void PlanarRectangle::InitUnit( const Rectangle & rect, const vec3f & integrationPoint )
{
// copy src points here
std::memcpy( &p0, &rect.p0, 4 * sizeof( vec3f ) );
// Normalize each vertex to get the inscribed triangle,
// and find the average vertex plane
vec3f bary( 0 );
vec3f *verts = &p0;
for ( int i = 0; i < 4; ++i )
{
verts[i] = Normalize( verts[i] - integrationPoint ); // put in intPos frame
bary += verts[i];
}
bary *= 0.25f;
// project each point on the tangent plane at the barycenter
f32 rayLenSq = Dot( bary, bary );
f32 rayLen = std::sqrt( rayLenSq );
ez = bary / rayLen; // plane normal
// bary is in relative coordinates to the integration pt already
const Plane P{ bary, ez };
for ( int i = 0; i < 4; ++i )
{
// with 0 as origin since the vertices are in relative coordinates already
verts[i] = P.RayIntersection( vec3f( 0 ), verts[i] );
}
const vec3f d0 = p1 - p0;
const vec3f d1 = p3 - p0;
const vec3f d2 = p2 - p3;
const vec3f d3 = p2 - p1;
w = Len( d0 );
h = Len( d1 );
ex = d0 / w;
ey = d1 / h;
area = 0.5f * ( w * h + Len( d2 ) * Len( d3 ) );
}
void PlanarRectangle::InitBary( const Rectangle & rect, const vec3f & integrationPoint )
{
// copy src points here
std::memcpy( &p0, &rect.p0, 4 * sizeof( vec3f ) );
const vec3f bary = ( p0 + p1 + p2 + p3 ) * 0.25f;
vec3f org = Normalize( bary - integrationPoint );
const f32 rayLenSqr = Dot( org, org );
const f32 rayLen = std::sqrt( rayLenSqr );
const vec3f nrm = org / rayLen;
// org is bary in relative coordinates
const Plane P{ org, nrm };
// project each point on the plane P
vec3f *verts = &p0;
for ( int i = 0; i < 4; ++i )
{
vec3f rayDir = Normalize( verts[i] - integrationPoint );
// with 0 as origin since the vertices are in relative coordinates already
verts[i] = P.RayIntersection( vec3f( 0 ), rayDir );
}
const vec3f d0 = p1 - p0;
const vec3f d1 = p3 - p0;
const vec3f d2 = p2 - p3;
const vec3f d3 = p2 - p1;
w = Len( d0 );
h = Len( d1 );
ex = d0 / w;
ey = d1 / h;
ez = nrm; // normal pointing away from origin
area = 0.5f * ( w * h + Len( d2 ) * Len( d3 ) );
}
f32 Rectangle::IntegrateMRP( const vec3f & integrationPos, const vec3f & integrationNrm ) const
{
const vec3f d0p = -ez;
const vec3f d1p = integrationNrm;
const f32 nDotpN = std::max( 0.f, Dot( integrationNrm, ez ) );
vec3f d0 = Normalize( d0p + integrationNrm * nDotpN );
vec3f d1 = Normalize( d1p - ez * nDotpN );
vec3f dh = Normalize( d0 + d1 );
Plane rectPlane = { position, ez };
vec3f pH = rectPlane.RayIntersection( integrationPos, dh );
pH = rectPlane.ClampPointInRect( *this, pH );
const f32 solidAngle = SolidAngle( integrationPos );
vec3f rayDir = Normalize( pH - integrationPos );
return solidAngle * std::max( 0.f, Dot( integrationNrm, rayDir ) );
}