void Cube::ComputeArea()
{
//Extra credit to implement this
glm::vec4 vertices[]{
{ -.5f, -.5f, .5f, 1.f, },
{ .5f, -.5f, .5f, 1.f, },
{ -.5f, .5f, .5f, 1.f, },
{ -.5f, -.5f, .5f, 1.f, },
};
glm::vec4 vertices_world[ 4 ];
for( int i = 0; i < 4; ++i ){
vertices_world[ i ] = transform.T() * vertices[ i ];
}
glm::vec3 v01( vertices_world[ 1 ] - vertices_world[ 0 ] );
glm::vec3 v03( vertices_world[ 2 ] - vertices_world[ 0 ] );
glm::vec3 v04( vertices_world[ 3 ] - vertices_world[ 0 ] );
area = 0.f;
area += glm::length( glm::cross( v01, v03 ) );
area += glm::length( glm::cross( v03, v04 ) );
area += glm::length( glm::cross( v04, v01 ) );
area *= 2.f;
}
void DragRect::TrackPoints03(const DPoint& pt0, const DPoint& pt3) {
// width constant, height variable, theta variable
Vec2d v03(pt0, pt3);
DPoint pt1 = v03.flip270().unit().scale(v01_.mag()).add(pt0);
pt0_ = pt0;
v01_ = Vec2d(pt0, pt1);
v02_ = Vec2d(pt0, v03.add(pt1));
}
Real Pyramid5::volume () const
{
// The pyramid with a bilinear base has volume given by the
// formula in: "Calculation of the Volume of a General Hexahedron
// for Flow Predictions", AIAA Journal v.23, no.6, 1984, p.954-
Node * node0 = this->get_node(0);
Node * node1 = this->get_node(1);
Node * node2 = this->get_node(2);
Node * node3 = this->get_node(3);
Node * node4 = this->get_node(4);
// Construct Various edge and diagonal vectors
Point v40 ( *node0 - *node4 );
Point v13 ( *node3 - *node1 );
Point v02 ( *node2 - *node0 );
Point v03 ( *node3 - *node0 );
Point v01 ( *node1 - *node0 );
// Finally, ready to return the volume!
return (1./6.)*(v40*(v13.cross(v02))) + (1./12.)*(v02*(v01.cross(v03)));
}