 3)
{
double meanX = 0;
double meanY = 0;
foreach (Point p in intersections)
{
meanX += p.X;
meanY += p.Y;
}
meanX /= intersections.Count;
meanY /= intersections.Count;
Point pt = new Point(meanX, meanY);
try
{
Point3D pt3D1 = this.Deproject(pt, triangle1);
Point3D pt3D2 = this.Deproject(pt, triangle2);
double dist1 = this.ZDepth(pt3D1);
double dist2 = this.ZDepth(pt3D2);
if (double.IsNaN(dist1 - dist2))
{
return(0);
}
int sign = -Math.Sign(dist1 - dist2);
if (Math.Abs(dist1 - dist2) < Camera.Tolerance)
{
sign = 0;
}
return(sign);
}
catch { return(0); }
}
else
{
return(0);
}
}
else
{
throw new NotImplementedException();
}
}
else
{
throw new NotImplementedException();
}
}
public static List <Point> Intersect(Point l11, Point l12, Point A, Point B, Point C, double lineThickness, double tolerance)
{
double lineLength = new Point(l11.X - l12.X, l11.Y - l12.Y).Modulus();
double AB = new Point(A.X - B.X, A.Y - B.Y).Modulus();
double BC = new Point(B.X - C.X, B.Y - C.Y).Modulus();
double CA = new Point(C.X - A.X, C.Y - A.Y).Modulus();
(Point inters, double t, double s)? intersAB = Intersections2D.Intersect(l11, l12, A, B);
(Point inters, double t, double s)? intersBC = Intersections2D.Intersect(l11, l12, B, C);
(Point inters, double t, double s)? intersCA = Intersections2D.Intersect(l11, l12, C, A);
bool ABtrue = intersAB != null && intersAB.Value.s >= -tolerance && intersAB.Value.s <= AB + tolerance;
bool BCtrue = intersBC != null && intersBC.Value.s >= -tolerance && intersBC.Value.s <= BC + tolerance;
bool CAtrue = intersCA != null && intersCA.Value.s >= -tolerance && intersCA.Value.s <= CA + tolerance;
List <Point> intersections = new List <Point>(3);
if (ABtrue)
{
Point inters;
if (intersAB.Value.t >= -lineThickness && intersAB.Value.t <= lineLength + lineThickness)
{
inters = intersAB.Value.inters;
}
else if (intersAB.Value.t < -lineThickness)
{
inters = l11;
}
else
{
inters = l12;
}
bool found = false;
foreach (Point pt in intersections)
{
if (AreEqual(pt, inters, tolerance))
{
found = true;
break;
}
}
if (!found)
{
intersections.Add(inters);
}
}
if (BCtrue)
{
Point inters;
if (intersBC.Value.t >= -lineThickness && intersBC.Value.t <= lineLength + lineThickness)
{
inters = intersBC.Value.inters;
}
else if (intersBC.Value.t < -lineThickness)
{
inters = l11;
}
else
{
inters = l12;
}
bool found = false;
foreach (Point pt in intersections)
{
if (AreEqual(pt, inters, tolerance))
{
found = true;
break;
}
}
if (!found)
{
intersections.Add(inters);
}
}
if (CAtrue)
{
Point inters;
if (intersCA.Value.t >= -lineThickness && intersCA.Value.t <= lineLength + lineThickness)
{
inters = intersCA.Value.inters;
}
else if (intersCA.Value.t < -lineThickness)
{
inters = l11;
}
else
{
inters = l12;
}
bool found = false;
foreach (Point pt in intersections)
{
if (AreEqual(pt, inters, tolerance))
{
found = true;
break;
}
}
if (!found)
{
intersections.Add(inters);
}
}
return(intersections);
}
