Add API to calculate innerTangents for 2 circles

qgis · Jan 13, 2019 · 0ba9a32 · 0ba9a32
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diff --git a/python/core/auto_generated/geometry/qgscircle.sip.in b/python/core/auto_generated/geometry/qgscircle.sip.in
@@ -188,6 +188,31 @@ Note that this method is 2D only and does not consider the z-value of the circle
 .. seealso:: :py:func:`tangentToPoint`
 
 .. versionadded:: 3.2
+%End
+
+    int innerTangents( const QgsCircle &other,
+                       QgsPointXY &line1P1 /Out/, QgsPointXY &line1P2 /Out/,
+                       QgsPointXY &line2P1 /Out/, QgsPointXY &line2P2 /Out/ ) const;
+%Docstring
+Calculates the inner tangent points between this circle
+and an ``other`` circle.
+
+The inner tangent points correspond to the points at which the two lines
+which are drawn so that they are tangential to both circles but on
+different sides, touching the circles and crossing each other.
+
+The first tangent line is described by the points
+stored in ``line1P1`` and ``line1P2``,
+and the second line is described by the points stored in ``line2P1``
+and ``line2P2``.
+
+Returns the number of tangents (either 0 or 2).
+
+Note that this method is 2D only and does not consider the z-value of the circle.
+
+.. seealso:: :py:func:`tangentToPoint`
+
+.. versionadded:: 3.6
 %End
 
     virtual double area() const;

diff --git a/python/core/auto_generated/geometry/qgsgeometryutils.sip.in b/python/core/auto_generated/geometry/qgsgeometryutils.sip.in
@@ -202,6 +202,29 @@ and ``line2P2``.
 Returns the number of tangents (either 0 or 2).
 
 .. versionadded:: 3.2
+%End
+
+    static int circleCircleInnerTangents(
+      const QgsPointXY &center1, double radius1, const QgsPointXY &center2, double radius2,
+      QgsPointXY &line1P1 /Out/, QgsPointXY &line1P2 /Out/,
+      QgsPointXY &line2P1 /Out/, QgsPointXY &line2P2 /Out/ );
+%Docstring
+Calculates the inner tangent points for two circles, centered at \a
+center1 and ``center2`` and with radii of ``radius1`` and ``radius2``
+respectively.
+
+The inner tangent points correspond to the points at which the two lines
+which are drawn so that they are tangential to both circles and are
+crossing each other.
+
+The first tangent line is described by the points
+stored in ``line1P1`` and ``line1P2``,
+and the second line is described by the points stored in ``line2P1``
+and ``line2P2``.
+
+Returns the number of tangents (either 0 or 2).
+
+.. versionadded:: 3.6
 %End
 
     static QgsPoint projectPointOnSegment( const QgsPoint &p, const QgsPoint &s1, const QgsPoint &s2 );

diff --git a/src/core/geometry/qgscircle.cpp b/src/core/geometry/qgscircle.cpp
@@ -270,6 +270,12 @@ int QgsCircle::outerTangents( const QgsCircle &other, QgsPointXY &line1P1, QgsPo
          QgsPointXY( other.center() ), other.radius(), line1P1, line1P2, line2P1, line2P2 );
 }
 
+int QgsCircle::innerTangents( const QgsCircle &other, QgsPointXY &line1P1, QgsPointXY &line1P2, QgsPointXY &line2P1, QgsPointXY &line2P2 ) const
+{
+  return QgsGeometryUtils::circleCircleInnerTangents( QgsPointXY( mCenter ), radius(),
+         QgsPointXY( other.center() ), other.radius(), line1P1, line1P2, line2P1, line2P2 );
+}
+
 QgsCircle QgsCircle::fromExtent( const QgsPoint &pt1, const QgsPoint &pt2 )
 {
   double delta_x = std::fabs( pt1.x() - pt2.x() );

diff --git a/src/core/geometry/qgscircle.h b/src/core/geometry/qgscircle.h
@@ -166,7 +166,7 @@ class CORE_EXPORT QgsCircle : public QgsEllipse
      * \returns true if tangent was found.
      *
      *
-     * \see outerTangents()
+     * \see outerTangents() and innerTangents()
      * \since QGIS 3.2
      */
     bool tangentToPoint( const QgsPointXY &p, QgsPointXY &pt1 SIP_OUT, QgsPointXY &pt2 SIP_OUT ) const;
@@ -189,13 +189,38 @@ class CORE_EXPORT QgsCircle : public QgsEllipse
      * Note that this method is 2D only and does not consider the z-value of the circle.
      *
      *
-     * \see tangentToPoint()
+     * \see tangentToPoint() and innerTangents()
      * \since QGIS 3.2
      */
     int outerTangents( const QgsCircle &other,
                        QgsPointXY &line1P1 SIP_OUT, QgsPointXY &line1P2 SIP_OUT,
                        QgsPointXY &line2P1 SIP_OUT, QgsPointXY &line2P2 SIP_OUT ) const;
 
+    /**
+     * Calculates the inner tangent points between this circle
+     * and an \a other circle.
+     *
+     * The inner tangent points correspond to the points at which the two lines
+     * which are drawn so that they are tangential to both circles but on
+     * different sides, touching the circles and crossing each other.
+     *
+     * The first tangent line is described by the points
+     * stored in \a line1P1 and \a line1P2,
+     * and the second line is described by the points stored in \a line2P1
+     * and \a line2P2.
+     *
+     * Returns the number of tangents (either 0 or 2).
+     *
+     * Note that this method is 2D only and does not consider the z-value of the circle.
+     *
+     *
+     * \see tangentToPoint() and outerTangents()
+     * \since QGIS 3.6
+     */
+    int innerTangents( const QgsCircle &other,
+                       QgsPointXY &line1P1 SIP_OUT, QgsPointXY &line1P2 SIP_OUT,
+                       QgsPointXY &line2P1 SIP_OUT, QgsPointXY &line2P2 SIP_OUT ) const;
+
     double area() const override;
     double perimeter() const override;
 

diff --git a/src/core/geometry/qgsgeometryutils.cpp b/src/core/geometry/qgsgeometryutils.cpp
@@ -489,6 +489,52 @@ int QgsGeometryUtils::circleCircleOuterTangents( const QgsPointXY &center1, doub
   return 2;
 }
 
+// inspired by http://csharphelper.com/blog/2014/12/find-the-tangent-lines-between-two-circles-in-c/
+int QgsGeometryUtils::circleCircleInnerTangents( const QgsPointXY &center1, double radius1, const QgsPointXY &center2, double radius2, QgsPointXY &line1P1, QgsPointXY &line1P2, QgsPointXY &line2P1, QgsPointXY &line2P2 )
+{
+  if ( radius1 > radius2 )
+    return circleCircleInnerTangents( center2, radius2, center1, radius1, line1P1, line1P2, line2P1, line2P2 );
+
+  // determine the straight-line distance between the centers
+  const double d = center1.distance( center2 );
+
+  // check for solvability
+  if ( ( d <= ( radius1 + radius2 ) ) or ( qgsDoubleNear( d, ( radius1 + radius2 ) ) ) )
+  {
+    // no solution. circles intersect or touch.
+    return 0;
+  }
+
+  const double radius1a = radius1 + radius2;
+  if ( !tangentPointAndCircle( center1, radius1a, center2, line1P2, line2P2 ) )
+  {
+    // there are no tangents
+    return 0;
+  }
+
+  // get the vector perpendicular to the
+  // first tangent with length radius2
+  QgsVector v1( ( line1P2.y() - center2.y() ), -( line1P2.x() - center2.x() ) );
+  const double v1Length = v1.length();
+  v1 = v1 * ( radius2 / v1Length );
+
+  // offset the tangent vector's points
+  line1P1 = center2 + v1;
+  line1P2 = line1P2 + v1;
+
+  // get the vector perpendicular to the
+  // second tangent with length radius2
+  QgsVector v2( -( line2P2.y() - center2.y() ), line2P2.x() - center2.x() );
+  const double v2Length = v2.length();
+  v2 = v2 * ( radius2 / v2Length );
+
+  // offset the tangent vector's points in opposite direction
+  line2P1 = center2 + v2;
+  line2P2 = line2P2 + v2;
+
+  return 2;
+}
+
 QVector<QgsGeometryUtils::SelfIntersection> QgsGeometryUtils::selfIntersections( const QgsAbstractGeometry *geom, int part, int ring, double tolerance )
 {
   QVector<SelfIntersection> intersections;

diff --git a/src/core/geometry/qgsgeometryutils.h b/src/core/geometry/qgsgeometryutils.h
@@ -202,6 +202,29 @@ class CORE_EXPORT QgsGeometryUtils
       QgsPointXY &line1P1 SIP_OUT, QgsPointXY &line1P2 SIP_OUT,
       QgsPointXY &line2P1 SIP_OUT, QgsPointXY &line2P2 SIP_OUT );
 
+    /**
+     * Calculates the inner tangent points for two circles, centered at \a
+     * center1 and \a center2 and with radii of \a radius1 and \a radius2
+     * respectively.
+     *
+     * The inner tangent points correspond to the points at which the two lines
+     * which are drawn so that they are tangential to both circles and are
+     * crossing each other.
+     *
+     * The first tangent line is described by the points
+     * stored in \a line1P1 and \a line1P2,
+     * and the second line is described by the points stored in \a line2P1
+     * and \a line2P2.
+     *
+     * Returns the number of tangents (either 0 or 2).
+     *
+     * \since QGIS 3.6
+     */
+    static int circleCircleInnerTangents(
+      const QgsPointXY &center1, double radius1, const QgsPointXY &center2, double radius2,
+      QgsPointXY &line1P1 SIP_OUT, QgsPointXY &line1P2 SIP_OUT,
+      QgsPointXY &line2P1 SIP_OUT, QgsPointXY &line2P2 SIP_OUT );
+
     /**
      * \brief Project the point on a segment
      * \param p The point

diff --git a/tests/src/core/testqgsgeometry.cpp b/tests/src/core/testqgsgeometry.cpp
@@ -7812,7 +7812,7 @@ void TestQgsGeometry::circle()
   QGSCOMPARENEAR( t2.x(), 2.2, 0.01 );
   QGSCOMPARENEAR( t2.y(), 5.82, 0.01 );
 
-  // two circle tangents
+  // two outer circle tangents
   QgsPointXY l1p1, l1p2, l2p1, l2p2;
   QCOMPARE( QgsCircle( QgsPoint( 1, 2 ), 4 ).outerTangents( QgsCircle( QgsPoint( 2, 3 ), 1 ), l1p1, l1p2, l2p1, l2p2 ), 0 );
   QCOMPARE( QgsCircle( QgsPoint( 1, 2 ), 1 ).outerTangents( QgsCircle( QgsPoint( 10, 3 ), 4 ), l1p1, l1p2, l2p1, l2p2 ), 2 );
@@ -7824,6 +7824,20 @@ void TestQgsGeometry::circle()
   QGSCOMPARENEAR( l2p1.y(), 1.025, 0.01 );
   QGSCOMPARENEAR( l2p2.x(), 9.099, 0.01 );
   QGSCOMPARENEAR( l2p2.y(), -0.897, 0.01 );
+
+  // two inner circle tangents
+  QCOMPARE( QgsCircle( QgsPoint( 1, 2 ), 4 ).innerTangents( QgsCircle( QgsPoint( 2, 3 ), 1 ), l1p1, l1p2, l2p1, l2p2 ), 0 );
+  QCOMPARE( QgsCircle( QgsPoint( 0, 0 ), 4 ).innerTangents( QgsCircle( QgsPoint( 8, 0 ), 5 ), l1p1, l1p2, l2p1, l2p2 ), 0 );
+  QCOMPARE( QgsCircle( QgsPoint( 0, 0 ), 4 ).innerTangents( QgsCircle( QgsPoint( 8, 0 ), 4 ), l1p1, l1p2, l2p1, l2p2 ), 0 );
+  QCOMPARE( QgsCircle( QgsPoint( 1, 2 ), 1 ).innerTangents( QgsCircle( QgsPoint( 10, 3 ), 4 ), l1p1, l1p2, l2p1, l2p2 ), 2 );
+  QGSCOMPARENEAR( l1p1.x(), 7.437, 0.01 );
+  QGSCOMPARENEAR( l1p1.y(), 6.071, 0.01 );
+  QGSCOMPARENEAR( l1p2.x(), 1.641, 0.01 );
+  QGSCOMPARENEAR( l1p2.y(), 1.232, 0.01 );
+  QGSCOMPARENEAR( l2p1.x(), 8.173, 0.01 );
+  QGSCOMPARENEAR( l2p1.y(), -0.558, 0.01 );
+  QGSCOMPARENEAR( l2p2.x(), 1.457, 0.01 );
+  QGSCOMPARENEAR( l2p2.y(), 2.89, 0.01 );
 }
 
 void TestQgsGeometry::regularPolygon()

diff --git a/tests/src/core/testqgsgeometryutils.cpp b/tests/src/core/testqgsgeometryutils.cpp
@@ -64,6 +64,7 @@ class TestQgsGeometryUtils: public QObject
     void testCircleCircleIntersection();
     void testTangentPointAndCircle();
     void testCircleCircleOuterTangents();
+    void testCircleCircleInnerTangents();
     void testGml();
     void testInterpolatePointOnLineQgsPoint();
     void testInterpolatePointOnLine();
@@ -970,6 +971,45 @@ void TestQgsGeometryUtils::testCircleCircleOuterTangents()
   QGSCOMPARENEAR( l2p2.y(), -0.897, 0.01 );
 }
 
+void TestQgsGeometryUtils::testCircleCircleInnerTangents()
+{
+  QgsPointXY l1p1;
+  QgsPointXY l1p2;
+  QgsPointXY l2p1;
+  QgsPointXY l2p2;
+
+  // no tangents, intersecting circles
+  QCOMPARE( QgsGeometryUtils::circleCircleInnerTangents( QgsPointXY( 1, 2 ), 4, QgsPointXY( 2, 3 ), 1, l1p1, l1p2, l2p1, l2p2 ), 0 );
+
+  // no tangents, same circles
+  QCOMPARE( QgsGeometryUtils::circleCircleInnerTangents( QgsPointXY( 1, 2 ), 4, QgsPointXY( 1, 2 ), 4, l1p1, l1p2, l2p1, l2p2 ), 0 );
+
+  // no tangents, touching circles
+  QCOMPARE( QgsGeometryUtils::circleCircleInnerTangents( QgsPointXY( 0, 0 ), 4, QgsPointXY( 0, 8 ), 4, l1p1, l1p2, l2p1, l2p2 ), 0 );
+
+  // tangents
+  QCOMPARE( QgsGeometryUtils::circleCircleInnerTangents( QgsPointXY( 1, 2 ), 1, QgsPointXY( 10, 3 ), 4, l1p1, l1p2, l2p1, l2p2 ), 2 );
+  QGSCOMPARENEAR( l1p1.x(), 7.437, 0.01 );
+  QGSCOMPARENEAR( l1p1.y(), 6.071, 0.01 );
+  QGSCOMPARENEAR( l1p2.x(), 1.641, 0.01 );
+  QGSCOMPARENEAR( l1p2.y(), 1.232, 0.01 );
+  QGSCOMPARENEAR( l2p1.x(), 8.173, 0.01 );
+  QGSCOMPARENEAR( l2p1.y(), -0.558, 0.01 );
+  QGSCOMPARENEAR( l2p2.x(), 1.457, 0.01 );
+  QGSCOMPARENEAR( l2p2.y(), 2.89, 0.01 );
+
+  // tangents, larger circle first
+  QCOMPARE( QgsGeometryUtils::circleCircleInnerTangents( QgsPointXY( 10, 3 ), 4, QgsPointXY( 1, 2 ), 1, l1p1, l1p2, l2p1, l2p2 ), 2 );
+  QGSCOMPARENEAR( l1p1.x(), 7.437, 0.01 );
+  QGSCOMPARENEAR( l1p1.y(), 6.071, 0.01 );
+  QGSCOMPARENEAR( l1p2.x(), 1.641, 0.01 );
+  QGSCOMPARENEAR( l1p2.y(), 1.232, 0.01 );
+  QGSCOMPARENEAR( l2p1.x(), 8.173, 0.01 );
+  QGSCOMPARENEAR( l2p1.y(), -0.558, 0.01 );
+  QGSCOMPARENEAR( l2p2.x(), 1.457, 0.01 );
+  QGSCOMPARENEAR( l2p2.y(), 2.89, 0.01 );
+}
+
 void TestQgsGeometryUtils::testGml()
 {
   QgsPoint point = QgsPoint( 1, 2 );