/*-------------------------------------------------------------------------*
* Dual *
* *
* Construct the dual triangle of the current triangle, which is another *
* spherical triangle. *
* *
*-------------------------------------------------------------------------*/
SphericalTriangle SphericalTriangle::Dual() const
{
Vec3 dual_A = B() ^ C(); if( dual_A * A() < 0.0 ) dual_A *= -1.0;
Vec3 dual_B = A() ^ C(); if( dual_B * B() < 0.0 ) dual_B *= -1.0;
Vec3 dual_C = A() ^ B(); if( dual_C * C() < 0.0 ) dual_C *= -1.0;
return SphericalTriangle( dual_A, dual_B, dual_C );
}
/*-------------------------------------------------------------------------*
* Dual *
* *
* Construct the dual triangle of the current triangle, which is another *
* spherical triangle. *
* *
*-------------------------------------------------------------------------*/
SphericalTriangle SphericalTriangle::Dual() const
{
Vector3d dual_A = B() ^ C(); if( dual_A * A() < 0.0 ) dual_A = -1.0 * dual_A ;
Vector3d dual_B = A() ^ C(); if( dual_B * B() < 0.0 ) dual_B = -1.0 * dual_B ;
Vector3d dual_C = A() ^ B(); if( dual_C * C() < 0.0 ) dual_C = -1.0 * dual_C ;
return SphericalTriangle( dual_A, dual_B, dual_C );
}
/*-------------------------------------------------------------------------*
* New_Alpha *
* *
* Returns a new spherical triangle derived from the original one by *
* moving the "C" vertex along the edge "BC" until the new "alpha" angle *
* equals the given argument. *
* *
*-------------------------------------------------------------------------*/
SphericalTriangle SphericalTriangle::New_Alpha( float alpha ) const
{
Vec3 V1( A() ), V2( B() ), V3( C() );
Vec3 E1 = Unit( V2 ^ V1 );
Vec3 E2 = E1 ^ V1;
Vec3 G = ( cos(alpha) * E1 ) + ( sin(alpha) * E2 );
Vec3 D = Unit( V3 / V2 );
Vec3 C2 = ((G * D) * V2) - ((G * V2) * D);
if( Triple( V1, V2, C2 ) > 0.0 ) C2 *= -1.0;
return SphericalTriangle( V1, V2, C2 );
}
/*-------------------------------------------------------------------------*
* New_Alpha *
* *
* Returns a new spherical triangle derived from the original one by *
* moving the "C" vertex along the edge "BC" until the new "alpha" angle *
* equals the given argument. *
* *
*-------------------------------------------------------------------------*/
SphericalTriangle SphericalTriangle::New_Alpha( double alpha ) const
{
Vector3d V1( A() ), V2( B() ), V3( C() );
Vector3d E1 = Unit( V2 ^ V1 );
Vector3d E2 = E1 ^ V1;
Vector3d G = ( cos(alpha) * E1 ) + ( sin(alpha) * E2 );
Vector3d D = Unit( V3 / V2 );
Vector3d C2 = ((G * D) * V2) - ((G * V2) * D);
if( Triple( V1, V2, C2 ) > 0.0 ) C2 = -1.0 * C2 ;
return SphericalTriangle( V1, V2, C2 );
}
