From b939a13923e9630064b6840e1b46ceea8e4dc8d6 Mon Sep 17 00:00:00 2001
From: azv <azv@opencascade.com>
Date: Tue, 7 Jul 2020 17:40:50 +0300
Subject: [PATCH] 0031016: Projection of an ellipse is a B-spline in some cases

Improve projection of ellipse and circle on a plane in case of the same parametrization of the original curve and the projected one is not necessary. Now the projection is a canonical curve instead of B-spline.
---
 src/ProjLib/ProjLib_ProjectOnPlane.cxx | 146 +++++++++++++++++++------
 tests/bugs/modalg_7/begin              |  50 +++++++--
 tests/bugs/modalg_7/bug31016_01        |  27 +++++
 tests/bugs/modalg_7/bug31016_02        |  29 +++++
 tests/bugs/modalg_7/bug31016_03        |  27 +++++
 tests/bugs/modalg_7/bug31016_04        |  29 +++++
 tests/bugs/modalg_7/bug31016_05        |  27 +++++
 tests/bugs/modalg_7/bug31016_06        |  29 +++++
 tests/bugs/modalg_7/bug31016_07        |  23 ++++
 tests/bugs/modalg_7/bug31016_08        |  25 +++++
 tests/bugs/modalg_7/bug31016_09        |  23 ++++
 tests/bugs/modalg_7/bug31016_10        |  25 +++++
 tests/bugs/modalg_7/bug31016_11        |  23 ++++
 tests/bugs/modalg_7/bug31016_12        |  25 +++++
 tests/bugs/modalg_7/bug31016_13        |  32 ++++++
 tests/bugs/modalg_7/bug31016_14        |  33 ++++++
 tests/bugs/modalg_7/bug31016_15        |  32 ++++++
 tests/bugs/modalg_7/bug31016_16        |  33 ++++++
 tests/bugs/modalg_7/bug31016_17        |  32 ++++++
 tests/bugs/modalg_7/bug31016_18        |  33 ++++++
 tests/bugs/modalg_7/bug31016_19        |  27 +++++
 tests/bugs/modalg_7/bug31016_20        |  28 +++++
 tests/bugs/modalg_7/bug31016_21        |  27 +++++
 tests/bugs/modalg_7/bug31016_22        |  28 +++++
 tests/bugs/modalg_7/bug31016_23        |  27 +++++
 tests/bugs/modalg_7/bug31016_24        |  28 +++++
 26 files changed, 826 insertions(+), 42 deletions(-)
 create mode 100644 tests/bugs/modalg_7/bug31016_01
 create mode 100644 tests/bugs/modalg_7/bug31016_02
 create mode 100644 tests/bugs/modalg_7/bug31016_03
 create mode 100644 tests/bugs/modalg_7/bug31016_04
 create mode 100644 tests/bugs/modalg_7/bug31016_05
 create mode 100644 tests/bugs/modalg_7/bug31016_06
 create mode 100644 tests/bugs/modalg_7/bug31016_07
 create mode 100644 tests/bugs/modalg_7/bug31016_08
 create mode 100644 tests/bugs/modalg_7/bug31016_09
 create mode 100644 tests/bugs/modalg_7/bug31016_10
 create mode 100644 tests/bugs/modalg_7/bug31016_11
 create mode 100644 tests/bugs/modalg_7/bug31016_12
 create mode 100644 tests/bugs/modalg_7/bug31016_13
 create mode 100644 tests/bugs/modalg_7/bug31016_14
 create mode 100644 tests/bugs/modalg_7/bug31016_15
 create mode 100644 tests/bugs/modalg_7/bug31016_16
 create mode 100644 tests/bugs/modalg_7/bug31016_17
 create mode 100644 tests/bugs/modalg_7/bug31016_18
 create mode 100644 tests/bugs/modalg_7/bug31016_19
 create mode 100644 tests/bugs/modalg_7/bug31016_20
 create mode 100644 tests/bugs/modalg_7/bug31016_21
 create mode 100644 tests/bugs/modalg_7/bug31016_22
 create mode 100644 tests/bugs/modalg_7/bug31016_23
 create mode 100644 tests/bugs/modalg_7/bug31016_24

diff --git a/src/ProjLib/ProjLib_ProjectOnPlane.cxx b/src/ProjLib/ProjLib_ProjectOnPlane.cxx
index b059fcadfa..7a876ab7e8 100644
--- a/src/ProjLib/ProjLib_ProjectOnPlane.cxx
+++ b/src/ProjLib/ProjLib_ProjectOnPlane.cxx
@@ -44,6 +44,9 @@
 #include <Geom_Parabola.hxx>
 #include <Geom_Hyperbola.hxx>
 #include <Geom_Ellipse.hxx>
+#include <GeomLib_Tool.hxx>
+#include <math_Jacobi.hxx>
+#include <math_Matrix.hxx>
 
 
 
@@ -516,10 +519,7 @@ void ProjLib_ProjectOnPlane::Load(const Handle(Adaptor3d_HCurve)&    C,
   gp_Ax2 Axis;
   Standard_Real R1 =0., R2 =0.;
 
-  if ( Type != GeomAbs_Line)  // on garde le parametrage
-    myKeepParam = Standard_True;
-  else                        // on prend le choix utilisateur.
-    myKeepParam = KeepParametrization;
+  myKeepParam = KeepParametrization;
 
   switch ( Type) {
   case GeomAbs_Line: 
@@ -648,12 +648,14 @@ void ProjLib_ProjectOnPlane::Load(const Handle(Adaptor3d_HCurve)&    C,
 
       Standard_Real Tol2 = myTolerance*myTolerance;
       if (VDx.SquareMagnitude() < Tol2 ||
-	  VDy.SquareMagnitude() < Tol2    ) {
-	myIsApprox = Standard_True;
+          VDy.SquareMagnitude() < Tol2 ||
+          VDx.CrossSquareMagnitude(VDy) < Tol2)
+      {
+        myIsApprox = Standard_True;
       }
 
-      if (!myIsApprox && 
-	  gp_Dir(VDx).IsNormal(gp_Dir(VDy),Precision::Angular())) {
+      if (!myIsApprox)
+      {
 	Dx = gp_Dir(VDx);
 	Dy = gp_Dir(VDy);
 	gp_Pnt O    = Axis.Location();
@@ -662,39 +664,93 @@ void ProjLib_ProjectOnPlane::Load(const Handle(Adaptor3d_HCurve)&    C,
 	gp_Pnt Py   = ProjectPnt(myPlane,myDirection,O.Translated(R2*gp_Vec(Y)));
 	Standard_Real Major = P.Distance(Px);
 	Standard_Real Minor = P.Distance(Py);
-	gp_Ax2 Axe( P, Dx^Dy,Dx);
 
-	if ( Abs( Major - Minor) < Precision::Confusion()) {
-	  myType = GeomAbs_Circle;
- 	  gp_Circ Circ(Axe, Major);
-	  GeomCirclePtr  = new Geom_Circle(Circ);
-//  Modified by Sergey KHROMOV - Tue Jan 29 16:57:29 2002 Begin
-	  GeomAdaptor_Curve aGACurve(GeomCirclePtr);
-	  myResult = new GeomAdaptor_HCurve(aGACurve);
-//  Modified by Sergey KHROMOV - Tue Jan 29 16:57:30 2002 End
-	}
-	else if ( Major > Minor) {
-	  myType = GeomAbs_Ellipse;
-	  Elips  = gp_Elips( Axe, Major, Minor);
-	  
-          GeomEllipsePtr = new Geom_Ellipse(Elips) ;
+        if (myKeepParam)
+        {
+          myIsApprox = !gp_Dir(VDx).IsNormal(gp_Dir(VDy), Precision::Angular());
+        }
+        else
+        {
+          // Since it is not necessary to keep the same parameter for the point on the original and on the projected curves,
+          // we will use the following approach to find axes of the projected ellipse and provide the canonical curve:
+          // https://www.geometrictools.com/Documentation/ParallelProjectionEllipse.pdf
+          math_Matrix aMatrA(1, 2, 1, 2);
+          // A = Jp^T * Pr(Je), where
+          //   Pr(Je) - projection of axes of original ellipse to the target plane
+          //   Jp - X and Y axes of the target plane
+          aMatrA(1, 1) = myPlane.XDirection().XYZ().Dot(VDx.XYZ());
+          aMatrA(1, 2) = myPlane.XDirection().XYZ().Dot(VDy.XYZ());
+          aMatrA(2, 1) = myPlane.YDirection().XYZ().Dot(VDx.XYZ());
+          aMatrA(2, 2) = myPlane.YDirection().XYZ().Dot(VDy.XYZ());
+
+          math_Matrix aMatrDelta2(1, 2, 1, 2, 0.0);
+          //           | 1/MajorRad^2       0       |
+          // Delta^2 = |                            |
+          //           |      0        1/MajorRad^2 |
+          aMatrDelta2(1, 1) = 1.0 / (R1 * R1);
+          aMatrDelta2(2, 2) = 1.0 / (R2 * R2);
+
+          math_Matrix aMatrAInv = aMatrA.Inverse();
+          math_Matrix aMatrM = aMatrAInv.Transposed() * aMatrDelta2 * aMatrAInv;
+
+          // perform eigenvalues calculation
+          math_Jacobi anEigenCalc(aMatrM);
+          if (anEigenCalc.IsDone())
+          {
+            // radii of the projected ellipse
+            Minor = 1.0 / Sqrt(anEigenCalc.Value(1));
+            Major = 1.0 / Sqrt(anEigenCalc.Value(2));
+
+            // calculate the rotation angle for the plane axes to meet the correct axes of the projected ellipse
+            // (swap eigenvectors in respect to major and minor axes)
+            const math_Matrix& anEigenVec = anEigenCalc.Vectors();
+            gp_Trsf2d aTrsfInPlane;
+            aTrsfInPlane.SetValues(anEigenVec(1, 2), anEigenVec(1, 1), 0.0,
+                                   anEigenVec(2, 2), anEigenVec(2, 1), 0.0);
+            gp_Trsf aRot;
+            aRot.SetRotation(gp_Ax1(P, myPlane.Direction()), aTrsfInPlane.RotationPart());
+
+            Dx = myPlane.XDirection().Transformed(aRot);
+            Dy = myPlane.YDirection().Transformed(aRot);
+          }
+          else
+          {
+            myIsApprox = Standard_True;
+          }
+        }
+
+        if (!myIsApprox)
+        {
+          gp_Ax2 Axe(P, Dx^Dy, Dx);
+
+          if (Abs(Major - Minor) < Precision::Confusion()) {
+            myType = GeomAbs_Circle;
+            gp_Circ Circ(Axe, Major);
+            GeomCirclePtr  = new Geom_Circle(Circ);
 //  Modified by Sergey KHROMOV - Tue Jan 29 16:57:29 2002 Begin
-	  GeomAdaptor_Curve aGACurve(GeomEllipsePtr);
-	  myResult = new GeomAdaptor_HCurve(aGACurve);
+            GeomAdaptor_Curve aGACurve(GeomCirclePtr);
+            myResult = new GeomAdaptor_HCurve(aGACurve);
 //  Modified by Sergey KHROMOV - Tue Jan 29 16:57:30 2002 End
-	}
-	else {
-	  myIsApprox = Standard_True;
-	  myType = GeomAbs_BSplineCurve;
-          PerformApprox(myCurve,myPlane,myDirection,ApproxCurve);
+          }
+          else if ( Major > Minor) {
+            myType = GeomAbs_Ellipse;
+            Elips  = gp_Elips( Axe, Major, Minor);
+
+            GeomEllipsePtr = new Geom_Ellipse(Elips);
 //  Modified by Sergey KHROMOV - Tue Jan 29 16:57:29 2002 Begin
-	  GeomAdaptor_Curve aGACurve(ApproxCurve);
-	  myResult = new GeomAdaptor_HCurve(aGACurve);
+            GeomAdaptor_Curve aGACurve(GeomEllipsePtr);
+            myResult = new GeomAdaptor_HCurve(aGACurve);
 //  Modified by Sergey KHROMOV - Tue Jan 29 16:57:30 2002 End
-	}
+          }
+          else {
+            myIsApprox = Standard_True;
+          }
+        }
       }
-      else {
-	myIsApprox = Standard_True;
+
+      // No way to build the canonical curve, approximate as B-spline
+      if (myIsApprox)
+      {
 	myType     = GeomAbs_BSplineCurve;
         PerformApprox(myCurve,myPlane,myDirection,ApproxCurve);
 //  Modified by Sergey KHROMOV - Tue Jan 29 16:57:29 2002 Begin
@@ -702,10 +758,26 @@ void ProjLib_ProjectOnPlane::Load(const Handle(Adaptor3d_HCurve)&    C,
 	myResult = new GeomAdaptor_HCurve(aGACurve);
 //  Modified by Sergey KHROMOV - Tue Jan 29 16:57:30 2002 End
       }
+      else if (GeomCirclePtr || GeomEllipsePtr)
+      {
+        Handle(Geom_Curve) aResultCurve = GeomCirclePtr;
+        if (aResultCurve.IsNull())
+          aResultCurve = GeomEllipsePtr;
+        // start and end parameters of the projected curve
+        Standard_Real aParFirst = myCurve->FirstParameter();
+        Standard_Real aParLast = myCurve->LastParameter();
+        gp_Pnt aPntFirst = ProjectPnt(myPlane, myDirection, myCurve->Value(aParFirst));
+        gp_Pnt aPntLast = ProjectPnt(myPlane, myDirection, myCurve->Value(aParLast));
+        GeomLib_Tool::Parameter(aResultCurve, aPntFirst, Precision::Confusion(), myFirstPar);
+        GeomLib_Tool::Parameter(aResultCurve, aPntLast, Precision::Confusion(), myLastPar);
+        while (myLastPar <= myFirstPar)
+          myLastPar += myResult->Period();
+      }
     }
     break;
   case GeomAbs_Parabola:
     {
+      myKeepParam = Standard_True;
       //     P(u) = O + (u*u)/(4*f) * Xc + u * Yc
       // ==> Q(u) = f(P(u)) 
       //          = f(O) + (u*u)/(4*f) * f(Xc) + u * f(Yc)
@@ -757,6 +829,7 @@ void ProjLib_ProjectOnPlane::Load(const Handle(Adaptor3d_HCurve)&    C,
     break;
   case GeomAbs_Hyperbola:
     {
+      myKeepParam = Standard_True;
       //     P(u) = O + R1 * Cosh(u) * Xc + R2 * Sinh(u) * Yc
       // ==> Q(u) = f(P(u)) 
       //          = f(O) + R1 * Cosh(u) * f(Xc) + R2 * Sinh(u) * f(Yc)
@@ -824,6 +897,7 @@ void ProjLib_ProjectOnPlane::Load(const Handle(Adaptor3d_HCurve)&    C,
       Handle(Geom_BezierCurve) ProjCu = 
 	Handle(Geom_BezierCurve)::DownCast(BezierCurvePtr->Copy());
 
+      myKeepParam = Standard_True;
       myIsApprox = Standard_False;
       myType = Type;
       for ( Standard_Integer i = 1; i <= NbPoles; i++) {
@@ -847,6 +921,7 @@ void ProjLib_ProjectOnPlane::Load(const Handle(Adaptor3d_HCurve)&    C,
       Handle(Geom_BSplineCurve) ProjectedBSplinePtr =
 	Handle(Geom_BSplineCurve)::DownCast(BSplineCurvePtr->Copy()) ;
       
+      myKeepParam = Standard_True;
       myIsApprox = Standard_False;
       myType = Type;
       for ( Standard_Integer i = 1; i <= BSplineCurvePtr->NbPoles(); i++) {
@@ -862,6 +937,7 @@ void ProjLib_ProjectOnPlane::Load(const Handle(Adaptor3d_HCurve)&    C,
     break;
   default:
     {
+      myKeepParam = Standard_True;
       myIsApprox = Standard_True;
       myType     = GeomAbs_BSplineCurve;
       PerformApprox(myCurve,myPlane,myDirection,ApproxCurve);
diff --git a/tests/bugs/modalg_7/begin b/tests/bugs/modalg_7/begin
index f40c35f0a3..80bc788a08 100644
--- a/tests/bugs/modalg_7/begin
+++ b/tests/bugs/modalg_7/begin
@@ -10,11 +10,47 @@ proc OFFSETSHAPE {distance faces calcul type} {
         uplevel #0 offsetperform result
 }
 
+proc ProjectCurvePointToPlaneAlongDir {curve param pln {dir {}}} {
+  upvar $pln p
+  upvar $curve c
+  cvalue c $param x y z
+  if {[llength $dir] == 0 } {
+    # project to plane along the normal
+    regexp {Axis   :([-0-9.+eE]+), ([-0-9.+eE]+), ([-0-9.+eE]+)} [dump p] full dx dy dz
+    lappend dir $dx $dy $dz
+  }
+  line ln x y z [lindex $dir 0] [lindex $dir 1] [lindex $dir 2]
+  intersect pt ln p
+  regexp {Point : ([-0-9.+eE]+), ([-0-9.+eE]+), ([-0-9.+eE]+)} [dump pt] full x y z
+
+  set pntOnPlane {}
+  lappend pntOnPlane $x $y $z
+  return $pntOnPlane
+}
 
-
-
-
-
-
-
-
+proc CheckProjectionToPlane {nbSamples origCurve origParam0 origParam1 projCurve projParam0 projParam1 pln {dir {}} {tolerance 1.e-7}} {
+  upvar $pln p
+  upvar $origCurve origC
+  upvar $projCurve projC
+
+  set isOk 1
+  for {set i 0} {$i <= $nbSamples} {incr i} {
+    set parOrig [expr $origParam0 + ($origParam1 - $origParam0) * $i / $nbSamples]
+    set parProj [expr $projParam0 + ($projParam1 - $projParam0) * $i / $nbSamples]
+
+    set pnt [ProjectCurvePointToPlaneAlongDir origC $parOrig p $dir]
+    cvalue projC $parProj X Y Z
+
+    set dx [expr [lindex $pnt 0]-[dval X]]
+    set dy [expr [lindex $pnt 1]-[dval Y]]
+    set dz [expr [lindex $pnt 2]-[dval Z]]
+
+    if {[expr $dx*$dx + $dy*$dy + $dz*$dz] < [expr $tolerance*$tolerance]} {
+      puts "OK: Projection correct"
+    } else {
+      puts "ERROR: Projection incorrect"
+      set isOk 0
+    }
+  }
+  return $isOk
+}
diff --git a/tests/bugs/modalg_7/bug31016_01 b/tests/bugs/modalg_7/bug31016_01
new file mode 100644
index 0000000000..f446bbfe96
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_01
@@ -0,0 +1,27 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+ellipse c 0 0 0  0 0 1  2 1 0  20 10
+plane p 0 0 0  0 1 10
+projonplane r c p 0
+
+if {![regexp {Ellipse} [dump r]]} {
+  puts "ERROR: Projected curve is not an ellipse"
+}
+
+# calculate a parametric shift on the projected curve
+set pnt [ProjectCurvePointToPlaneAlongDir c 0 p]
+parameters r [lindex $pnt 0] [lindex $pnt 1] [lindex $pnt 2] 0.1 shift
+
+if {[CheckProjectionToPlane 100 c 0 [expr 2*[dval pi]] r [dval shift] [expr [dval shift]+2*[dval pi]] p]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_02 b/tests/bugs/modalg_7/bug31016_02
new file mode 100644
index 0000000000..3feaaa5eb8
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_02
@@ -0,0 +1,29 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+set projDir { 1 1 1 }
+
+ellipse c 0 0 0  0 0 1  2 1 0  20 10
+plane p 0 0 0  0 1 10
+projonplane r c p [lindex $projDir 0] [lindex $projDir 1] [lindex $projDir 2] 0
+
+if {![regexp {Ellipse} [dump r]]} {
+  puts "ERROR: Projected curve is not an ellipse"
+}
+
+# calculate a parametric shift on the projected curve
+set pnt [ProjectCurvePointToPlaneAlongDir c 0 p $projDir]
+parameters r [lindex $pnt 0] [lindex $pnt 1] [lindex $pnt 2] 0.1 shift
+
+if {[CheckProjectionToPlane 100 c 0 [expr 2*[dval pi]] r [dval shift] [expr [dval shift]+2*[dval pi]] p $projDir]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_03 b/tests/bugs/modalg_7/bug31016_03
new file mode 100644
index 0000000000..6e137104e0
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_03
@@ -0,0 +1,27 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+circle c 0 0 0  10
+plane p 0 0 0  1 0 1
+projonplane r c p 0
+
+if {![regexp {Ellipse} [dump r]]} {
+  puts "ERROR: Projected curve is not an ellipse"
+}
+
+# calculate a parametric shift on the projected curve
+set pnt [ProjectCurvePointToPlaneAlongDir c 0 p]
+parameters r [lindex $pnt 0] [lindex $pnt 1] [lindex $pnt 2] 0.1 shift
+
+if {[CheckProjectionToPlane 100 c 0 [expr 2*[dval pi]] r [dval shift] [expr [dval shift]+2*[dval pi]] p]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_04 b/tests/bugs/modalg_7/bug31016_04
new file mode 100644
index 0000000000..90a241b3c0
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_04
@@ -0,0 +1,29 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+set projDir { 1 1 1 }
+
+circle c 0 0 0  10
+plane p 0 0 0  1 0 1
+projonplane r c p [lindex $projDir 0] [lindex $projDir 1] [lindex $projDir 2] 0
+
+if {![regexp {Ellipse} [dump r]]} {
+  puts "ERROR: Projected curve is not an ellipse"
+}
+
+# calculate a parametric shift on the projected curve
+set pnt [ProjectCurvePointToPlaneAlongDir c 0 p $projDir]
+parameters r [lindex $pnt 0] [lindex $pnt 1] [lindex $pnt 2] 0.1 shift
+
+if {[CheckProjectionToPlane 100 c 0 [expr 2*[dval pi]] r [dval shift] [expr [dval shift]+2*[dval pi]] p $projDir]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_05 b/tests/bugs/modalg_7/bug31016_05
new file mode 100644
index 0000000000..3177ee9635
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_05
@@ -0,0 +1,27 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+ellipse c 0 0 0  0.866025403784439 0 0.5  0.5 0 -0.866025403784439  20 10
+plane p 0 0 0  0 0 1
+projonplane r c p 0
+
+if {![regexp {Circle} [dump r]]} {
+  puts "ERROR: Projected curve is not a circle"
+}
+
+# calculate a parametric shift on the projected curve
+set pnt [ProjectCurvePointToPlaneAlongDir c 0 p]
+parameters r [lindex $pnt 0] [lindex $pnt 1] [lindex $pnt 2] 0.1 shift
+
+if {[CheckProjectionToPlane 100 c 0 [expr 2*[dval pi]] r [dval shift] [expr [dval shift]+2*[dval pi]] p]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_06 b/tests/bugs/modalg_7/bug31016_06
new file mode 100644
index 0000000000..5b9c24a5ab
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_06
@@ -0,0 +1,29 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+set projDir { 1 1 1 }
+
+ellipse c 0 0 0  0 0 1  2 1 0  20 10
+plane p 0 0 0  0 0 1
+projonplane r c p [lindex $projDir 0] [lindex $projDir 1] [lindex $projDir 2] 0
+
+if {![regexp {Ellipse} [dump r]]} {
+  puts "ERROR: Projected curve is not an ellipse"
+}
+
+# calculate a parametric shift on the projected curve
+set pnt [ProjectCurvePointToPlaneAlongDir c 0 p $projDir]
+parameters r [lindex $pnt 0] [lindex $pnt 1] [lindex $pnt 2] 0.1 shift
+
+if {[CheckProjectionToPlane 100 c 0 [expr 2*[dval pi]] r [dval shift] [expr [dval shift]+2*[dval pi]] p $projDir]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_07 b/tests/bugs/modalg_7/bug31016_07
new file mode 100644
index 0000000000..9c05fd689e
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_07
@@ -0,0 +1,23 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+ellipse c 0 0 0  0 0 1  2 1 0  20 10
+plane p 0 0 0  0 1 10
+projonplane r c p 1
+
+if {![regexp {BSplineCurve} [dump r]]} {
+  puts "ERROR: Projected curve is not a B-spline curve"
+}
+
+if {[CheckProjectionToPlane 100 c 0 [expr 2*[dval pi]] r 0 [expr 2*[dval pi]] p {} 1.e-6]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_08 b/tests/bugs/modalg_7/bug31016_08
new file mode 100644
index 0000000000..79b282cf8f
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_08
@@ -0,0 +1,25 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+set projDir { 1 1 1 }
+
+ellipse c 0 0 0  0 0 1  2 1 0  20 10
+plane p 0 0 0  0 1 10
+projonplane r c p [lindex $projDir 0] [lindex $projDir 1] [lindex $projDir 2] 1
+
+if {![regexp {BSplineCurve} [dump r]]} {
+  puts "ERROR: Projected curve is not a B-spline curve"
+}
+
+if {[CheckProjectionToPlane 100 c 0 [expr 2*[dval pi]] r 0 [expr 2*[dval pi]] p $projDir 1.e-6]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_09 b/tests/bugs/modalg_7/bug31016_09
new file mode 100644
index 0000000000..e2aa57772a
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_09
@@ -0,0 +1,23 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+circle c 0 0 0  10
+plane p 0 0 0  1 0 1
+projonplane r c p 1
+
+if {![regexp {BSplineCurve} [dump r]]} {
+  puts "ERROR: Projected curve is not a B-spline curve"
+}
+
+if {[CheckProjectionToPlane 100 c 0 [expr 2*[dval pi]] r 0 [expr 2*[dval pi]] p {} 1.e-6]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_10 b/tests/bugs/modalg_7/bug31016_10
new file mode 100644
index 0000000000..164266e769
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_10
@@ -0,0 +1,25 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+set projDir { 1 1 1 }
+
+circle c 0 0 0  10
+plane p 0 0 0  1 0 1
+projonplane r c p [lindex $projDir 0] [lindex $projDir 1] [lindex $projDir 2] 1
+
+if {![regexp {BSplineCurve} [dump r]]} {
+  puts "ERROR: Projected curve is not a B-spline curve"
+}
+
+if {[CheckProjectionToPlane 100 c 0 [expr 2*[dval pi]] r 0 [expr 2*[dval pi]] p $projDir 1.e-6]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_11 b/tests/bugs/modalg_7/bug31016_11
new file mode 100644
index 0000000000..eff29bc8e2
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_11
@@ -0,0 +1,23 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+ellipse c 0 0 0  0.866025403784439 0 0.5  0.5 0 -0.866025403784439  20 10
+plane p 0 0 0  0 0 1
+projonplane r c p 1
+
+if {![regexp {Circle} [dump r]]} {
+  puts "ERROR: Projected curve is not a circle"
+}
+
+if {[CheckProjectionToPlane 100 c 0 [expr 2*[dval pi]] r 0 [expr 2*[dval pi]] p {} 1.e-6]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_12 b/tests/bugs/modalg_7/bug31016_12
new file mode 100644
index 0000000000..d8c1ae564e
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_12
@@ -0,0 +1,25 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+set projDir { 1 1 1 }
+
+ellipse c 0 0 0  0 0 1  2 1 0  20 10
+plane p 0 0 0  0 0 1
+projonplane r c p [lindex $projDir 0] [lindex $projDir 1] [lindex $projDir 2] 1
+
+if {![regexp {Ellipse} [dump r]]} {
+  puts "ERROR: Projected curve is not an ellipse"
+}
+
+if {[CheckProjectionToPlane 100 c 0 [expr 2*[dval pi]] r 0 [expr 2*[dval pi]] p $projDir 1.e-6]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_13 b/tests/bugs/modalg_7/bug31016_13
new file mode 100644
index 0000000000..204ef081e5
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_13
@@ -0,0 +1,32 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+set startPar 1
+set endPar 4.5
+
+ellipse c 0 0 0  0 0 1  2 1 0  20 10
+trim c c $startPar $endPar
+plane p 0 0 0  0 1 10
+projonplane r c p 0
+
+if {![regexp {Ellipse} [dump r]]} {
+  puts "ERROR: Projected curve is not an ellipse"
+}
+
+# calculate a parametric shift on the projected curve
+set pnt [ProjectCurvePointToPlaneAlongDir c $startPar p]
+trim ru r
+parameters ru [lindex $pnt 0] [lindex $pnt 1] [lindex $pnt 2] 0.1 shift
+
+if {[CheckProjectionToPlane 100 c $startPar $endPar r [dval shift] [expr $endPar-$startPar+[dval shift]] p]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_14 b/tests/bugs/modalg_7/bug31016_14
new file mode 100644
index 0000000000..18727e59ac
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_14
@@ -0,0 +1,33 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+set projDir { 1 1 1 }
+set startPar 1
+set endPar 4.5
+
+ellipse c 0 0 0  0 0 1  2 1 0  20 10
+trim c c $startPar $endPar
+plane p 0 0 0  0 1 10
+projonplane r c p [lindex $projDir 0] [lindex $projDir 1] [lindex $projDir 2] 0
+
+if {![regexp {Ellipse} [dump r]]} {
+  puts "ERROR: Projected curve is not an ellipse"
+}
+
+# calculate a parametric shift on the projected curve
+set pnt [ProjectCurvePointToPlaneAlongDir c $startPar p $projDir]
+trim ru r
+parameters ru [lindex $pnt 0] [lindex $pnt 1] [lindex $pnt 2] 0.1 shift
+
+if {[CheckProjectionToPlane 100 c $startPar $endPar r [dval shift] [expr $endPar-$startPar+[dval shift]] p $projDir]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_15 b/tests/bugs/modalg_7/bug31016_15
new file mode 100644
index 0000000000..d5d1373ae9
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_15
@@ -0,0 +1,32 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+set startPar 1
+set endPar 4.5
+
+circle c 0 0 0  10
+trim c c $startPar $endPar
+plane p 0 0 0  1 0 1
+projonplane r c p 0
+
+if {![regexp {Ellipse} [dump r]]} {
+  puts "ERROR: Projected curve is not an ellipse"
+}
+
+# calculate a parametric shift on the projected curve
+set pnt [ProjectCurvePointToPlaneAlongDir c $startPar p]
+trim ru r
+parameters ru [lindex $pnt 0] [lindex $pnt 1] [lindex $pnt 2] 0.1 shift
+
+if {[CheckProjectionToPlane 100 c $startPar $endPar r [dval shift] [expr $endPar-$startPar+[dval shift]] p]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_16 b/tests/bugs/modalg_7/bug31016_16
new file mode 100644
index 0000000000..ef07e64465
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_16
@@ -0,0 +1,33 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+set projDir { 1 1 1 }
+set startPar 1
+set endPar 4.5
+
+circle c 0 0 0  10
+trim c c $startPar $endPar
+plane p 0 0 0  1 0 1
+projonplane r c p [lindex $projDir 0] [lindex $projDir 1] [lindex $projDir 2] 0
+
+if {![regexp {Ellipse} [dump r]]} {
+  puts "ERROR: Projected curve is not an ellipse"
+}
+
+# calculate a parametric shift on the projected curve
+set pnt [ProjectCurvePointToPlaneAlongDir c $startPar p $projDir]
+trim ru r
+parameters ru [lindex $pnt 0] [lindex $pnt 1] [lindex $pnt 2] 0.1 shift
+
+if {[CheckProjectionToPlane 100 c $startPar $endPar r [dval shift] [expr $endPar-$startPar+[dval shift]] p $projDir]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_17 b/tests/bugs/modalg_7/bug31016_17
new file mode 100644
index 0000000000..12c4e5e60f
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_17
@@ -0,0 +1,32 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+set startPar 1
+set endPar 4.5
+
+ellipse c 0 0 0  0.866025403784439 0 0.5  0.5 0 -0.866025403784439  20 10
+trim c c $startPar $endPar
+plane p 0 0 0  0 0 1
+projonplane r c p 0
+
+if {![regexp {Circle} [dump r]]} {
+  puts "ERROR: Projected curve is not a circle"
+}
+
+# calculate a parametric shift on the projected curve
+set pnt [ProjectCurvePointToPlaneAlongDir c $startPar p]
+trim ru r
+parameters ru [lindex $pnt 0] [lindex $pnt 1] [lindex $pnt 2] 0.1 shift
+
+if {[CheckProjectionToPlane 100 c $startPar $endPar r [dval shift] [expr $endPar-$startPar+[dval shift]] p]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_18 b/tests/bugs/modalg_7/bug31016_18
new file mode 100644
index 0000000000..a2c20a000e
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_18
@@ -0,0 +1,33 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+set projDir { 1 1 1 }
+set startPar 1
+set endPar 4.5
+
+ellipse c 0 0 0  0 0 1  2 1 0  20 10
+trim c c $startPar $endPar
+plane p 0 0 0  0 0 1
+projonplane r c p [lindex $projDir 0] [lindex $projDir 1] [lindex $projDir 2] 0
+
+if {![regexp {Ellipse} [dump r]]} {
+  puts "ERROR: Projected curve is not an ellipse"
+}
+
+# calculate a parametric shift on the projected curve
+set pnt [ProjectCurvePointToPlaneAlongDir c $startPar p $projDir]
+trim ru r
+parameters ru [lindex $pnt 0] [lindex $pnt 1] [lindex $pnt 2] 0.1 shift
+
+if {[CheckProjectionToPlane 100 c $startPar $endPar r [dval shift] [expr $endPar-$startPar+[dval shift]] p $projDir]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_19 b/tests/bugs/modalg_7/bug31016_19
new file mode 100644
index 0000000000..1c7471763b
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_19
@@ -0,0 +1,27 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+set startPar 1
+set endPar 4.5
+
+ellipse c 0 0 0  0 0 1  2 1 0  20 10
+trim c c $startPar $endPar
+plane p 0 0 0  0 1 10
+projonplane r c p 1
+
+if {![regexp {BSplineCurve} [dump r]]} {
+  puts "ERROR: Projected curve is not a B-spline curve"
+}
+
+if {[CheckProjectionToPlane 100 c $startPar $endPar r $startPar $endPar p {} 1.e-6]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_20 b/tests/bugs/modalg_7/bug31016_20
new file mode 100644
index 0000000000..f7afbd1dec
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_20
@@ -0,0 +1,28 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+set projDir { 1 1 1 }
+set startPar 1
+set endPar 4.5
+
+ellipse c 0 0 0  0 0 1  2 1 0  20 10
+trim c c $startPar $endPar
+plane p 0 0 0  0 1 10
+projonplane r c p [lindex $projDir 0] [lindex $projDir 1] [lindex $projDir 2] 1
+
+if {![regexp {BSplineCurve} [dump r]]} {
+  puts "ERROR: Projected curve is not a B-spline curve"
+}
+
+if {[CheckProjectionToPlane 100 c $startPar $endPar r $startPar $endPar p $projDir 1.e-6]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_21 b/tests/bugs/modalg_7/bug31016_21
new file mode 100644
index 0000000000..6e8cbc0a8e
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_21
@@ -0,0 +1,27 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+set startPar 1
+set endPar 4.5
+
+circle c 0 0 0  10
+trim c c $startPar $endPar
+plane p 0 0 0  1 0 1
+projonplane r c p 1
+
+if {![regexp {BSplineCurve} [dump r]]} {
+  puts "ERROR: Projected curve is not a B-spline curve"
+}
+
+if {[CheckProjectionToPlane 100 c $startPar $endPar r $startPar $endPar p {} 1.e-6]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_22 b/tests/bugs/modalg_7/bug31016_22
new file mode 100644
index 0000000000..84e87c19ea
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_22
@@ -0,0 +1,28 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+set projDir { 1 1 1 }
+set startPar 1
+set endPar 4.5
+
+circle c 0 0 0  10
+trim c c $startPar $endPar
+plane p 0 0 0  1 0 1
+projonplane r c p [lindex $projDir 0] [lindex $projDir 1] [lindex $projDir 2] 1
+
+if {![regexp {BSplineCurve} [dump r]]} {
+  puts "ERROR: Projected curve is not a B-spline curve"
+}
+
+if {[CheckProjectionToPlane 100 c $startPar $endPar r $startPar $endPar p $projDir 1.e-6]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_23 b/tests/bugs/modalg_7/bug31016_23
new file mode 100644
index 0000000000..04b0d5cbf8
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_23
@@ -0,0 +1,27 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+set startPar 1
+set endPar 4.5
+
+ellipse c 0 0 0  0.866025403784439 0 0.5  0.5 0 -0.866025403784439  20 10
+trim c c $startPar $endPar
+plane p 0 0 0  0 0 1
+projonplane r c p 1
+
+if {![regexp {Circle} [dump r]]} {
+  puts "ERROR: Projected curve is not a circle"
+}
+
+if {[CheckProjectionToPlane 100 c $startPar $endPar r $startPar $endPar p {} 1.e-6]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
diff --git a/tests/bugs/modalg_7/bug31016_24 b/tests/bugs/modalg_7/bug31016_24
new file mode 100644
index 0000000000..b733a6dcae
--- /dev/null
+++ b/tests/bugs/modalg_7/bug31016_24
@@ -0,0 +1,28 @@
+puts ""
+puts "=========================================================================="
+puts "OCC31016: Projection of an ellipse or a circle is a B-spline in some cases"
+puts "=========================================================================="
+puts ""
+
+set projDir { 1 1 1 }
+set startPar 1
+set endPar 4.5
+
+ellipse c 0 0 0  0 0 1  2 1 0  20 10
+trim c c $startPar $endPar
+plane p 0 0 0  0 0 1
+projonplane r c p [lindex $projDir 0] [lindex $projDir 1] [lindex $projDir 2] 1
+
+if {![regexp {Ellipse} [dump r]]} {
+  puts "ERROR: Projected curve is not an ellipse"
+}
+
+if {[CheckProjectionToPlane 100 c $startPar $endPar r $startPar $endPar p $projDir 1.e-6]} {
+  puts ""
+  puts "OK: All sample points are projected correctly"
+  puts ""
+} else {
+  puts ""
+  puts "ERROR: Projection is incorrect for some points"
+  puts ""
+}
-- 
2.20.1