Interval
atan2(Interval yInterval, Interval xInterval) {
if (yInterval.isEmpty() || xInterval.isEmpty()) {
return Interval::EMPTY();
} else if (xInterval.lowerBound() > 0.0) {
return atan(yInterval / xInterval);
} else if (yInterval.lowerBound() > 0.0) {
return atan(-xInterval / yInterval) + M_PI / 2;
} else if (yInterval.upperBound() < 0.0) {
return atan(-xInterval / yInterval) - M_PI / 2;
} else {
return Interval(-M_PI, M_PI);
}
}
Intervals Interval::unionize(Interval& other) {
Intervals result;
if (isEmpty()) {
result.push_back(other);
return result;
}
else if (other.isEmpty()) {
result.push_back(*this);
return result;
}
else if (intersects(*this, other)) {
//std::cout << "intersecting" << std::endl;
Interval newInt(std::min(_min, other._min), std::max(_max, other._max));
result.push_back(newInt);
return result;
}
else {
if (_min < other._min) {
result.push_back(*this);
result.push_back(other);
return result;
}
else {
result.push_back(other);
result.push_back(*this);
return result;
}
}
return result;
}
bool Interval::operator == ( const Interval& other ) const
{
if ( isEmpty() && other.isEmpty() )
return true ;
return _lower == other._lower && _upper == other._upper ;
}
bool Interval::intersects( const Interval & other ) const
{
//empty intervals never intersects
if ( isEmpty() || other.isEmpty() )
return false ;
return ! ( _lower > other._upper || _upper < other._lower ) ;
}
Interval
exp(Interval interval) {
if (interval.isEmpty()) {
return Interval::EMPTY();
} else {
return Interval(exp(interval.lowerBound()), exp(interval.upperBound()));
}
}
Interval Interval::intersect(Interval& other) {
Interval result;
if (isEmpty() || other.isEmpty()) {
return result;
}
if (intersects(*this, other)) {
result = Interval(std::max(_min, other._min), std::min(_max, other._max));
}
return result;
}
Interval
acos(Interval interval) {
if (interval.isEmpty() || interval.lowerBound() > 1.0 || interval.upperBound() < -1.0) {
return Interval::EMPTY();
} else {
return Interval(
acos(min(interval.upperBound(), 1.0)),
acos(max(interval.lowerBound(), -1.0))
);
}
}
Interval
log(Interval interval) {
if (interval.isEmpty() || interval.upperBound() < 0.0) {
return Interval::EMPTY();
} else if (interval.lowerBound() > 0.0) {
return Interval(log(interval.lowerBound()), log(interval.upperBound()));
} else if (interval.upperBound() > 0.0) {
return Interval(-std::numeric_limits<double>::infinity(), log(interval.upperBound()));
} else {
return -std::numeric_limits<double>::infinity();
}
}
void Interval::expandToInclude( const Interval & other )
{
//ignore empty interval
if ( other.isEmpty() )
return ;
if ( isEmpty() ){
(*this) = other ;
}else{
_lower = std::min( _lower, other._lower );
_upper = std::max( _upper, other._upper );
}
}
Intervals Interval::difference(Interval& diff) {
Intervals result;
if (isEmpty()) {
return result;
}
else if (diff.isEmpty()) {
result.push_back(*this);
return result;
}
if (intersects(*this, diff)) {
if (_min < diff._min) {
Interval temp(_min, diff._min);
result.push_back(temp);
}
if (_max > diff._max) {
Interval temp(diff._max, _max);
result.push_back(temp);
}
}
else {
result.push_back(*this);
}
return result;
}