void Path::addArcTo(const FloatPoint& p1, const FloatPoint& p2, float radius)
{
FloatPoint p0(m_path.currentPosition());
FloatPoint p1p0((p0.x() - p1.x()), (p0.y() - p1.y()));
FloatPoint p1p2((p2.x() - p1.x()), (p2.y() - p1.y()));
float p1p0_length = sqrtf(p1p0.x() * p1p0.x() + p1p0.y() * p1p0.y());
float p1p2_length = sqrtf(p1p2.x() * p1p2.x() + p1p2.y() * p1p2.y());
double cos_phi = (p1p0.x() * p1p2.x() + p1p0.y() * p1p2.y()) / (p1p0_length * p1p2_length);
// The points p0, p1, and p2 are on the same straight line (HTML5, 4.8.11.1.8)
// We could have used areCollinear() here, but since we're reusing
// the variables computed above later on we keep this logic.
if (qFuzzyCompare(qAbs(cos_phi), 1.0)) {
m_path.lineTo(p1);
return;
}
float tangent = radius / tan(acos(cos_phi) / 2);
float factor_p1p0 = tangent / p1p0_length;
FloatPoint t_p1p0((p1.x() + factor_p1p0 * p1p0.x()), (p1.y() + factor_p1p0 * p1p0.y()));
FloatPoint orth_p1p0(p1p0.y(), -p1p0.x());
float orth_p1p0_length = sqrt(orth_p1p0.x() * orth_p1p0.x() + orth_p1p0.y() * orth_p1p0.y());
float factor_ra = radius / orth_p1p0_length;
// angle between orth_p1p0 and p1p2 to get the right vector orthographic to p1p0
double cos_alpha = (orth_p1p0.x() * p1p2.x() + orth_p1p0.y() * p1p2.y()) / (orth_p1p0_length * p1p2_length);
if (cos_alpha < 0.f)
orth_p1p0 = FloatPoint(-orth_p1p0.x(), -orth_p1p0.y());
FloatPoint p((t_p1p0.x() + factor_ra * orth_p1p0.x()), (t_p1p0.y() + factor_ra * orth_p1p0.y()));
// calculate angles for addArc
orth_p1p0 = FloatPoint(-orth_p1p0.x(), -orth_p1p0.y());
float sa = acos(orth_p1p0.x() / orth_p1p0_length);
if (orth_p1p0.y() < 0.f)
sa = 2 * piDouble - sa;
// anticlockwise logic
bool anticlockwise = false;
float factor_p1p2 = tangent / p1p2_length;
FloatPoint t_p1p2((p1.x() + factor_p1p2 * p1p2.x()), (p1.y() + factor_p1p2 * p1p2.y()));
FloatPoint orth_p1p2((t_p1p2.x() - p.x()), (t_p1p2.y() - p.y()));
float orth_p1p2_length = sqrtf(orth_p1p2.x() * orth_p1p2.x() + orth_p1p2.y() * orth_p1p2.y());
float ea = acos(orth_p1p2.x() / orth_p1p2_length);
if (orth_p1p2.y() < 0)
ea = 2 * piDouble - ea;
if ((sa > ea) && ((sa - ea) < piDouble))
anticlockwise = true;
if ((sa < ea) && ((ea - sa) > piDouble))
anticlockwise = true;
m_path.lineTo(t_p1p0);
addArc(p, radius, sa, ea, anticlockwise);
}
void Path::addArcTo(const FloatPoint& p1, const FloatPoint& p2, float radius)
{
if (isEmpty())
return;
cairo_t* cr = platformPath()->context();
double x0, y0;
cairo_get_current_point(cr, &x0, &y0);
FloatPoint p0(x0, y0);
// Draw only a straight line to p1 if any of the points are equal or the radius is zero
// or the points are collinear (triangle that the points form has area of zero value).
if ((p1.x() == p0.x() && p1.y() == p0.y()) || (p1.x() == p2.x() && p1.y() == p2.y()) || !radius
|| !areaOfTriangleFormedByPoints(p0, p1, p2)) {
cairo_line_to(cr, p1.x(), p1.y());
return;
}
FloatPoint p1p0((p0.x() - p1.x()),(p0.y() - p1.y()));
FloatPoint p1p2((p2.x() - p1.x()),(p2.y() - p1.y()));
float p1p0_length = sqrtf(p1p0.x() * p1p0.x() + p1p0.y() * p1p0.y());
float p1p2_length = sqrtf(p1p2.x() * p1p2.x() + p1p2.y() * p1p2.y());
double cos_phi = (p1p0.x() * p1p2.x() + p1p0.y() * p1p2.y()) / (p1p0_length * p1p2_length);
// all points on a line logic
if (cos_phi == -1) {
cairo_line_to(cr, p1.x(), p1.y());
return;
}
if (cos_phi == 1) {
// add infinite far away point
unsigned int max_length = 65535;
double factor_max = max_length / p1p0_length;
FloatPoint ep((p0.x() + factor_max * p1p0.x()), (p0.y() + factor_max * p1p0.y()));
cairo_line_to(cr, ep.x(), ep.y());
return;
}
float tangent = radius / tan(acos(cos_phi) / 2);
float factor_p1p0 = tangent / p1p0_length;
FloatPoint t_p1p0((p1.x() + factor_p1p0 * p1p0.x()), (p1.y() + factor_p1p0 * p1p0.y()));
FloatPoint orth_p1p0(p1p0.y(), -p1p0.x());
float orth_p1p0_length = sqrt(orth_p1p0.x() * orth_p1p0.x() + orth_p1p0.y() * orth_p1p0.y());
float factor_ra = radius / orth_p1p0_length;
// angle between orth_p1p0 and p1p2 to get the right vector orthographic to p1p0
double cos_alpha = (orth_p1p0.x() * p1p2.x() + orth_p1p0.y() * p1p2.y()) / (orth_p1p0_length * p1p2_length);
if (cos_alpha < 0.f)
orth_p1p0 = FloatPoint(-orth_p1p0.x(), -orth_p1p0.y());
FloatPoint p((t_p1p0.x() + factor_ra * orth_p1p0.x()), (t_p1p0.y() + factor_ra * orth_p1p0.y()));
// calculate angles for addArc
orth_p1p0 = FloatPoint(-orth_p1p0.x(), -orth_p1p0.y());
float sa = acos(orth_p1p0.x() / orth_p1p0_length);
if (orth_p1p0.y() < 0.f)
sa = 2 * piDouble - sa;
// anticlockwise logic
bool anticlockwise = false;
float factor_p1p2 = tangent / p1p2_length;
FloatPoint t_p1p2((p1.x() + factor_p1p2 * p1p2.x()), (p1.y() + factor_p1p2 * p1p2.y()));
FloatPoint orth_p1p2((t_p1p2.x() - p.x()),(t_p1p2.y() - p.y()));
float orth_p1p2_length = sqrtf(orth_p1p2.x() * orth_p1p2.x() + orth_p1p2.y() * orth_p1p2.y());
float ea = acos(orth_p1p2.x() / orth_p1p2_length);
if (orth_p1p2.y() < 0)
ea = 2 * piDouble - ea;
if ((sa > ea) && ((sa - ea) < piDouble))
anticlockwise = true;
if ((sa < ea) && ((ea - sa) > piDouble))
anticlockwise = true;
cairo_line_to(cr, t_p1p0.x(), t_p1p0.y());
addArc(p, radius, sa, ea, anticlockwise);
}
void Path::addArcTo(const FloatPoint& p1, const FloatPoint& p2, float radius)
{
FloatPoint p0(m_path->currentPosition());
if ((p1.x() == p0.x() && p1.y() == p0.y()) || (p1.x() == p2.x() && p1.y() == p2.y()) || radius == 0.f) {
m_path->lineTo(p1);
return;
}
FloatPoint p1p0((p0.x() - p1.x()),(p0.y() - p1.y()));
FloatPoint p1p2((p2.x() - p1.x()),(p2.y() - p1.y()));
float p1p0_length = sqrtf(p1p0.x() * p1p0.x() + p1p0.y() * p1p0.y());
float p1p2_length = sqrtf(p1p2.x() * p1p2.x() + p1p2.y() * p1p2.y());
double cos_phi = (p1p0.x() * p1p2.x() + p1p0.y() * p1p2.y()) / (p1p0_length * p1p2_length);
// all points on a line logic
if (cos_phi == -1) {
m_path->lineTo(p1);
return;
}
if (cos_phi == 1) {
// add infinite far away point
unsigned int max_length = 65535;
double factor_max = max_length / p1p0_length;
FloatPoint ep((p0.x() + factor_max * p1p0.x()), (p0.y() + factor_max * p1p0.y()));
m_path->lineTo(ep);
return;
}
float tangent = radius / tan(acos(cos_phi) / 2);
float factor_p1p0 = tangent / p1p0_length;
FloatPoint t_p1p0((p1.x() + factor_p1p0 * p1p0.x()), (p1.y() + factor_p1p0 * p1p0.y()));
FloatPoint orth_p1p0(p1p0.y(), -p1p0.x());
float orth_p1p0_length = sqrt(orth_p1p0.x() * orth_p1p0.x() + orth_p1p0.y() * orth_p1p0.y());
float factor_ra = radius / orth_p1p0_length;
// angle between orth_p1p0 and p1p2 to get the right vector orthographic to p1p0
double cos_alpha = (orth_p1p0.x() * p1p2.x() + orth_p1p0.y() * p1p2.y()) / (orth_p1p0_length * p1p2_length);
if (cos_alpha < 0.f)
orth_p1p0 = FloatPoint(-orth_p1p0.x(), -orth_p1p0.y());
FloatPoint p((t_p1p0.x() + factor_ra * orth_p1p0.x()), (t_p1p0.y() + factor_ra * orth_p1p0.y()));
// calculate angles for addArc
orth_p1p0 = FloatPoint(-orth_p1p0.x(), -orth_p1p0.y());
float sa = acos(orth_p1p0.x() / orth_p1p0_length);
if (orth_p1p0.y() < 0.f)
sa = 2 * piDouble - sa;
// anticlockwise logic
bool anticlockwise = false;
float factor_p1p2 = tangent / p1p2_length;
FloatPoint t_p1p2((p1.x() + factor_p1p2 * p1p2.x()), (p1.y() + factor_p1p2 * p1p2.y()));
FloatPoint orth_p1p2((t_p1p2.x() - p.x()),(t_p1p2.y() - p.y()));
float orth_p1p2_length = sqrtf(orth_p1p2.x() * orth_p1p2.x() + orth_p1p2.y() * orth_p1p2.y());
float ea = acos(orth_p1p2.x() / orth_p1p2_length);
if (orth_p1p2.y() < 0)
ea = 2 * piDouble - ea;
if ((sa > ea) && ((sa - ea) < piDouble))
anticlockwise = true;
if ((sa < ea) && ((ea - sa) > piDouble))
anticlockwise = true;
m_path->lineTo(t_p1p0);
addArc(p, radius, sa, ea, anticlockwise);
}
