Ellipse implementation: Several bug fixes

I. Fix minor bug where wrong b was used to create ellipse internal geometry.

Tweak the internal geometry code a bit and reformat it so it isn't so wide.
Also begin debugging constraint conflicts on small circular ellipses.

There seem to be two issues currently in major/minor internal geometry lines:
  1) Sometimes minorLength > majorLength due to round-tripping doubles, and
  2) Constraint conflicts when majorLength > minorLength by an epsilon on the order of 1e-6

(cherry picked from commit 5c3e20a)

II. When testing for a valid ellipse, also ensure that the mangled major axis length > the mangled axis length.

This additional condition ensures that major and minor axis constraints don't conflict in the case of small
(nearly) circular ellipses.

The is still a potential bug in the solver when the major length is just slightly larger than the minor, but this fix
makes it nigh impossible to reproduce.
(cherry picked from commit 7e274bc)

III. Code clean up

Remove redundant 3d vectors.

(cherry picked from commit c656d51)

src/Mod/Sketcher/Gui/CommandCreateGeo.cpp

@@ -2061,6 +2061,8 @@ class DrawSketchHandlerEllipse : public DrawSketchHandler
      * +Z coming out of the sketch, this b position is in the +Y direction from the centroid.
      */
     Base::Vector2D positiveB;
+    /// the other b position
+    Base::Vector2D negativeB;
     /// cart. position vector for primary focus
     Base::Vector2D f;
     /// cart. position vector for other focus
@@ -2396,19 +2398,27 @@ class DrawSketchHandlerEllipse : public DrawSketchHandler
          * limit of 25 attempts, I have been unable to make it fail.
          */
 
-        // simulate loss of precision in centroid and periapsis
+        // simulate loss of precision in centroid, periapsis, and apoapsis
         char cx[64];
         char cy[64];
         char px[64];
         char py[64];
+        char ax[64];
+        char ay[64];
         sprintf(cx, "%.6lf\n", centroid.fX);
         sprintf(cy, "%.6lf\n", centroid.fY);
         sprintf(px, "%.6lf\n", periapsis.fX);
         sprintf(py, "%.6lf\n", periapsis.fY);
+        sprintf(ax, "%.6lf\n", apoapsis.fX);
+        sprintf(ay, "%.6lf\n", apoapsis.fY);
         centroid.fX = atof(cx);
         centroid.fY = atof(cy);
         periapsis.fX = atof(px);
         periapsis.fY = atof(py);
+        apoapsis.fX = atof(ax);
+        apoapsis.fY = atof(ay);
+        double majorLength = (periapsis - apoapsis).Length();
+        double minorLength = 0;
 
         /* GC_MakeEllipse requires a right-handed coordinate system, with +X
          * from centroid to periapsis, +Z out of the page.
@@ -2420,87 +2430,127 @@ class DrawSketchHandlerEllipse : public DrawSketchHandler
         int count = 0;
         int limit = 25;             // no infinite loops!
         bool success = false;
+        double tempB = b;
 
-        // adjust b until our mangled vectors produce a good ellispe
+        // adjust b until our mangled vectors produce a good ellipse in GC_MakeEllipse
+        // and the mangled major and minor lines in LinePy::PyInit(...) are such that
+        // major is at least slightly larger than minor
         do {
-            j = j.Normalize() * (b - double(count * beta));
+            tempB = b - double(count * beta);
+            j = j.Normalize() * tempB;
             positiveB.fX = centroid.fX + j.x;
             positiveB.fY = centroid.fY + j.y;
-            char bx[64];
-            char by[64];
-            sprintf(bx, "%.6lf\n", positiveB.fX);
-            sprintf(by, "%.6lf\n", positiveB.fY);
-            positiveB.fX = atof(bx);
-            positiveB.fY = atof(by);
+            negativeB.fX = centroid.fX + (j.x * -1);
+            negativeB.fY = centroid.fY + (j.y * -1);
+            char bpx[64];
+            char bpy[64];
+            char bnx[64];
+            char bny[64];
+            sprintf(bpx, "%.6lf\n", positiveB.fX);
+            sprintf(bpy, "%.6lf\n", positiveB.fY);
+            sprintf(bnx, "%.6lf\n", negativeB.fX);
+            sprintf(bny, "%.6lf\n", negativeB.fY);
+            positiveB.fX = atof(bpx);
+            positiveB.fY = atof(bpy);
+            negativeB.fX = atof(bnx);
+            negativeB.fY = atof(bny);
             GC_MakeEllipse me(gp_Pnt(periapsis.fX,periapsis.fY,0),
                               gp_Pnt(positiveB.fX,positiveB.fY,0),
                               gp_Pnt(centroid.fX,centroid.fY,0));
+            minorLength = (negativeB - positiveB).Length();
             count++;
-            success = me.IsDone();
+            success = me.IsDone() && (minorLength + beta < majorLength);
         } while (!success && (count <= limit));
         if (!success) {
             qDebug() << "Failed to create a valid mangled ellipse after" << count << "attempts";
         }
-
-        Base::Vector3d center = Base::Vector3d(centroid.fX,centroid.fY,0);
-
-        Base::Vector3d majorpositiveend = center + a * Base::Vector3d(cos(phi),sin(phi),0);
-        Base::Vector3d majornegativeend = center - a * Base::Vector3d(cos(phi),sin(phi),0);
-        Base::Vector3d minorpositiveend = center + b * Base::Vector3d(-sin(phi),cos(phi),0);
-        Base::Vector3d minornegativeend = center - b * Base::Vector3d(-sin(phi),cos(phi),0);
 
-        double cf = sqrt( abs(a*a - b*b) );//using abs, avoided using different formula for a>b/a<b cases
+        // save any changes to b, then recalculate ellipse as required due to change in b
+        b = tempB;
+        e = sqrt(1 - ((b * b) / (a * a)));
+        ae = a * e;
+        f = apseHat;
+        f.Scale(ae);
+        f = centroid + f;
+        fPrime = apseHat;
+        fPrime.Scale(-1 * ae);
+        fPrime = centroid + fPrime;
 
-        Base::Vector3d focus1P = center + cf * Base::Vector3d(cos(phi),sin(phi),0);
-        Base::Vector3d focus2P = center - cf * Base::Vector3d(cos(phi),sin(phi),0);
-
-        int currentgeoid = getHighestCurveIndex();//index of the arc of ellipse we just created
+        int currentgeoid = getHighestCurveIndex(); // index of the ellipse we just created
 
         Gui::Command::openCommand("Add sketch ellipse");
         Gui::Command::doCommand(Gui::Command::Doc,
-            "App.ActiveDocument.%s.addGeometry(Part.Ellipse"
-            "(App.Vector(%f,%f,0),App.Vector(%f,%f,0),App.Vector(%f,%f,0)))",
-                sketchgui->getObject()->getNameInDocument(),
-                periapsis.fX, periapsis.fY,
-                positiveB.fX, positiveB.fY,
-                centroid.fX, centroid.fY);
+                                "App.ActiveDocument.%s.addGeometry(Part.Ellipse"
+                                "(App.Vector(%f,%f,0),App.Vector(%f,%f,0),App.Vector(%f,%f,0)))",
+                                sketchgui->getObject()->getNameInDocument(),
+                                periapsis.fX, periapsis.fY,
+                                positiveB.fX, positiveB.fY,
+                                centroid.fX, centroid.fY);
 
         currentgeoid++;
 
         try {
-            Gui::Command::doCommand(Gui::Command::Doc,"App.ActiveDocument.%s.addGeometry(Part.Line(App.Vector(%f,%f,0),App.Vector(%f,%f,0)))",
-            sketchgui->getObject()->getNameInDocument(),
-            majorpositiveend.x,majorpositiveend.y,majornegativeend.x,majornegativeend.y); // create line for major axis
+            // create line for major axis
+            Gui::Command::doCommand(Gui::Command::Doc,
+                                    "App.ActiveDocument.%s.addGeometry(Part.Line"
+                                    "(App.Vector(%f,%f,0),App.Vector(%f,%f,0)))",
+                                    sketchgui->getObject()->getNameInDocument(),
+                                    periapsis.fX,periapsis.fY,
+                                    apoapsis.fX,apoapsis.fY);
 
             Gui::Command::doCommand(Gui::Command::Doc,"App.ActiveDocument.%s.toggleConstruction(%d) ",
-            sketchgui->getObject()->getNameInDocument(),currentgeoid+1);
+                                    sketchgui->getObject()->getNameInDocument(),currentgeoid+1);
 
-            Gui::Command::doCommand(Gui::Command::Doc,"App.ActiveDocument.%s.addConstraint(Sketcher.Constraint('InternalAlignment:EllipseMajorDiameter',%d,%d)) ",
-            sketchgui->getObject()->getNameInDocument(),currentgeoid+1,currentgeoid); // constrain major axis
+            // constrain major axis
+            Gui::Command::doCommand(Gui::Command::Doc,
+                                    "App.ActiveDocument.%s.addConstraint(Sketcher.Constraint"
+                                    "('InternalAlignment:EllipseMajorDiameter',%d,%d)) ",
+                                    sketchgui->getObject()->getNameInDocument(),
+                                    currentgeoid+1,currentgeoid);
 
-            Gui::Command::doCommand(Gui::Command::Doc,"App.ActiveDocument.%s.addGeometry(Part.Line(App.Vector(%f,%f,0),App.Vector(%f,%f,0)))",
-            sketchgui->getObject()->getNameInDocument(),
-            minorpositiveend.x,minorpositiveend.y,minornegativeend.x,minornegativeend.y); // create line for minor axis
+            // create line for minor axis
+            Gui::Command::doCommand(Gui::Command::Doc,
+                                    "App.ActiveDocument.%s.addGeometry(Part.Line"
+                                    "(App.Vector(%f,%f,0),App.Vector(%f,%f,0)))",
+                                    sketchgui->getObject()->getNameInDocument(),
+                                    positiveB.fX,positiveB.fY,
+                                    negativeB.fX,negativeB.fY);
 
             Gui::Command::doCommand(Gui::Command::Doc,"App.ActiveDocument.%s.toggleConstruction(%d) ",
-            sketchgui->getObject()->getNameInDocument(),currentgeoid+2);
+                                    sketchgui->getObject()->getNameInDocument(),currentgeoid+2);
 
-            Gui::Command::doCommand(Gui::Command::Doc,"App.ActiveDocument.%s.addConstraint(Sketcher.Constraint('InternalAlignment:EllipseMinorDiameter',%d,%d)) ",
-            sketchgui->getObject()->getNameInDocument(),currentgeoid+2,currentgeoid); // constrain minor axis
+            // constrain minor axis
+            Gui::Command::doCommand(Gui::Command::Doc,
+                                    "App.ActiveDocument.%s.addConstraint(Sketcher.Constraint"
+                                    "('InternalAlignment:EllipseMinorDiameter',%d,%d)) ",
+                                    sketchgui->getObject()->getNameInDocument(),
+                                    currentgeoid+2,currentgeoid);
 
-            Gui::Command::doCommand(Gui::Command::Doc,"App.ActiveDocument.%s.addGeometry(Part.Point(App.Vector(%f,%f,0)))",
-            sketchgui->getObject()->getNameInDocument(),
-            focus1P.x,focus1P.y);
+            // create point for focus
+            Gui::Command::doCommand(Gui::Command::Doc,
+                                    "App.ActiveDocument.%s.addGeometry(Part.Point(App.Vector(%f,%f,0)))",
+                                    sketchgui->getObject()->getNameInDocument(),
+                                    f.fX,f.fY);
 
-            Gui::Command::doCommand(Gui::Command::Doc,"App.ActiveDocument.%s.addConstraint(Sketcher.Constraint('InternalAlignment:EllipseFocus1',%d,%d,%d)) ",
-            sketchgui->getObject()->getNameInDocument(),currentgeoid+3,Sketcher::start,currentgeoid);
+            // constrain focus
+            Gui::Command::doCommand(Gui::Command::Doc,
+                                    "App.ActiveDocument.%s.addConstraint(Sketcher.Constraint"
+                                    "('InternalAlignment:EllipseFocus1',%d,%d,%d)) ",
+                                    sketchgui->getObject()->getNameInDocument(),
+                                    currentgeoid+3,Sketcher::start,currentgeoid);
 
-            Gui::Command::doCommand(Gui::Command::Doc,"App.ActiveDocument.%s.addGeometry(Part.Point(App.Vector(%f,%f,0)))",
-            sketchgui->getObject()->getNameInDocument(),
-            focus2P.x,focus2P.y);
+            // create point for second focus
+            Gui::Command::doCommand(Gui::Command::Doc,
+                                    "App.ActiveDocument.%s.addGeometry(Part.Point(App.Vector(%f,%f,0)))",
+                                    sketchgui->getObject()->getNameInDocument(),
+                                    fPrime.fX,fPrime.fY);
 
-            Gui::Command::doCommand(Gui::Command::Doc,"App.ActiveDocument.%s.addConstraint(Sketcher.Constraint('InternalAlignment:EllipseFocus2',%d,%d,%d)) ",
-            sketchgui->getObject()->getNameInDocument(),currentgeoid+4,Sketcher::start,currentgeoid);
+            // constrain second focus
+            Gui::Command::doCommand(Gui::Command::Doc,
+                                    "App.ActiveDocument.%s.addConstraint(Sketcher.Constraint"
+                                    "('InternalAlignment:EllipseFocus2',%d,%d,%d)) ",
+                                    sketchgui->getObject()->getNameInDocument(),
+                                    currentgeoid+4,Sketcher::start,currentgeoid);
         }
         catch (const Base::Exception& e) {
             Base::Console().Error("%s\n", e.what());