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#i105459# enhanced circles/ellipes for more mathematical correctness

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This commit is contained in:
Armin Le Grand
2009-10-08 17:35:07 +02:00
parent a6d693d985
commit f678fbae66
2 changed files with 139 additions and 193 deletions
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61
basegfx/inc/basegfx/polygon/b2dpolygontools.hxx
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@@ -288,14 +288,6 @@ namespace basegfx
*/ */
B2DPolygon createPolygonFromCircle( const B2DPoint& rCenter, double fRadius ); B2DPolygon createPolygonFromCircle( const B2DPoint& rCenter, double fRadius );
/** append a unit circle with one point and the control vectors to the given polygon
*/
void appendUnitCircleQuadrant(B2DPolygon& rPolygon, sal_uInt32 nQuadrant, bool bEndPoint);
/** append a segment of unit circle with one point and the control vectors to the given polygon
*/
void appendUnitCircleQuadrantSegment(B2DPolygon& rPolygon, sal_uInt32 nQuadrant, double fStart, double fEnd, bool bEndPoint);
/** create a polygon which describes the unit circle and close it /** create a polygon which describes the unit circle and close it
@param nStartQuadrant @param nStartQuadrant
@@ -325,59 +317,6 @@ namespace basegfx
*/ */
B2DPolygon createPolygonFromEllipse( const B2DPoint& rCenter, double fRadiusX, double fRadiusY ); B2DPolygon createPolygonFromEllipse( const B2DPoint& rCenter, double fRadiusX, double fRadiusY );
/** append a unit circle with one point and the control vectors to the given polygon
*/
void appendUnitCircleQuadrant(B2DPolygon& rPolygon, sal_uInt32 nQuadrant);
/** append a segment of unit circle with start point, the control vectors and end point to the given polygon
*/
void appendUnitCircleQuadrantSegment(B2DPolygon& rPolygon, sal_uInt32 nQuadrant, double fStart, double fEnd);
/** Create an ellipse polygon with given radii.
This method creates an ellipse approximation consisting of
four cubic bezier segments, which approximate the given
ellipse with an error of less than 0.5 percent.
@param rCenter
Center point of the circle
@param fRadiusX
Radius of the ellipse in X direction
@param fRadiusY
Radius of the ellipse in Y direction
@param fStart
Start angle where the ellipe segment starts in the range [0.0 .. 2PI[
@param fEnd
End angle where the ellipe segment ends in the range [0.0 .. 2PI[
*/
B2DPolygon createPolygonFromEllipse( const B2DPoint& rCenter, double fRadiusX, double fRadiusY );
/** Create an ellipse polygon with given radii and the given angles, from start to end
This method creates an ellipse approximation consisting of
four cubic bezier segments, which approximate the given
ellipse with an error of less than 0.5 percent.
@param rCenter
Center point of the circle
@param fRadiusX
Radius of the ellipse in X direction
@param fRadiusY
Radius of the ellipse in Y direction
@param fStart
Start angle where the ellipe segment starts in the range [0.0 .. 2PI[
@param fEnd
End angle where the ellipe segment ends in the range [0.0 .. 2PI[
*/
/** Create an unit ellipse polygon with the given angles, from start to end /** Create an unit ellipse polygon with the given angles, from start to end
*/ */
B2DPolygon createPolygonFromEllipseSegment( const B2DPoint& rCenter, double fRadiusX, double fRadiusY, double fStart, double fEnd ); B2DPolygon createPolygonFromEllipseSegment( const B2DPoint& rCenter, double fRadiusX, double fRadiusY, double fStart, double fEnd );

271
basegfx/source/polygon/b2dpolygontools.cxx
View File

@@ -44,6 +44,7 @@
#include <basegfx/matrix/b2dhommatrix.hxx> #include <basegfx/matrix/b2dhommatrix.hxx>
#include <basegfx/curve/b2dbeziertools.hxx> #include <basegfx/curve/b2dbeziertools.hxx>
#include <basegfx/matrix/b2dhommatrixtools.hxx> #include <basegfx/matrix/b2dhommatrixtools.hxx>
#include <osl/mutex.hxx>
#include <numeric> #include <numeric>
#include <limits> #include <limits>
@@ -55,6 +56,7 @@
#ifdef DBG_UTIL #ifdef DBG_UTIL
static double fAngleBoundStartValue = ANGLE_BOUND_START_VALUE; static double fAngleBoundStartValue = ANGLE_BOUND_START_VALUE;
#endif #endif
#define STEPSPERQUARTER (3)
////////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////////
@@ -1832,57 +1834,94 @@ namespace basegfx
return createPolygonFromEllipse( rCenter, fRadius, fRadius ); return createPolygonFromEllipse( rCenter, fRadius, fRadius );
} }
void appendUnitCircleQuadrant(B2DPolygon& rPolygon, sal_uInt32 nQuadrant) B2DPolygon impCreateUnitCircle(sal_uInt32 nStartQuadrant)
{ {
const double fZero(0.0); B2DPolygon aUnitCircle;
const double fOne(1.0);
const double fKappa((M_SQRT2 - 1.0) * 4.0 / 3.0); const double fKappa((M_SQRT2 - 1.0) * 4.0 / 3.0);
const double fScaledKappa(fKappa * (1.0 / STEPSPERQUARTER));
const B2DHomMatrix aRotateMatrix(createRotateB2DHomMatrix(F_PI2 / STEPSPERQUARTER));
// create closed unit-circle with 4 segments B2DPoint aPoint(1.0, 0.0);
switch(nQuadrant) B2DPoint aForward(1.0, fScaledKappa);
B2DPoint aBackward(1.0, -fScaledKappa);
if(0 != nStartQuadrant)
{ {
case 0 : // first quadrant const B2DHomMatrix aQuadrantMatrix(createRotateB2DHomMatrix(F_PI2 * (nStartQuadrant % 4)));
{ aPoint *= aQuadrantMatrix;
rPolygon.append(B2DPoint(fOne, fZero)); aBackward *= aQuadrantMatrix;
rPolygon.appendBezierSegment(B2DPoint(fOne, fKappa), B2DPoint(fKappa, fOne), B2DPoint(fZero, fOne)); aForward *= aQuadrantMatrix;
break;
}
case 1 : // second quadrant
{
rPolygon.append(B2DPoint(fZero, fOne));
rPolygon.appendBezierSegment(B2DPoint(-fKappa, fOne), B2DPoint(-fOne, fKappa), B2DPoint(-fOne, fZero));
break;
}
case 2 : // third quadrant
{
rPolygon.append(B2DPoint(-fOne, fZero));
rPolygon.appendBezierSegment(B2DPoint(-fOne, -fKappa), B2DPoint(-fKappa, -fOne), B2DPoint(fZero, -fOne));
break;
}
default : // last quadrant
{
rPolygon.append(B2DPoint(fZero, -fOne));
rPolygon.appendBezierSegment(B2DPoint(fKappa, -fOne), B2DPoint(fOne, -fKappa), B2DPoint(fOne, fZero));
break;
}
} }
aUnitCircle.append(aPoint);
for(sal_uInt32 a(0); a < STEPSPERQUARTER * 4; a++)
{
aPoint *= aRotateMatrix;
aBackward *= aRotateMatrix;
aUnitCircle.appendBezierSegment(aForward, aBackward, aPoint);
aForward *= aRotateMatrix;
}
aUnitCircle.setClosed(true);
aUnitCircle.removeDoublePoints();
return aUnitCircle;
} }
B2DPolygon createPolygonFromUnitCircle(sal_uInt32 nStartQuadrant) B2DPolygon createPolygonFromUnitCircle(sal_uInt32 nStartQuadrant)
{ {
B2DPolygon aRetval; switch(nStartQuadrant % 4)
{
case 1 :
{
static B2DPolygon aUnitCircleStartQuadrantOne;
// create unit-circle with all 4 segments, close it if(!aUnitCircleStartQuadrantOne.count())
appendUnitCircleQuadrant(aRetval, nStartQuadrant % 4); nStartQuadrant++; {
appendUnitCircleQuadrant(aRetval, nStartQuadrant % 4); nStartQuadrant++; ::osl::Mutex m_mutex;
appendUnitCircleQuadrant(aRetval, nStartQuadrant % 4); nStartQuadrant++; aUnitCircleStartQuadrantOne = impCreateUnitCircle(1);
appendUnitCircleQuadrant(aRetval, nStartQuadrant % 4); nStartQuadrant++; }
aRetval.setClosed(true);
// remove double points between segments created by segmented creation return aUnitCircleStartQuadrantOne;
aRetval.removeDoublePoints(); }
case 2 :
{
static B2DPolygon aUnitCircleStartQuadrantTwo;
return aRetval; if(!aUnitCircleStartQuadrantTwo.count())
{
::osl::Mutex m_mutex;
aUnitCircleStartQuadrantTwo = impCreateUnitCircle(2);
}
return aUnitCircleStartQuadrantTwo;
}
case 3 :
{
static B2DPolygon aUnitCircleStartQuadrantThree;
if(!aUnitCircleStartQuadrantThree.count())
{
::osl::Mutex m_mutex;
aUnitCircleStartQuadrantThree = impCreateUnitCircle(3);
}
return aUnitCircleStartQuadrantThree;
}
default : // case 0 :
{
static B2DPolygon aUnitCircleStartQuadrantZero;
if(!aUnitCircleStartQuadrantZero.count())
{
::osl::Mutex m_mutex;
aUnitCircleStartQuadrantZero = impCreateUnitCircle(0);
}
return aUnitCircleStartQuadrantZero;
}
}
} }
B2DPolygon createPolygonFromEllipse( const B2DPoint& rCenter, double fRadiusX, double fRadiusY ) B2DPolygon createPolygonFromEllipse( const B2DPoint& rCenter, double fRadiusX, double fRadiusY )
@@ -1895,63 +1934,6 @@ namespace basegfx
return aRetval; return aRetval;
} }
void appendUnitCircleQuadrantSegment(B2DPolygon& rPolygon, sal_uInt32 nQuadrant, double fStart, double fEnd)
{
OSL_ENSURE(fStart >= 0.0 && fStart <= 1.0, "appendUnitCircleQuadrantSegment: Access out of range (!)");
OSL_ENSURE(fEnd >= 0.0 && fEnd <= 1.0, "appendUnitCircleQuadrantSegment: Access out of range (!)");
OSL_ENSURE(fEnd >= fStart, "appendUnitCircleQuadrantSegment: Access out of range (!)");
const double fOne(1.0);
const bool bStartIsZero(fTools::equalZero(fStart));
const bool bEndIsOne(fTools::equal(fEnd, fOne));
if(bStartIsZero && bEndIsOne)
{
// add completely
appendUnitCircleQuadrant(rPolygon, nQuadrant);
}
else
{
// split and add
B2DPolygon aQuadrant;
appendUnitCircleQuadrant(aQuadrant, nQuadrant);
const bool bStartEndEqual(fTools::equal(fStart, fEnd));
if(bStartEndEqual)
{
if(bStartIsZero)
{
// both zero, add start point
rPolygon.append(aQuadrant.getB2DPoint(0L));
}
else if(bEndIsOne)
{
// both one, add end point
rPolygon.append(aQuadrant.getB2DPoint(1L));
}
else
{
// both equal but not zero, add split point
B2DCubicBezier aCubicBezier(
aQuadrant.getB2DPoint(0L), aQuadrant.getNextControlPoint(0L),
aQuadrant.getPrevControlPoint(1L), aQuadrant.getB2DPoint(1L));
aCubicBezier.split(fStart, &aCubicBezier, 0);
rPolygon.append(aCubicBezier.getEndPoint());
}
}
else
{
B2DCubicBezier aCubicBezier(
aQuadrant.getB2DPoint(0L), aQuadrant.getNextControlPoint(0L),
aQuadrant.getPrevControlPoint(1L), aQuadrant.getB2DPoint(1L));
aCubicBezier = aCubicBezier.snippet(fStart, fEnd);
rPolygon.append(aCubicBezier.getStartPoint());
rPolygon.appendBezierSegment(aCubicBezier.getControlPointA(), aCubicBezier.getControlPointB(), aCubicBezier.getEndPoint());
}
}
}
B2DPolygon createPolygonFromUnitEllipseSegment( double fStart, double fEnd ) B2DPolygon createPolygonFromUnitEllipseSegment( double fStart, double fEnd )
{ {
B2DPolygon aRetval; B2DPolygon aRetval;
@@ -1978,49 +1960,74 @@ namespace basegfx
fEnd = 0.0; fEnd = 0.0;
} }
const sal_uInt32 nQuadrantStart(sal_uInt32(fStart / F_PI2) % 4L); if(fTools::equal(fStart, fEnd))
const sal_uInt32 nQuadrantEnd(sal_uInt32(fEnd / F_PI2) % 4L);
sal_uInt32 nCurrentQuadrant(nQuadrantStart);
bool bStartDone(false);
bool bEndDone(false);
do
{ {
if(!bStartDone && nQuadrantStart == nCurrentQuadrant) // same start and end angle, add single point
aRetval.append(B2DPoint(cos(fStart), sin(fStart)));
}
else
{
const sal_uInt32 nSegments(STEPSPERQUARTER * 4);
const double fAnglePerSegment(F_PI2 / STEPSPERQUARTER);
const sal_uInt32 nStartSegment(sal_uInt32(fStart / fAnglePerSegment) % nSegments);
const sal_uInt32 nEndSegment(sal_uInt32(fEnd / fAnglePerSegment) % nSegments);
const double fKappa((M_SQRT2 - 1.0) * 4.0 / 3.0);
const double fScaledKappa(fKappa * (1.0 / STEPSPERQUARTER));
B2DPoint aSegStart(cos(fStart), sin(fStart));
aRetval.append(aSegStart);
if(nStartSegment == nEndSegment && fTools::more(fEnd, fStart))
{ {
if(nQuadrantStart == nQuadrantEnd && fTools::moreOrEqual(fEnd, fStart)) // start and end in one sector and in the right order, create in one segment
{ const B2DPoint aSegEnd(cos(fEnd), sin(fEnd));
// both in one quadrant and defining the complete segment, create start to end const double fFactor(fScaledKappa * ((fEnd - fStart) / fAnglePerSegment));
double fSplitOffsetStart((fStart - (nCurrentQuadrant * F_PI2)) / F_PI2);
double fSplitOffsetEnd((fEnd - (nCurrentQuadrant * F_PI2)) / F_PI2); aRetval.appendBezierSegment(
appendUnitCircleQuadrantSegment(aRetval, nCurrentQuadrant, fSplitOffsetStart, fSplitOffsetEnd); aSegStart + (B2DPoint(-aSegStart.getY(), aSegStart.getX()) * fFactor),
bStartDone = bEndDone = true; aSegEnd - (B2DPoint(-aSegEnd.getY(), aSegEnd.getX()) * fFactor),
} aSegEnd);
else
{
// create start to quadrant end
const double fSplitOffsetStart((fStart - (nCurrentQuadrant * F_PI2)) / F_PI2);
appendUnitCircleQuadrantSegment(aRetval, nCurrentQuadrant, fSplitOffsetStart, 1.0);
bStartDone = true;
}
}
else if(!bEndDone && nQuadrantEnd == nCurrentQuadrant)
{
// create quadrant start to end
const double fSplitOffsetEnd((fEnd - (nCurrentQuadrant * F_PI2)) / F_PI2);
appendUnitCircleQuadrantSegment(aRetval, nCurrentQuadrant, 0.0, fSplitOffsetEnd);
bEndDone = true;
} }
else else
{ {
// add quadrant completely double fSegEndRad((nStartSegment + 1) * fAnglePerSegment);
appendUnitCircleQuadrant(aRetval, nCurrentQuadrant); double fFactor(fScaledKappa * ((fSegEndRad - fStart) / fAnglePerSegment));
} B2DPoint aSegEnd(cos(fSegEndRad), sin(fSegEndRad));
// next step aRetval.appendBezierSegment(
nCurrentQuadrant = (nCurrentQuadrant + 1L) % 4L; aSegStart + (B2DPoint(-aSegStart.getY(), aSegStart.getX()) * fFactor),
aSegEnd - (B2DPoint(-aSegEnd.getY(), aSegEnd.getX()) * fFactor),
aSegEnd);
sal_uInt32 nSegment((nStartSegment + 1) % nSegments);
aSegStart = aSegEnd;
while(nSegment != nEndSegment)
{
// No end in this sector, add full sector.
fSegEndRad = (nSegment + 1) * fAnglePerSegment;
aSegEnd = B2DPoint(cos(fSegEndRad), sin(fSegEndRad));
aRetval.appendBezierSegment(
aSegStart + (B2DPoint(-aSegStart.getY(), aSegStart.getX()) * fScaledKappa),
aSegEnd - (B2DPoint(-aSegEnd.getY(), aSegEnd.getX()) * fScaledKappa),
aSegEnd);
nSegment = (nSegment + 1) % nSegments;
aSegStart = aSegEnd;
}
// End in this sector
const double fSegStartRad(nSegment * fAnglePerSegment);
fFactor = fScaledKappa * ((fEnd - fSegStartRad) / fAnglePerSegment);
aSegEnd = B2DPoint(cos(fEnd), sin(fEnd));
aRetval.appendBezierSegment(
aSegStart + (B2DPoint(-aSegStart.getY(), aSegStart.getX()) * fFactor),
aSegEnd - (B2DPoint(-aSegEnd.getY(), aSegEnd.getX()) * fFactor),
aSegEnd);
}
} }
while(!(bStartDone && bEndDone));
// remove double points between segments created by segmented creation // remove double points between segments created by segmented creation
aRetval.removeDoublePoints(); aRetval.removeDoublePoints();