/*!
*/
double
Segment2D::dist( const Vector2D & p ) const
{
double len = this->length();
if ( len == 0.0 )
{
return origin().dist( p );
}
const Vector2D vec = terminal() - origin();
const double prod = vec.innerProduct( p - origin() );
//
// A: p1 - p0
// A: p - p0
//
// check if 0 <= |B|cos(theta) <= |A|
// -> 0 <= |A||b|cos(theta) <= |A|^2
// -> 0 <= A.B <= |A|^2 // A.B = |A||B|cos(theta)
//
if ( 0.0 <= prod && prod <= len * len )
{
// return perpendicular distance
//return std::fabs( Triangle2D( *this, p ).doubleSignedArea() / len );
return std::fabs( Triangle2D::double_signed_area( origin(), terminal(), p ) / len );
}
return std::sqrt( std::min( origin().dist2( p ),
terminal().dist2( p ) ) );
}
/*!
*/
Vector2D
Segment2D::projection( const Vector2D & p ) const
{
Vector2D dir = terminal() - origin();
double len = dir.r();
if ( len < EPSILON )
{
return origin();
}
dir /= len; // normalize
double d = dir.innerProduct( p - origin() );
if ( -EPSILON < d && d < len + EPSILON )
{
dir *= d;
return Vector2D( origin() ) += dir;
}
return Vector2D::INVALIDATED;
#if 0
Line2D my_line = this->line();
Vector2D sol = my_line.projection( p );
if ( ! sol.isValid()
|| ! this->contains( sol ) )
{
return Vector2D::INVALIDATED;
}
return sol;
#endif
}
/*!
*/
Vector2D
Segment2D::nearestPoint( const Vector2D & p ) const
{
const Vector2D vec = terminal() - origin();
const double len_square = vec.r2();
if ( len_square == 0.0 )
{
return origin();
}
double inner_product = vec.innerProduct( (p - origin()) );
//
// A: p1 - p0
// B: p - p0
//
// check if 0 <= |B|cos(theta) <= |A|
// -> 0 <= |A||B|cos(theta) <= |A|^2
// -> 0 <= A.B <= |A|^2 // A.B = |A||B|cos(theta)
//
if ( inner_product <= 0.0 )
{
return origin();
}
else if ( inner_product >= len_square )
{
return terminal();
}
return origin() + vec * inner_product / len_square;
}
