Optimize U-notch shape.

ChangeLog.txt

@@ -57,6 +57,7 @@
 - [smart-pattern/valentina#188] Label %mFileName% file name punctuation.
 - Adding removing nodes of curved path.
 - New tools: Arc start point, Arc end point.
+- Optimize U-notch shape.
 
 # Valentina 0.7.52 September 12, 2022
 - Fix crash when default locale is ru.

src/libs/vgeometry/vabstractcurve.cpp

@@ -45,6 +45,39 @@
 constexpr qreal VAbstractCurve::minLength; // NOLINT(readability-redundant-declaration)
 #endif
 
+namespace
+{
+//---------------------------------------------------------------------------------------------------------------------
+double NodeCurvature(const QPointF &p1, const QPointF &p2, const QPointF &p3, double length)
+{
+    QLineF l1(p2, p1);
+    l1.setAngle(l1.angle() + 180);
+
+    QLineF l2(p2, p3);
+    double angle = qDegreesToRadians(l2.angleTo(l1));
+
+    return std::sin(angle / 2.0) / length;
+}
+
+//---------------------------------------------------------------------------------------------------------------------
+auto MinimalLength(const QVector<QPointF> &points) -> double
+{
+    vsizetype numPoints = points.size();
+    double smallestDistance = std::numeric_limits<double>::max();
+
+    for (int i = 0; i < numPoints - 1; ++i)
+    {
+        double distance = QLineF(points[i], points[i + 1]).length();
+        if (!qFuzzyIsNull(distance))
+        {
+            smallestDistance = std::min(smallestDistance, distance);
+        }
+    }
+
+    return smallestDistance;
+}
+} // namespace
+
 //---------------------------------------------------------------------------------------------------------------------
 VAbstractCurve::VAbstractCurve(const GOType &type, const quint32 &idObject, const Draw &mode)
   : VGObject(type, idObject, mode),
@@ -687,6 +720,27 @@ void VAbstractCurve::SetAliasSuffix(const QString &aliasSuffix)
     CreateAlias();
 }
 
+//---------------------------------------------------------------------------------------------------------------------
+auto VAbstractCurve::Curvature(const QVector<QPointF> &vertices) -> double
+{
+    vsizetype numVertices = vertices.size();
+    if (numVertices < 3)
+    {
+        // A polygonal chain needs at least 3 vertices
+        return 0.0;
+    }
+
+    qreal minLength = MinimalLength(vertices);
+
+    double sumCurvature = 0.0;
+    for (vsizetype i = 1; i < vertices.size() - 1; ++i)
+    {
+        sumCurvature += NodeCurvature(vertices[i - 1], vertices[i], vertices[i + 1], minLength);
+    }
+
+    return sumCurvature / static_cast<double>(vertices.size() - 2);
+}
+
 //---------------------------------------------------------------------------------------------------------------------
 auto VAbstractCurve::PathLength(const QVector<QPointF> &path) -> qreal
 {

src/libs/vgeometry/vabstractcurve.h

@@ -114,6 +114,8 @@ public:
 
     static constexpr qreal minLength = MmToPixel(1.);
 
+    static auto Curvature(const QVector<QPointF> &vertices) -> double;
+
 protected:
     virtual void CreateName() = 0;
     virtual void CreateAlias() = 0;

src/libs/vgeometry/varc.cpp

@@ -36,6 +36,7 @@
 #include "../ifc/ifcdef.h"
 #include "../vmisc/compatibility.h"
 #include "../vmisc/def.h"
+#include "../vmisc/defglobal.h"
 #include "../vmisc/vabstractapplication.h"
 #include "../vmisc/vmath.h"
 #include "vabstractcurve.h"
@@ -405,6 +406,33 @@ auto VArc::CutArc(qreal length, const QString &pointName) const -> QPointF
     return CutArc(length, arc1, arc2, pointName);
 }
 
+//---------------------------------------------------------------------------------------------------------------------
+auto VArc::OptimalApproximationScale(qreal radius, qreal f1, qreal f2, qreal tolerance) -> qreal
+{
+    if (qFuzzyIsNull(radius))
+    {
+        return maxCurveApproximationScale;
+    }
+
+    const qreal expectedCurvature = 1 / qAbs(radius);
+    qreal scale = minCurveApproximationScale;
+
+    do
+    {
+        VArc arc(VPointF(), radius, f1, f2);
+        arc.SetApproximationScale(scale);
+        qreal curvature = Curvature(arc.GetPoints());
+
+        if (expectedCurvature - curvature <= expectedCurvature * tolerance)
+        {
+            return scale;
+        }
+        scale += 0.1;
+    } while (scale <= maxCurveApproximationScale);
+
+    return maxCurveApproximationScale;
+}
+
 //---------------------------------------------------------------------------------------------------------------------
 void VArc::CreateName()
 {

src/libs/vgeometry/varc.h

@@ -83,6 +83,8 @@ public:
     auto CutArc(qreal length, VArc &arc1, VArc &arc2, const QString &pointName) const -> QPointF;
     auto CutArc(qreal length, const QString &pointName) const -> QPointF;
 
+    static auto OptimalApproximationScale(qreal radius, qreal f1, qreal f2, qreal tolerance) -> qreal;
+
 protected:
     void CreateName() override;
     void CreateAlias() override;

src/libs/vpatterndb/vpassmark.cpp

@@ -458,9 +458,10 @@ auto CreateUMarkPassmark(const VPiecePassmarkData &passmarkData, const QLineF &l
         points.append(seg.p1());
         points.append(seg.p2());
 
-        VArc arc(VPointF(baseLine.p2()), radius, QLineF(baseLine.p2(), l1p2).angle(),
+        const qreal f1 = QLineF(baseLine.p2(), l1p2).angle();
-                 QLineF(baseLine.p2(), l2p2).angle());
+        const qreal f2 = QLineF(baseLine.p2(), l2p2).angle();
-        arc.SetApproximationScale(10);
+        VArc arc(VPointF(baseLine.p2()), radius, f1, f2);
+        arc.SetApproximationScale(VArc::OptimalApproximationScale(radius, f1, f2, 0.3));
         points += arc.GetPoints();
 
         seg = VPassmark::FindIntersection(QLineF(l2p2, l2p1), seamAllowance);
@@ -469,9 +470,10 @@ auto CreateUMarkPassmark(const VPiecePassmarkData &passmarkData, const QLineF &l
     }
     else
     {
-        VArc arc(VPointF(baseLine.p1()), radius, QLineF(baseLine.p1(), l1p1).angle(),
+        const qreal f1 = QLineF(baseLine.p1(), l1p1).angle();
-                 QLineF(baseLine.p1(), l2p1).angle());
+        const qreal f2 = QLineF(baseLine.p1(), l2p1).angle();
-        arc.SetApproximationScale(10);
+        VArc arc(VPointF(baseLine.p1()), radius, f1, f2);
+        arc.SetApproximationScale(VArc::OptimalApproximationScale(radius, f1, f2, 0.3));
         points += arc.GetPoints();
     }
 

src/test/ValentinaTest/tst_varc.cpp

@@ -27,6 +27,7 @@
  *************************************************************************/
 
 #include "tst_varc.h"
+#include "../vgeometry/vabstractcurve.h"
 #include "../vgeometry/varc.h"
 #include "../vlayout/vabstractpiece.h"
 
@@ -596,3 +597,182 @@ void TST_VArc::EmptyArc()
     ComparePathsDistance(empty.GetPoints(), {QPointF()});
     QCOMPARE(empty.GetLength(), 0.);
 }
+
+//---------------------------------------------------------------------------------------------------------------------
+void TST_VArc::TestCurvature_data()
+{
+    QTest::addColumn<qreal>("radius");
+    QTest::addColumn<qreal>("startAngle");
+    QTest::addColumn<qreal>("endAngle");
+
+    QTest::newRow("Full circle: radius 10") << 10.0 << 0.0 << 360.0;
+    QTest::newRow("Full circle: radius -10") << -10.0 << 0.0 << 360.0;
+    QTest::newRow("Full circle: radius 150") << 150.0 << 0.0 << 360.0;
+    QTest::newRow("Full circle: radius -150") << -150.0 << 0.0 << 360.0;
+    QTest::newRow("Full circle: radius 1500") << 1500.0 << 0.0 << 360.0;
+    QTest::newRow("Full circle: radius -1500") << -1500.0 << 0.0 << 360.0;
+    QTest::newRow("Full circle: radius 50000") << 50000.0 << 0.0 << 360.0;
+    QTest::newRow("Full circle: radius -50000") << -50000.0 << 0.0 << 360.0;
+    QTest::newRow("Full circle: radius 90000") << 90000.0 << 0.0 << 360.0;
+    QTest::newRow("Full circle: radius -90000") << -90000.0 << 0.0 << 360.0;
+
+    QTest::newRow("Arc less than 45 degree, radius 100") << 100.0 << 0.0 << 10.5;
+    QTest::newRow("Arc less than 45 degree, radius -100") << -100.0 << 0.0 << 10.5;
+    QTest::newRow("Arc less than 45 degree, radius 150") << 150.0 << 0.0 << 10.5;
+    QTest::newRow("Arc less than 45 degree, radius -150") << -150.0 << 0.0 << 10.5;
+    QTest::newRow("Arc less than 45 degree, radius 1500") << 1500.0 << 0.0 << 10.5;
+    QTest::newRow("Arc less than 45 degree, radius -1500") << -1500.0 << 0.0 << 10.5;
+    QTest::newRow("Arc less than 45 degree, radius 50000") << 50000.0 << 0.0 << 10.5;
+    QTest::newRow("Arc less than 45 degree, radius -50000") << -50000.0 << 0.0 << 10.5;
+    QTest::newRow("Arc less than 45 degree, radius 90000") << 90000.0 << 0.0 << 10.5;
+    QTest::newRow("Arc less than 45 degree, radius -90000") << -90000.0 << 0.0 << 10.5;
+
+    QTest::newRow("Arc 45 degree, radius 100") << 100.0 << 0.0 << 45.0;
+    QTest::newRow("Arc 45 degree, radius -100") << -100.0 << 0.0 << 45.0;
+    QTest::newRow("Arc 45 degree, radius 150") << 150.0 << 0.0 << 45.0;
+    QTest::newRow("Arc 45 degree, radius -150") << -150.0 << 0.0 << 45.0;
+    QTest::newRow("Arc 45 degree, radius 1500") << 1500.0 << 0.0 << 45.0;
+    QTest::newRow("Arc 45 degree, radius -1500") << -1500.0 << 0.0 << 45.0;
+    QTest::newRow("Arc 45 degree, radius 50000") << 50000.0 << 0.0 << 45.0;
+    QTest::newRow("Arc 45 degree, radius -50000") << -50000.0 << 0.0 << 45.0;
+    QTest::newRow("Arc 45 degree, radius 90000") << 90000.0 << 0.0 << 45.0;
+    QTest::newRow("Arc 45 degree, radius -90000") << -90000.0 << 0.0 << 45.0;
+
+    QTest::newRow("Arc less than 90 degree, radius 100") << 100.0 << 0.0 << 75.0;
+    QTest::newRow("Arc less than 90 degree, radius -100") << -100.0 << 0.0 << 75.0;
+    QTest::newRow("Arc less than 90 degree, radius 150") << 150.0 << 0.0 << 75.0;
+    QTest::newRow("Arc less than 90 degree, radius -150") << -150.0 << 0.0 << 75.0;
+    QTest::newRow("Arc less than 90 degree, radius 1500") << 1500.0 << 0.0 << 75.0;
+    QTest::newRow("Arc less than 90 degree, radius -1500") << -1500.0 << 0.0 << 75.0;
+    QTest::newRow("Arc less than 90 degree, radius 50000") << 50000.0 << 0.0 << 75.0;
+    QTest::newRow("Arc less than 90 degree, radius -50000") << -50000.0 << 0.0 << 75.0;
+    QTest::newRow("Arc less than 90 degree, radius 90000") << 90000.0 << 0.0 << 75.0;
+    QTest::newRow("Arc less than 90 degree, radius -90000") << -90000.0 << 0.0 << 75.0;
+
+    QTest::newRow("Arc 90 degree, radius 100") << 100.0 << 0.0 << 90.0;
+    QTest::newRow("Arc 90 degree, radius -100") << -100.0 << 0.0 << 90.0;
+    QTest::newRow("Arc 90 degree, radius 150") << 150.0 << 0.0 << 90.0;
+    QTest::newRow("Arc 90 degree, radius -150") << -150.0 << 0.0 << 90.0;
+    QTest::newRow("Arc 90 degree, radius 1500") << 1500.0 << 0.0 << 90.0;
+    QTest::newRow("Arc 90 degree, radius -1500") << -1500.0 << 0.0 << 90.0;
+    QTest::newRow("Arc 90 degree, radius 50000") << 50000.0 << 0.0 << 90.0;
+    QTest::newRow("Arc 90 degree, radius -50000") << -50000.0 << 0.0 << 90.0;
+    QTest::newRow("Arc 90 degree, radius 90000") << 90000.0 << 0.0 << 90.0;
+    QTest::newRow("Arc 90 degree, radius -90000") << -90000.0 << 0.0 << 90.0;
+
+    QTest::newRow("Arc less than 135 degree, radius 100") << 100.0 << 0.0 << 110.6;
+    QTest::newRow("Arc less than 135 degree, radius -100") << -100.0 << 0.0 << 110.6;
+    QTest::newRow("Arc less than 135 degree, radius 150") << 150.0 << 0.0 << 110.6;
+    QTest::newRow("Arc less than 135 degree, radius -150") << -150.0 << 0.0 << 110.6;
+    QTest::newRow("Arc less than 135 degree, radius 1500") << 1500.0 << 0.0 << 110.6;
+    QTest::newRow("Arc less than 135 degree, radius -1500") << -1500.0 << 0.0 << 110.6;
+    QTest::newRow("Arc less than 135 degree, radius 50000") << 50000.0 << 0.0 << 110.6;
+    QTest::newRow("Arc less than 135 degree, radius -50000") << -50000.0 << 0.0 << 110.6;
+    QTest::newRow("Arc less than 135 degree, radius 90000") << 90000.0 << 0.0 << 110.6;
+    QTest::newRow("Arc less than 135 degree, radius -90000") << -90000.0 << 0.0 << 110.6;
+
+    QTest::newRow("Arc 135 degree, radius 100") << 100.0 << 0.0 << 135.0;
+    QTest::newRow("Arc 135 degree, radius -100") << -100.0 << 0.0 << 135.0;
+    QTest::newRow("Arc 135 degree, radius 150") << 150.0 << 0.0 << 135.0;
+    QTest::newRow("Arc 135 degree, radius -150") << -150.0 << 0.0 << 135.0;
+    QTest::newRow("Arc 135 degree, radius 1500") << 1500.0 << 0.0 << 135.0;
+    QTest::newRow("Arc 135 degree, radius -1500") << -1500.0 << 0.0 << 135.0;
+    QTest::newRow("Arc 135 degree, radius 50000") << 50000.0 << 0.0 << 135.0;
+    QTest::newRow("Arc 135 degree, radius -50000") << -50000.0 << 0.0 << 135.0;
+    QTest::newRow("Arc 135 degree, radius 90000") << 90000.0 << 0.0 << 135.0;
+    QTest::newRow("Arc 135 degree, radius -90000") << -90000.0 << 0.0 << 135.0;
+
+    QTest::newRow("Arc less than 180 degree, radius 100") << 100.0 << 0.0 << 160.7;
+    QTest::newRow("Arc less than 180 degree, radius -100") << -100.0 << 0.0 << 160.7;
+    QTest::newRow("Arc less than 180 degree, radius 150") << 150.0 << 0.0 << 160.7;
+    QTest::newRow("Arc less than 180 degree, radius -150") << -150.0 << 0.0 << 160.7;
+    QTest::newRow("Arc less than 180 degree, radius 1500") << 1500.0 << 0.0 << 160.7;
+    QTest::newRow("Arc less than 180 degree, radius -1500") << -1500.0 << 0.0 << 160.7;
+    QTest::newRow("Arc less than 180 degree, radius 50000") << 50000.0 << 0.0 << 160.7;
+    QTest::newRow("Arc less than 180 degree, radius -50000") << -50000.0 << 0.0 << 160.7;
+    QTest::newRow("Arc less than 180 degree, radius 90000") << 90000.0 << 0.0 << 160.7;
+    QTest::newRow("Arc less than 180 degree, radius -90000") << -90000.0 << 0.0 << 160.7;
+
+    QTest::newRow("Arc 180 degree, radius 100") << 100.0 << 0.0 << 180.0;
+    QTest::newRow("Arc 180 degree, radius -100") << -100.0 << 0.0 << 180.0;
+    QTest::newRow("Arc 180 degree, radius 150") << 150.0 << 0.0 << 180.0;
+    QTest::newRow("Arc 180 degree, radius -150") << -150.0 << 0.0 << 180.0;
+    QTest::newRow("Arc 180 degree, radius 1500") << 1500.0 << 0.0 << 180.0;
+    QTest::newRow("Arc 180 degree, radius -1500") << -1500.0 << 0.0 << 180.0;
+    QTest::newRow("Arc 180 degree, radius 50000") << 50000.0 << 0.0 << 180.0;
+    QTest::newRow("Arc 180 degree, radius -50000") << -50000.0 << 0.0 << 180.0;
+    QTest::newRow("Arc 180 degree, radius 90000") << 90000.0 << 0.0 << 180.0;
+    QTest::newRow("Arc 180 degree, radius -90000") << -90000.0 << 0.0 << 180.0;
+
+    QTest::newRow("Arc less than 270 degree, radius 100") << 100.0 << 0.0 << 150.3;
+    QTest::newRow("Arc less than 270 degree, radius -100") << -100.0 << 0.0 << 150.3;
+    QTest::newRow("Arc less than 270 degree, radius 150") << 150.0 << 0.0 << 150.3;
+    QTest::newRow("Arc less than 270 degree, radius -150") << -150.0 << 0.0 << 150.3;
+    QTest::newRow("Arc less than 270 degree, radius 1500") << 1500.0 << 0.0 << 150.3;
+    QTest::newRow("Arc less than 270 degree, radius -1500") << -1500.0 << 0.0 << 150.3;
+    QTest::newRow("Arc less than 270 degree, radius 50000") << 50000.0 << 0.0 << 150.3;
+    QTest::newRow("Arc less than 270 degree, radius -50000") << -50000.0 << 0.0 << 150.3;
+    QTest::newRow("Arc less than 270 degree, radius 90000") << 90000.0 << 0.0 << 150.3;
+    QTest::newRow("Arc less than 270 degree, radius -90000") << -90000.0 << 0.0 << 150.3;
+
+    QTest::newRow("Arc 270 degree, radius 100") << 100.0 << 0.0 << 270.0;
+    QTest::newRow("Arc 270 degree, radius -100") << -100.0 << 0.0 << 270.0;
+    QTest::newRow("Arc 270 degree, radius 150") << 150.0 << 0.0 << 270.0;
+    QTest::newRow("Arc 270 degree, radius -150") << -150.0 << 0.0 << 270.0;
+    QTest::newRow("Arc 270 degree, radius 1500") << 1500.0 << 0.0 << 270.0;
+    QTest::newRow("Arc 270 degree, radius -1500") << -1500.0 << 0.0 << 270.0;
+    QTest::newRow("Arc 270 degree, radius 50000") << 50000.0 << 0.0 << 270.0;
+    QTest::newRow("Arc 270 degree, radius -50000") << -50000.0 << 0.0 << 270.0;
+    QTest::newRow("Arc 270 degree, radius 90000") << 90000.0 << 0.0 << 270.0;
+    QTest::newRow("Arc 270 degree, radius -90000") << -90000.0 << 0.0 << 270.0;
+
+    QTest::newRow("Arc less than 360 degree, radius 100") << 100.0 << 0.0 << 340.0;
+    QTest::newRow("Arc less than 360 degree, radius -100") << -100.0 << 0.0 << 340.0;
+    QTest::newRow("Arc less than 360 degree, radius 150") << 150.0 << 0.0 << 340.0;
+    QTest::newRow("Arc less than 360 degree, radius -150") << -150.0 << 0.0 << 340.0;
+    QTest::newRow("Arc less than 360 degree, radius 1500") << 1500.0 << 0.0 << 340.0;
+    QTest::newRow("Arc less than 360 degree, radius -1500") << -1500.0 << 0.0 << 340.0;
+    QTest::newRow("Arc less than 360 degree, radius 50000") << 50000.0 << 0.0 << 340.0;
+    QTest::newRow("Arc less than 360 degree, radius -50000") << -50000.0 << 0.0 << 340.0;
+    QTest::newRow("Arc less than 360 degree, radius 90000") << 90000.0 << 0.0 << 340.0;
+    QTest::newRow("Arc less than 360 degree, radius -90000") << -90000.0 << 0.0 << 340.0;
+
+    QTest::newRow("Arc start 90 degree, angle 45 degree, radius 100") << 100.0 << 90.0 << 135.0;
+    QTest::newRow("Arc start 90 degree, angle 45 degree, radius -100") << -100.0 << 90.0 << 135.0;
+    QTest::newRow("Arc start 90 degree, angle 45 degree, radius 150") << 150.0 << 90.0 << 135.0;
+    QTest::newRow("Arc start 90 degree, angle 45 degree, radius -150") << -150.0 << 90.0 << 135.0;
+    QTest::newRow("Arc start 90 degree, angle 45 degree, radius 1500") << 1500.0 << 90.0 << 135.0;
+    QTest::newRow("Arc start 90 degree, angle 45 degree, radius -1500") << -1500.0 << 90.0 << 135.0;
+    QTest::newRow("Arc start 90 degree, angle 45 degree, radius 50000") << 50000.0 << 90.0 << 135.0;
+    QTest::newRow("Arc start 90 degree, angle 45 degree, radius -50000") << -50000.0 << 90.0 << 135.0;
+    QTest::newRow("Arc start 90 degree, angle 45 degree, radius 90000") << 90000.0 << 90.0 << 135.0;
+    QTest::newRow("Arc start 90 degree, angle 45 degree, radius -90000") << -90000.0 << 90.0 << 135.0;
+}
+
+//---------------------------------------------------------------------------------------------------------------------
+void TST_VArc::TestCurvature()
+{
+    QFETCH(qreal, radius);
+    QFETCH(qreal, startAngle);
+    QFETCH(qreal, endAngle);
+
+    const qreal tolerance = 0.1;
+    qreal expectedCurvature = 1. / qAbs(radius);
+    qreal scale = VArc::OptimalApproximationScale(radius, startAngle, endAngle, 0.1);
+
+    const VPointF center;
+    VArc arc(center, radius, startAngle, endAngle);
+    arc.SetApproximationScale(scale);
+
+    qreal curvature = VAbstractCurve::Curvature(arc.GetPoints());
+
+    if (scale < 10)
+    {
+        QVERIFY(expectedCurvature - curvature <= expectedCurvature * tolerance);
+
+        QVector<QPointF> p1 = arc.GetPoints();
+        arc.SetApproximationScale(10);
+        QVector<QPointF> p2 = arc.GetPoints();
+        QVERIFY(p1.size() <= p2.size());
+    }
+}

src/test/ValentinaTest/tst_varc.h

@@ -53,6 +53,8 @@ private slots:
     void TestCurveIntersectAxis_data();
     void TestCurveIntersectAxis();
     void EmptyArc();
+    void TestCurvature_data();
+    void TestCurvature();
 };
 
 #endif // TST_VARC_H