Added second adaptive subdivision method (this time with an angle differences as the stopping criterion

4 files changed, 513 insertions, 80 deletions

diff --git a/basegfx/inc/basegfx/curve/b2dbeziertools.hxx b/basegfx/inc/basegfx/curve/b2dbeziertools.hxx
index 23231bd9a763..f9d72cb47873 100644
--- a/basegfx/inc/basegfx/curve/b2dbeziertools.hxx
+++ b/basegfx/inc/basegfx/curve/b2dbeziertools.hxx
@@ -2,9 +2,9 @@
  *
  *  $RCSfile: b2dbeziertools.hxx,v $
  *
- *  $Revision: 1.1 $
+ *  $Revision: 1.2 $
  *
- *  last change: $Author: thb $ $Date: 2003-11-10 13:33:07 $
+ *  last change: $Author: thb $ $Date: 2003-11-12 12:09:50 $
  *
  *  The Contents of this file are made available subject to the terms of
  *  either of the following licenses
@@ -62,6 +62,11 @@
 #ifndef _BGFX_CURVE_B2DBEZIERTOOLS_HXX
 #define _BGFX_CURVE_B2DBEZIERTOOLS_HXX
 
+#ifndef _SAL_TYPES_H_
+#include <sal/types.h>
+#endif
+
+
 //////////////////////////////////////////////////////////////////////////////
 
 namespace basegfx
@@ -80,9 +85,10 @@ namespace basegfx
         /** Subdivide given cubic bezier segment.
 
             This function adaptively subdivides the given bezier
-            segment into as much straight line segments, such that the
-            maximal orthogonal distance from any of the segments to
-            the true curve is less than the given error value.
+            segment into as much straight line segments as necessary,
+            such that the maximal orthogonal distance from any of the
+            segments to the true curve is less than the given error
+            value.
 
             @param rPoly
             Output polygon. The subdivided bezier segment is added to
@@ -91,22 +97,100 @@ namespace basegfx
             @param rCurve
             The cubic bezier curve to subdivide
 
-            @param distanceBounds
-            Bounds on the maximal distance of the approximation to the
-            true curve
+            @param distanceBound
+            Bound on the maximal distance of the approximation to the
+            true curve.
 
             @return the number of line segments created
          */
-        int adaptiveSubdivide( polygon::B2DPolygon&     rPoly,
-                               const B2DCubicBezier&    rCurve,
-                               double                   distanceBounds );
+        sal_Int32 adaptiveSubdivideByDistance( polygon::B2DPolygon&     rPoly,
+                                               const B2DCubicBezier&    rCurve,
+                                               double                   distanceBound );
+
+        /** Subdivide given cubic bezier segment.
+
+            This function adaptively subdivides the given bezier
+            segment into as much quadratic bezier curve segments as
+            necessary, such that the maximal orthogonal distance from
+            any of the segments to the true curve is less than the
+            given error value.
+
+            @param rPoly
+            Output polygon. The subdivided bezier segments are added to
+            this polygon via B2DPolygon::append().
+
+            @param rCurve
+            The cubic bezier curve to subdivide
+
+            @param distanceBound
+            Bound on the maximal distance of the approximation to the
+            true curve.
+
+            @return the number of quadratic curve segments created
+         */
+        sal_Int32 adaptiveDegreeReductionByDistance( polygon::B2DPolygon&       rPoly,
+                                                     const B2DCubicBezier&  rCurve,
+                                                     double                 distanceBound );
+
+
+        /** Subdivide given cubic bezier segment.
+
+            This function adaptively subdivides the given bezier
+            segment into as much straight line segments as necessary,
+            such that the maximal angle change between any adjacent
+            lines is less than the given error value.
+
+            @param rPoly
+            Output polygon. The subdivided bezier segment is added to
+            this polygon via B2DPolygon::append().
+
+            @param rCurve
+            The cubic bezier curve to subdivide
+
+            @param angleBound
+            Bound on the maximal angle difference between two adjacent
+            polygon lines, in degrees.
+
+            @return the number of line segments created
+         */
+        sal_Int32 adaptiveSubdivideByAngle( polygon::B2DPolygon&    rPoly,
+                                            const B2DCubicBezier&   rCurve,
+                                            double                  angleBound );
+
+        /** Subdivide given cubic bezier segment.
+
+            This function adaptively subdivides the given bezier
+            segment into as much quadratic bezier curve segments as
+            necessary, such that the maximal angle difference of the
+            control vectors of any generated quadratic bezier segment
+            is less than the given error value.
+
+            @param rPoly
+            Output polygon. The subdivided bezier segments are added to
+            this polygon via B2DPolygon::append().
+
+            @param rCurve
+            The cubic bezier curve to subdivide
+
+            @param distanceBound
+            Bound on the maximal angle difference between the control
+            vectors of any of the generated quadratic bezier
+            segments. The angle must be given in degrees.
+
+            @return the number of quadratic curve segments created
+         */
+        sal_Int32 adaptiveDegreeReductionByAngle( polygon::B2DPolygon&  rPoly,
+                                                  const B2DCubicBezier& rCurve,
+                                                  double                angleBound );
+
 
         /** Subdivide given quadratic bezier segment.
 
             This function adaptively subdivides the given bezier
-            segment into as much straight line segments, such that the
-            maximal orthogonal distance from any of the segments to
-            the true curve is less than the given error value.
+            segment into as much straight line segments as necessary,
+            such that the maximal orthogonal distance from any of the
+            segments to the true curve is less than the given error
+            value.
 
             @param rPoly
             Output polygon. The subdivided bezier segment is added to
@@ -115,15 +199,39 @@ namespace basegfx
             @param rCurve
             The cubic bezier curve to subdivide
 
-            @param distanceBounds
-            Bounds on the maximal distance of the approximation to the
+            @param distanceBound
+            Bound on the maximal distance of the approximation to the
             true curve
 
             @return the number of line segments created
          */
-        int adaptiveSubdivide( polygon::B2DPolygon&         rPoly,
-                               const B2DQuadraticBezier&    rCurve,
-                               double                       distanceBounds );
+        sal_Int32 adaptiveSubdivideByDistance( polygon::B2DPolygon&         rPoly,
+                                               const B2DQuadraticBezier&    rCurve,
+                                               double                       distanceBound );
+
+        /** Subdivide given quadratic bezier segment.
+
+            This function adaptively subdivides the given bezier
+            segment into as much straight line segments as necessary,
+            such that the maximal angle change between any adjacent
+            lines is less than the given error value.
+
+            @param rPoly
+            Output polygon. The subdivided bezier segment is added to
+            this polygon via B2DPolygon::append().
+
+            @param rCurve
+            The cubic bezier curve to subdivide
+
+            @param angleBound
+            Bound on the maximal angle difference between two adjacent
+            polygon lines, in degrees.
+
+            @return the number of line segments created
+         */
+        sal_Int32 adaptiveSubdivideByAngle( polygon::B2DPolygon&        rPoly,
+                                            const B2DQuadraticBezier&   rCurve,
+                                            double                      angleBound );
 
     }
 }
diff --git a/basegfx/inc/basegfx/vector/b2dvector.hxx b/basegfx/inc/basegfx/vector/b2dvector.hxx
index 0735d52cd7e0..0a3a896733a0 100644
--- a/basegfx/inc/basegfx/vector/b2dvector.hxx
+++ b/basegfx/inc/basegfx/vector/b2dvector.hxx
@@ -2,9 +2,9 @@
  *
  *  $RCSfile: b2dvector.hxx,v $
  *
- *  $Revision: 1.5 $
+ *  $Revision: 1.6 $
  *
- *  last change: $Author: aw $ $Date: 2003-11-11 09:56:09 $
+ *  last change: $Author: thb $ $Date: 2003-11-12 12:09:51 $
  *
  *  The Contents of this file are made available subject to the terms of
  *  either of the following licenses
@@ -200,6 +200,23 @@ namespace basegfx
             */
             double scalar( const B2DVector& rVec ) const;
 
+            /** Calculate the length of the cross product with another 2D Vector
+
+                In 2D, returning an actual vector does not make much
+                sense here. The magnitude, although, can be readily
+                used for tasks such as angle calculations, since for
+                the returned value, the following equation holds:
+                retVal = getLength(this)*getLength(rVec)*sin(theta),
+                with theta being the angle between the two vectors.
+
+                @param rVec
+                The second 2D Vector
+
+                @return
+                The length of the cross product of the two involved 2D Vectors
+            */
+            double cross( const B2DVector& rVec ) const;
+
             /** Calculate the Angle with another 2D Vector
 
                 @param rVec
diff --git a/basegfx/source/curve/b2dbeziertools.cxx b/basegfx/source/curve/b2dbeziertools.cxx
index eadbd52a56ba..0e6e24a071da 100644
--- a/basegfx/source/curve/b2dbeziertools.cxx
+++ b/basegfx/source/curve/b2dbeziertools.cxx
@@ -2,9 +2,9 @@
  *
  *  $RCSfile: b2dbeziertools.cxx,v $
  *
- *  $Revision: 1.1 $
+ *  $Revision: 1.2 $
  *
- *  last change: $Author: thb $ $Date: 2003-11-10 13:32:04 $
+ *  last change: $Author: thb $ $Date: 2003-11-12 12:09:52 $
  *
  *  The Contents of this file are made available subject to the terms of
  *  either of the following licenses
@@ -76,10 +76,18 @@
 #include <basegfx/polygon/b2dpolygon.hxx>
 #endif
 
+#ifndef _BGFX_VECTOR_B2DVECTOR_HXX
+#include <basegfx/vector/b2dvector.hxx>
+#endif
+
 #ifndef _BGFX_POINT_B2DPOINT_HXX
 #include <basegfx/point/b2dpoint.hxx>
 #endif
 
+#ifndef _BGFX_NUMERIC_FTOOLS_HXX
+#include <basegfx/numeric/ftools.hxx>
+#endif
+
 
 namespace basegfx
 {
@@ -87,6 +95,150 @@ namespace basegfx
     {
         namespace
         {
+            class DistanceErrorFunctor
+            {
+            public:
+                DistanceErrorFunctor( const double& distance ) :
+                    mfDistance2( distance*distance ),
+                    mfLastDistanceError2( ::std::numeric_limits<double>::max() )
+                {
+                }
+
+                bool subdivideFurther( const double& P1x, const double& P1y,
+                                       const double& P2x, const double& P2y,
+                                       const double& P3x, const double& P3y,
+                                       const double& P4x, const double& P4y,
+                                       const double&, const double& ) // last two values not used here
+                {
+                    // Perform bezier flatness test (lecture notes from R. Schaback,
+                    // Mathematics of Computer-Aided Design, Uni Goettingen, 2000)
+                    //
+                    // ||P(t) - L(t)|| <= max     ||b_j - b_0 - j/n(b_n - b_0)||
+                    //                    0<=j<=n
+                    //
+                    // What is calculated here is an upper bound to the distance from
+                    // a line through b_0 and b_3 (P1 and P4 in our notation) and the
+                    // curve. We can drop 0 and n from the running indices, since the
+                    // argument of max becomes zero for those cases.
+                    const double fJ1x( P2x - P1x - 1.0/3.0*(P4x - P1x) );
+                    const double fJ1y( P2y - P1y - 1.0/3.0*(P4y - P1y) );
+                    const double fJ2x( P3x - P1x - 2.0/3.0*(P4x - P1x) );
+                    const double fJ2y( P3y - P1y - 2.0/3.0*(P4y - P1y) );
+                    const double distanceError2( ::std::max( fJ1x*fJ1x + fJ1y*fJ1y,
+                                                             fJ2x*fJ2x + fJ2y*fJ2y) );
+
+                    // stop if error measure does not improve anymore. This is a
+                    // safety guard against floating point inaccuracies.
+                    // stop if distance from line is guaranteed to be bounded by d
+                    bool bRet( mfLastDistanceError2 > distanceError2 &&
+                               distanceError2 >= mfDistance2 );
+
+                    mfLastDistanceError2 = distanceError2;
+
+                    return bRet;
+                }
+
+            private:
+                double mfDistance2;
+                double mfLastDistanceError2;
+            };
+
+
+            class AngleErrorFunctor
+            {
+            public:
+                AngleErrorFunctor( const double& angleBounds ) :
+                    mfTanAngle( tan( angleBounds ) ),
+                    mfLastTanAngle( ::std::numeric_limits<double>::max() )
+                {
+                }
+
+                bool subdivideFurther( const double P1x, const double P1y,
+                                       const double P2x, const double P2y,
+                                       const double P3x, const double P3y,
+                                       const double P4x, const double P4y,
+                                       const double Pdx, const double Pdy )
+                {
+                    // Test angle differences between two lines (ad
+                    // and bd), meeting in the t=0.5 division point
+                    // (d), and the angle from the other ends of those
+                    // lines (b and a, resp.) to the tangents to the
+                    // curve at this points:
+                    //
+                    //        *__________
+                    //             ......*b
+                    //          ...
+                    //        ..
+                    //       .
+                    // *    *d
+                    // |   .
+                    // |  .
+                    // | .
+                    // | .
+                    // |.
+                    // |.
+                    // *
+                    // a
+                    //
+                    // When using half of the angle bound for the
+                    // difference to the tangents at a or b, resp.,
+                    // this procedure guarantees that no angle in the
+                    // resulting line polygon is larger than the
+                    // specified angle bound. This is because during
+                    // subdivision, adjacent curve segments will have
+                    // collinear tangent vectors, thus, when each
+                    // side's line segments differs by at most angle/2
+                    // from that tangent, the summed difference will
+                    // be at most angle (this was modeled after an
+                    // idea from Armin Weiss).
+
+                    // To stay within the notation above, a equals P1,
+                    // the other end point of the tangent starting at
+                    // a is P2, d is Pd, and so forth. The
+                    const vector::B2DVector vecAD( Pdx - P1x, Pdy - P1y );
+                    const vector::B2DVector vecDB( P4x - Pdx, P4y - Pdy );
+
+                    const double scalarVecADDB( vecAD.scalar( vecDB ) );
+                    const double crossVecADDB( vecAD.cross( vecDB ) );
+
+                    const vector::B2DVector vecStartTangent( P2x - P1x, P2y - P1y );
+                    const vector::B2DVector vecEndTangent( P4x - P3x, P4y - P3y );
+
+                    const double scalarVecStartTangentAD( vecStartTangent.scalar( vecAD ) );
+                    const double crossVecStartTangentAD( vecStartTangent.cross( vecAD ) );
+
+                    const double scalarVecDBEndTangent( vecDB.scalar( vecEndTangent ) );
+                    const double crossVecDBEndTangent( vecDB.cross( vecEndTangent ) );
+
+
+                    double fCurrAngle( ::std::numeric_limits<double>::max() );
+
+                    if( !numeric::fTools::equalZero( scalarVecADDB ) )
+                        fCurrAngle = fabs( crossVecADDB / scalarVecADDB );
+
+                    if( !numeric::fTools::equalZero( scalarVecStartTangentAD ) )
+                        fCurrAngle = ::std::min( fCurrAngle, fabs( crossVecStartTangentAD / scalarVecStartTangentAD ) );
+
+                    if( !numeric::fTools::equalZero( scalarVecDBEndTangent ) )
+                        fCurrAngle = ::std::min( fCurrAngle, fabs( crossVecDBEndTangent / scalarVecDBEndTangent ) );
+
+                    // stop if error measure does not improve anymore. This is a
+                    // safety guard against floating point inaccuracies.
+                    // stop if angle difference is guaranteed to be bounded by mfTanAngle
+                    bool bRet( mfLastTanAngle > fCurrAngle &&
+                               fCurrAngle >= mfTanAngle );
+
+                    mfLastTanAngle = fCurrAngle;
+
+                    return bRet;
+                }
+
+            private:
+                double mfTanAngle;
+                double mfLastTanAngle;
+            };
+
+
             /* Recursively subdivide cubic bezier curve via deCasteljau.
 
                @param rPoly
@@ -108,63 +260,52 @@ namespace basegfx
                Depth of recursion. Used as a termination criterion, to
                prevent endless looping.
             */
-            int ImplAdaptiveSubdivide( polygon::B2DPolygon&           rPoly,
-                                       const double                   d2,
-                                       const double P1x, const double P1y,
-                                       const double P2x, const double P2y,
-                                       const double P3x, const double P3y,
-                                       const double P4x, const double P4y,
-                                       const double                   old_distance2,
-                                       int                            recursionDepth )
+            template < class ErrorFunctor > int ImplAdaptiveSubdivide( polygon::B2DPolygon&           rPoly,
+                                                                       const ErrorFunctor&            rErrorFunctor,
+                                                                       const double P1x, const double P1y,
+                                                                       const double P2x, const double P2y,
+                                                                       const double P3x, const double P3y,
+                                                                       const double P4x, const double P4y,
+                                                                       int                            recursionDepth )
             {
                 // Hard limit on recursion depth, empiric number.
                 enum {maxRecursionDepth=128};
 
-                // Perform bezier flatness test (lecture notes from R. Schaback,
-                // Mathematics of Computer-Aided Design, Uni Goettingen, 2000)
-                //
-                // ||P(t) - L(t)|| <= max     ||b_j - b_0 - j/n(b_n - b_0)||
-                //                    0<=j<=n
-                //
-                // What is calculated here is an upper bound to the distance from
-                // a line through b_0 and b_3 (P1 and P4 in our notation) and the
-                // curve. We can drop 0 and n from the running indices, since the
-                // argument of max becomes zero for those cases.
-                const double fJ1x( P2x - P1x - 1.0/3.0*(P4x - P1x) );
-                const double fJ1y( P2y - P1y - 1.0/3.0*(P4y - P1y) );
-                const double fJ2x( P3x - P1x - 2.0/3.0*(P4x - P1x) );
-                const double fJ2y( P3y - P1y - 2.0/3.0*(P4y - P1y) );
-                const double distance2( ::std::max( fJ1x*fJ1x + fJ1y*fJ1y,
-                                                    fJ2x*fJ2x + fJ2y*fJ2y) );
-
-                // stop if error measure does not improve anymore. This is a
-                // safety guard against floating point inaccuracies.
+                // deCasteljau bezier arc, split at t=0.5
+                // Foley/vanDam, p. 508
+
+                // Note that for the pure distance error method, this
+                // subdivision could be moved into the if-branch. But
+                // since this accounts for saved work only for the
+                // very last subdivision step, and we need the
+                // subdivided curve for the angle criterium, I think
+                // it's justified here.
+                const double L1x( P1x ),             L1y( P1y );
+                const double L2x( (P1x + P2x)*0.5 ), L2y( (P1y + P2y)*0.5 );
+                const double Hx ( (P2x + P3x)*0.5 ), Hy ( (P2y + P3y)*0.5 );
+                const double L3x( (L2x + Hx)*0.5 ),  L3y( (L2y + Hy)*0.5 );
+                const double R4x( P4x ),             R4y( P4y );
+                const double R3x( (P3x + P4x)*0.5 ), R3y( (P3y + P4y)*0.5 );
+                const double R2x( (Hx + R3x)*0.5 ),  R2y( (Hy + R3y)*0.5 );
+                const double R1x( (L3x + R2x)*0.5 ), R1y( (L3y + R2y)*0.5 );
+                const double L4x( R1x ),             L4y( R1y );
+
                 // stop at recursion level 128. This is a safety guard against
                 // floating point inaccuracies.
-                // stop if distance from line is guaranteed to be bounded by d
-                if( old_distance2 > d2 &&
-                    recursionDepth < maxRecursionDepth &&
-                    distance2 >= d2 )
+                if( recursionDepth < maxRecursionDepth &&
+                    rErrorFunctor.subdivideFurther( P1x, P1y,
+                                                    P2x, P2y,
+                                                    P3x, P3y,
+                                                    P4x, P4y,
+                                                    R1x, R1y ) )
                 {
-                    // deCasteljau bezier arc, split at t=0.5
-                    // Foley/vanDam, p. 508
-                    const double L1x( P1x ),             L1y( P1y );
-                    const double L2x( (P1x + P2x)*0.5 ), L2y( (P1y + P2y)*0.5 );
-                    const double Hx ( (P2x + P3x)*0.5 ), Hy ( (P2y + P3y)*0.5 );
-                    const double L3x( (L2x + Hx)*0.5 ),  L3y( (L2y + Hy)*0.5 );
-                    const double R4x( P4x ),             R4y( P4y );
-                    const double R3x( (P3x + P4x)*0.5 ), R3y( (P3y + P4y)*0.5 );
-                    const double R2x( (Hx + R3x)*0.5 ),  R2y( (Hy + R3y)*0.5 );
-                    const double R1x( (L3x + R2x)*0.5 ), R1y( (L3y + R2y)*0.5 );
-                    const double L4x( R1x ),             L4y( R1y );
-
                     // subdivide further
                     ++recursionDepth;
 
                     int nGeneratedPoints(0);
 
-                    nGeneratedPoints += ImplAdaptiveSubdivide(rPoly, d2, L1x, L1y, L2x, L2y, L3x, L3y, L4x, L4y, distance2, recursionDepth);
-                    nGeneratedPoints += ImplAdaptiveSubdivide(rPoly, d2, R1x, R1y, R2x, R2y, R3x, R3y, R4x, R4y, distance2, recursionDepth);
+                    nGeneratedPoints += ImplAdaptiveSubdivide(rPoly, rErrorFunctor, L1x, L1y, L2x, L2y, L3x, L3y, L4x, L4y, recursionDepth);
+                    nGeneratedPoints += ImplAdaptiveSubdivide(rPoly, rErrorFunctor, R1x, R1y, R2x, R2y, R3x, R3y, R4x, R4y, recursionDepth);
 
                     // return number of points generated in this
                     // recursion branch
@@ -182,31 +323,198 @@ namespace basegfx
                     return 1;
                 }
             }
+
+// LATER
+#if 0
+            /* Approximate given cubic bezier curve by quadratic bezier segments */
+            void ImplQuadBezierApprox( polygon::B2DPolygon&           rPoly,
+                                       BitStream& rBits,
+                                       Point& rLastPoint,
+                                       const double d2,
+                                       const double P1x, const double P1y,
+                                       const double P2x, const double P2y,
+                                       const double P3x, const double P3y,
+                                       const double P4x, const double P4y )
+            {
+                // Check for degenerate case, where the given cubic bezier curve
+                // is already quadratic: P4 == 3P3 - 3P2 + P1
+                if( P4x == 3.0*P3x - 3.0*P2x + P1x &&
+                    P4y == 3.0*P3y - 3.0*P2y + P1y )
+                {
+                    Impl_addQuadBezier( rBits, rLastPoint,
+                                        3.0/2.0*P2x - 1.0/2.0*P1x, 3.0/2.0*P2y - 1.0/2.0*P1y,
+                                        P4x, P4y);
+                }
+                else
+                {
+                    // Create quadratic segment for given cubic:
+                    // Start and end point must coincide, determine quadratic control
+                    // point in such a way that it lies on the intersection of the
+                    // tangents at start and end point, resp. Thus, both cubic and
+                    // quadratic curve segments will match in 0th and 1st derivative
+                    // at the start and end points
+
+                    // Intersection of P2P1 and P4P3
+                    //           (P2y-P4y)(P3x-P4x)-(P2x-P4x)(P3y-P4y)
+                    //  lambda = -------------------------------------
+                    //           (P1x-P2x)(P3y-P4y)-(P1y-P2y)(P3x-P4x)
+                    //
+                    // Intersection point IP is now
+                    // IP = P2 + lambda(P1-P2)
+                    //
+                    const double nominator( (P2y-P4y)*(P3x-P4x) - (P2x-P4x)*(P3y-P4y) );
+                    const double denominator( (P1x-P2x)*(P3y-P4y) - (P1y-P2y)*(P3x-P4x) );
+                    const double lambda( nominator / denominator );
+
+                    const double IPx( P2x + lambda*( P1x - P2x) );
+                    const double IPy( P2y + lambda*( P1y - P2y) );
+
+                    // Introduce some alias names: quadratic start point is P1, end
+                    // point is P4, control point is IP
+                    const double QP1x( P1x );
+                    const double QP1y( P1y );
+                    const double QP2x( IPx );
+                    const double QP2y( IPy );
+                    const double QP3x( P4x );
+                    const double QP3y( P4y );
+
+                    // Adapted bezier flatness test (lecture notes from R. Schaback,
+                    // Mathematics of Computer-Aided Design, Uni Goettingen, 2000)
+                    //
+                    // ||C(t) - Q(t)|| <= max     ||c_j - q_j||
+                    //                    0<=j<=n
+                    //
+                    // In this case, we don't need the distance from the cubic bezier
+                    // to a straight line, but to a quadratic bezier. The c_j's are
+                    // the cubic bezier's bernstein coefficients, the q_j's the
+                    // quadratic bezier's. We have the c_j's given, the q_j's can be
+                    // calculated from QPi like this (sorry, mixed index notation, we
+                    // use [1,n], formulas use [0,n-1]):
+                    //
+                    // q_0 = QP1 = P1
+                    // q_1 = 1/3 QP1 + 2/3 QP2
+                    // q_2 = 2/3 QP2 + 1/3 QP3
+                    // q_3 = QP3 = P4
+                    //
+                    // We can drop case 0 and 3, since there the curves coincide
+                    // (distance is zero)
+
+                    // calculate argument of max for j=1 and j=2
+                    const double fJ1x( P2x - 1.0/3.0*QP1x - 2.0/3.0*QP2x );
+                    const double fJ1y( P2y - 1.0/3.0*QP1y - 2.0/3.0*QP2y );
+                    const double fJ2x( P3x - 2.0/3.0*QP2x - 1.0/3.0*QP3x );
+                    const double fJ2y( P3y - 2.0/3.0*QP2y - 1.0/3.0*QP3y );
+
+                    // stop if distance from cubic curve is guaranteed to be bounded by d
+                    // Should denominator be 0: then P1P2 and P3P4 are parallel (P1P2^T R[90,P3P4] = 0.0),
+                    // meaning that either we have a straight line or an inflexion point (see else block below)
+                    if( 0.0 != denominator &&
+                        ::std::max( fJ1x*fJ1x + fJ1y*fJ1y,
+                                    fJ2x*fJ2x + fJ2y*fJ2y) < d2 )
+                    {
+                        // requested resolution reached.
+                        // Add end points to output file.
+                        // order is preserved, since this is so to say depth first traversal.
+                        Impl_addQuadBezier( rBits, rLastPoint,
+                                            QP2x, QP2y,
+                                            QP3x, QP3y);
+                    }
+                    else
+                    {
+                        // Maybe subdivide further
+
+                        // This is for robustness reasons, since the line intersection
+                        // method below gets instable if the curve gets closer to a
+                        // straight line. If the given cubic bezier does not deviate by
+                        // more than d/4 from a straight line, either:
+                        //  - take the line (that's what we do here)
+                        //  - express the line by a quadratic bezier
+
+                        // Perform bezier flatness test (lecture notes from R. Schaback,
+                        // Mathematics of Computer-Aided Design, Uni Goettingen, 2000)
+                        //
+                        // ||P(t) - L(t)|| <= max     ||b_j - b_0 - j/n(b_n - b_0)||
+                        //                    0<=j<=n
+                        //
+                        // What is calculated here is an upper bound to the distance from
+                        // a line through b_0 and b_3 (P1 and P4 in our notation) and the
+                        // curve. We can drop 0 and n from the running indices, since the
+                        // argument of max becomes zero for those cases.
+                        const double fJ1x( P2x - P1x - 1.0/3.0*(P4x - P1x) );
+                        const double fJ1y( P2y - P1y - 1.0/3.0*(P4y - P1y) );
+                        const double fJ2x( P3x - P1x - 2.0/3.0*(P4x - P1x) );
+                        const double fJ2y( P3y - P1y - 2.0/3.0*(P4y - P1y) );
+
+                        // stop if distance from line is guaranteed to be bounded by d/4
+                        if( ::std::max( fJ1x*fJ1x + fJ1y*fJ1y,
+                                        fJ2x*fJ2x + fJ2y*fJ2y) < d2/16.0 )
+                        {
+                            // do not subdivide further, add straight line instead
+                            Impl_addStraightLine( rBits, rLastPoint, P4x, P4y);
+                        }
+                        else
+                        {
+                            // deCasteljau bezier arc, split at t=0.5
+                            // Foley/vanDam, p. 508
+                            const double L1x( P1x ),             L1y( P1y );
+                            const double L2x( (P1x + P2x)*0.5 ), L2y( (P1y + P2y)*0.5 );
+                            const double Hx ( (P2x + P3x)*0.5 ), Hy ( (P2y + P3y)*0.5 );
+                            const double L3x( (L2x + Hx)*0.5 ),  L3y( (L2y + Hy)*0.5 );
+                            const double R4x( P4x ),             R4y( P4y );
+                            const double R3x( (P3x + P4x)*0.5 ), R3y( (P3y + P4y)*0.5 );
+                            const double R2x( (Hx + R3x)*0.5 ),  R2y( (Hy + R3y)*0.5 );
+                            const double R1x( (L3x + R2x)*0.5 ), R1y( (L3y + R2y)*0.5 );
+                            const double L4x( R1x ),             L4y( R1y );
+
+                            // subdivide further
+                            Impl_quadBezierApprox(rBits, rLastPoint, d2, L1x, L1y, L2x, L2y, L3x, L3y, L4x, L4y);
+                            Impl_quadBezierApprox(rBits, rLastPoint, d2, R1x, R1y, R2x, R2y, R3x, R3y, R4x, R4y);
+                        }
+                    }
+                }
+            }
+#endif
+        }
+
+        sal_Int32 adaptiveSubdivideByDistance( polygon::B2DPolygon&     rPoly,
+                                               const B2DCubicBezier&    rCurve,
+                                               double                   distanceBounds )
+        {
+            const point::B2DPoint start( rCurve.getStartPoint() );
+            const point::B2DPoint control1( rCurve.getControlPointA() );
+            const point::B2DPoint control2( rCurve.getControlPointB() );
+            const point::B2DPoint end( rCurve.getEndPoint() );
+
+            return ImplAdaptiveSubdivide( rPoly,
+                                          DistanceErrorFunctor( distanceBounds ),
+                                          start.getX(),     start.getY(),
+                                          control1.getX(),  control1.getY(),
+                                          control2.getX(),  control2.getY(),
+                                          end.getX(),       end.getY(),
+                                          0 );
         }
 
-        int adaptiveSubdivide( polygon::B2DPolygon&     rPoly,
-                               const B2DCubicBezier&    rCurve,
-                               double                   distanceBounds )
+        sal_Int32 adaptiveSubdivideByAngle( polygon::B2DPolygon&    rPoly,
+                                            const B2DCubicBezier&   rCurve,
+                                            double                  angleBounds )
         {
-            const double distance2( distanceBounds*distanceBounds );
             const point::B2DPoint start( rCurve.getStartPoint() );
             const point::B2DPoint control1( rCurve.getControlPointA() );
             const point::B2DPoint control2( rCurve.getControlPointB() );
             const point::B2DPoint end( rCurve.getEndPoint() );
 
             return ImplAdaptiveSubdivide( rPoly,
-                                          distance2,
+                                          AngleErrorFunctor( angleBounds ),
                                           start.getX(),     start.getY(),
                                           control1.getX(),  control1.getY(),
                                           control2.getX(),  control2.getY(),
                                           end.getX(),       end.getY(),
-                                          ::std::numeric_limits<double>::max(),
                                           0 );
         }
 
-        int adaptiveSubdivide( polygon::B2DPolygon&         rPoly,
-                               const B2DQuadraticBezier&    rCurve,
-                               double                       distanceBounds )
+        sal_Int32 adaptiveSubdivideByDistance( polygon::B2DPolygon&     rPoly,
+                                               const B2DQuadraticBezier&    rCurve,
+                                               double                       distanceBounds )
         {
             // TODO
             return 0;
diff --git a/basegfx/source/polygon/b2dpolygontools.cxx b/basegfx/source/polygon/b2dpolygontools.cxx
index bef74f8389ef..28aa2bd7aeab 100644
--- a/basegfx/source/polygon/b2dpolygontools.cxx
+++ b/basegfx/source/polygon/b2dpolygontools.cxx
@@ -2,9 +2,9 @@
  *
  *  $RCSfile: b2dpolygontools.cxx,v $
  *
- *  $Revision: 1.6 $
+ *  $Revision: 1.7 $
  *
- *  last change: $Author: aw $ $Date: 2003-11-11 09:48:13 $
+ *  last change: $Author: thb $ $Date: 2003-11-12 12:09:52 $
  *
  *  The Contents of this file are made available subject to the terms of
  *  either of the following licenses
@@ -293,7 +293,7 @@ namespace basegfx
                             }
 
                             // call adaptive subdivide
-                            ::basegfx::curve::adaptiveSubdivide(aRetval, aBezier, fBound);
+                            ::basegfx::curve::adaptiveSubdivideByDistance(aRetval, aBezier, fBound);
                         }
                         else
                         {