toxi::geom::Matrix4x4 toxi::geom::Matrix4x4::lookAt( Vec3D & eye, Vec3D & target, Vec3D & up )
{
Vec3D f = eye.sub( target ).normalize();
Vec3D s = up.cross( f ).normalize();
Vec3D t = f.cross( s ).normalize();
return set( s.getX(), s.getY(), s.getZ(), -s.dot( eye ), t.getX(), t.getY(), t.getZ(), -t.dot( eye ), f.getX(),
f.getY(), f.getZ(), -f.dot( eye ), 0, 0, 0, 1 );
}
toxi::geom::Triangle3D toxi::geom::Triangle3D::createEquilateralFrom( Vec3D & a, Vec3D & b )
{
Vec3D c = a.interpolateTo( b, 0.5 );
Vec3D dir = b.sub( a );
Vec3D n = a.cross( dir.normalize( ) );
c.addSelf( n.normalizeTo( dir.magnitude() * toxi::math::MathUtils::SQRT3 / 2 ) );
return Triangle3D( a, b, c );
}
toxi::geom::Vec3D toxi::geom::Triangle3D::getClosestPointTo( Vec3D & v )
{
Line3D edge = Line3D( a, b );
Vec3D Rab = edge.closestPointTo( v );
Vec3D Rbc = edge.set( b, c ).closestPointTo( v );
Vec3D Rca = edge.set( c, a ).closestPointTo( v );
float dAB = v.sub( Rab ).magSquared();
float dBC = v.sub( Rbc ).magSquared();
float dCA = v.sub( Rca ).magSquared();
float min = dAB;
Vec3D result = Rab;
if (dBC < min) {
min = dBC;
result = Rbc;
}
if (dCA < min) {
result = Rca;
}
return result;
}
toxi::geom::Vec3D toxi::geom::AABB::getNormalForPoint( Vec3D & p )
{
p = p.sub( Vec3D( x, y, z ) );
Vec3D pabs = extent.sub( p.getAbs() );
Vec3D psign = p.getSignum();
Vec3D normal = Vec3D::X_AXIS().scale( static_cast< float > ( psign.getX() ) );
double minDist = pabs.getX();
if (pabs.getY() < minDist) {
minDist = pabs.getY();
normal = Vec3D::Y_AXIS().scale( static_cast< float > ( psign.getY() ) );
}
if (pabs.getZ() < minDist) {
normal = Vec3D::Z_AXIS().scale( static_cast< float > ( psign.getZ() ) );
}
return normal;
}
bool toxi::geom::Triangle3D::containsPoint( Vec3D & p )
{
Vec3D v0 = c.sub( a );
Vec3D v1 = b.sub( a );
Vec3D v2 = p.sub( a );
// Compute dot products
float dot00 = v0.dot( v0 );
float dot01 = v0.dot( v1 );
float dot02 = v0.dot( v2 );
float dot11 = v1.dot( v1 );
float dot12 = v1.dot( v2 );
// Compute barycentric coordinates
float invDenom = 1.0f / ( dot00 * dot11 - dot01 * dot01 );
float u = ( dot11 * dot02 - dot01 * dot12 ) * invDenom;
float v = ( dot00 * dot12 - dot01 * dot02 ) * invDenom;
// Check if point is in triangle
return ( u >= 0.0 ) && ( v >= 0.0 ) && ( u + v <= 1.0 );
}
toxi::geom::Vec3D toxi::geom::Triangle3D::closestPointOnSurface( Vec3D & p )
{
Vec3D ab = b.sub( a );
Vec3D ac = c.sub( a );
Vec3D bc = c.sub( b );
Vec3D pa = p.sub( a );
Vec3D pb = p.sub( b );
Vec3D pc = p.sub( c );
Vec3D ap = a.sub( p );
Vec3D bp = b.sub( p );
Vec3D cp = c.sub( p );
// Compute parametric position s for projection P' of P on AB,
// P' = A + s*AB, s = snom/(snom+sdenom)
float snom = pa.dot( ab );
// Compute parametric position t for projection P' of P on AC,
// P' = A + t*AC, s = tnom/(tnom+tdenom)
float tnom = pa.dot( ac );
if ( snom <= 0.0f && tnom <= 0.0f ) {
return a; // Vertex region early out
}
float sdenom = pb.dot( a.sub( b ) );
float tdenom = pc.dot( a.sub( c ) );
// Compute parametric position u for projection P' of P on BC,
// P' = B + u*BC, u = unom/(unom+udenom)
float unom = pb.dot( bc );
float udenom = pc.dot( b.sub( c ) );
if ( sdenom <= 0.0f && unom <= 0.0f ) {
return b; // Vertex region early out
}
if ( tdenom <= 0.0f && udenom <= 0.0f ) {
return c; // Vertex region early out
}
// P is outside (or on) AB if the triple scalar product [N PA PB] <= 0
Vec3D n = ab.cross( ac );
float vc = n.dot( ap.crossSelf( bp ) );
// If P outside AB and within feature region of AB,
// return projection of P onto AB
if ( vc <= 0.0f && snom >= 0.0f && sdenom >= 0.0f ) {
// return a + snom / (snom + sdenom) * ab;
return a.add( ab.scaleSelf( snom / ( snom + sdenom ) ) );
}
// P is outside (or on) BC if the triple scalar product [N PB PC] <= 0
float va = n.dot( bp.crossSelf( cp ) );
// If P outside BC and within feature region of BC,
// return projection of P onto BC
if ( va <= 0.0f && unom >= 0.0f && udenom >= 0.0f ) {
// return b + unom / (unom + udenom) * bc;
return b.add( bc.scaleSelf( unom / ( unom + udenom ) ) );
}
// P is outside (or on) CA if the triple scalar product [N PC PA] <= 0
float vb = n.dot( cp.crossSelf( ap ) );
// If P outside CA and within feature region of CA,
// return projection of P onto CA
if ( vb <= 0.0f && tnom >= 0.0f && tdenom >= 0.0f ) {
// return a + tnom / (tnom + tdenom) * ac;
return a.add( ac.scaleSelf( tnom / ( tnom + tdenom ) ) );
}
// P must project inside face region. Compute Q using barycentric
// coordinates
float u = va / ( va + vb + vc );
float v = vb / ( va + vb + vc );
float w = 1.0f - u - v; // = vc / (va + vb + vc)
// return u * a + v * b + w * c;
return a.scale( u ).addSelf( b.scale( v ) ).addSelf( c.scale( w ) );
}