/*===========================================================================*/
bool StreamlineBase::integrate_by_runge_kutta_2nd(
const kvs::Vec3& current_vertex,
const kvs::Vec3& current_direction,
kvs::Vec3* next_vertex )
{
if ( m_enable_boundary_condition )
{
if ( !this->check_for_inside_volume( current_vertex ) ) return false;
}
const float integration_direction = static_cast<float>( m_integration_direction );
const kvs::Vec3 k1 = current_direction.normalized() * integration_direction;
// Interpolate vector from vertex of cell.
const kvs::Vec3 vertex = current_vertex + 0.5f * m_integration_interval * k1;
if ( m_enable_boundary_condition )
{
if ( !this->check_for_inside_volume( vertex ) ) return false;
}
const kvs::Vec3 direction = this->interpolate_vector( vertex, current_direction );
const kvs::Vec3 k2 = direction.normalized() * integration_direction;
*next_vertex = vertex + m_integration_interval * k2;
return true;
}
void TextEngine::draw( const kvs::Vec3& p, const std::string& text, kvs::ScreenBase* screen ) const
{
GLdouble model[16]; kvs::OpenGL::GetModelViewMatrix( model );
GLdouble proj[16]; kvs::OpenGL::GetProjectionMatrix( proj );
GLint view[4]; kvs::OpenGL::GetViewport( view );
GLdouble winx = 0, winy = 0, winz = 0;
kvs::OpenGL::Project( p.x(), p.y(), p.z(), model, proj, view, &winx, &winy, &winz );
kvs::OpenGL::WithPushedAttrib attrib( GL_ALL_ATTRIB_BITS );
attrib.disable( GL_TEXTURE_1D );
attrib.disable( GL_TEXTURE_2D );
// attrib.enable( GL_TEXTURE_2D );
attrib.disable( GL_TEXTURE_3D );
attrib.enable( GL_DEPTH_TEST );
attrib.enable( GL_BLEND );
{
kvs::OpenGL::SetBlendFunc( GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA );
kvs::OpenGL::WithPushedMatrix modelview( GL_MODELVIEW );
modelview.loadIdentity();
{
kvs::OpenGL::WithPushedMatrix projection( GL_PROJECTION );
projection.loadIdentity();
{
const GLint left = view[0];
const GLint top = view[1];
const GLint right = view[0] + view[2];
const GLint bottom = view[1] + view[3];
kvs::OpenGL::SetOrtho( left, right, bottom, top, 0, 1 );
kvs::OpenGL::Translate( 0, 0, -winz );
m_font.draw( kvs::Vec2( winx, top - ( winy - bottom ) ), text );
}
}
}
}
/*===========================================================================*/
kvs::Real32 TetrahedralCell::volume() const
{
const kvs::Vec3 v01( BaseClass::coord(1) - BaseClass::coord(0) );
const kvs::Vec3 v02( BaseClass::coord(2) - BaseClass::coord(0) );
const kvs::Vec3 v03( BaseClass::coord(3) - BaseClass::coord(0) );
return kvs::Math::Abs( ( v01.cross( v02 ) ).dot( v03 ) ) * 0.166666f;
}
/*===========================================================================*/
const kvs::Vec3 Quaternion::Rotate(
const kvs::Vec3& pos,
const kvs::Quaternion& q )
{
const Quaternion p( pos.x(), pos.y(), pos.z(), 0.0f );
const Quaternion rotate_conj = q.conjugated();
const Quaternion rotate_pos = q * p * rotate_conj;
return rotate_pos.m_elements.xyz();
}
/*===========================================================================*/
const kvs::Vec3 Quaternion::Rotate(
const kvs::Vec3& pos,
const kvs::Vec3& axis,
float rad )
{
const Quaternion p( pos.x(), pos.y(), pos.z(), 0.0f );
const Quaternion rotate_quat( axis, rad );
const Quaternion rotate_conj = rotate_quat.conjugated();
const Quaternion rotate_pos = rotate_quat * p * rotate_conj;
return rotate_pos.m_elements.xyz();
}
/*===========================================================================*/
bool TetrahedralCell::containsLocalPoint( const kvs::Vec3& local ) const
{
if ( local.x() < 0 || 1 < local.x() ) { return false; }
if ( local.y() < 0 || 1 < local.y() ) { return false; }
if ( local.z() < 0 || 1 < local.z() ) { return false; }
if ( local.x() + local.y() + local.z() > 1 ) { return false; }
return true;
}
/*==========================================================================*/
void QuadraticTetrahedralCell::updateDifferentialFunctions( const kvs::Vec3& local ) const
{
KVS_ASSERT( BaseClass::containsLocalPoint( local ) );
const float p = local.x();
const float q = local.y();
const float r = local.z();
const float w = 1 - p - q - r;
const size_t nnodes = BaseClass::numberOfCellNodes();
kvs::Real32* dN = BaseClass::differentialFunctions();
kvs::Real32* dNdp = dN;
kvs::Real32* dNdq = dNdp + nnodes;
kvs::Real32* dNdr = dNdq + nnodes;
// dNdp
dNdp[0] = -4 * w + 1;
dNdp[1] = 4 * p - 1;
dNdp[2] = 0;
dNdp[3] = 0;
dNdp[4] = 4 * (w - p);
dNdp[5] = -4 * r;
dNdp[6] = -4 * q;
dNdp[7] = 4 * r;
dNdp[8] = 0;
dNdp[9] = 4 * q;
// dNdq
dNdq[0] = -4 * w + 1;
dNdq[1] = 0;
dNdq[2] = 0;
dNdq[3] = 4 * q - 1;
dNdq[4] = -4 * p;
dNdq[5] = -4 * r;
dNdq[6] = 4 * (w - q);
dNdq[7] = 0;
dNdq[8] = 4 * r;
dNdq[9] = 4 * p;
// dNdr
dNdr[0] = -4 * w + 1;
dNdr[1] = 0;
dNdr[2] = 4 * r - 1;
dNdr[3] = 0;
dNdr[4] = -4 * p;
dNdr[5] = 4 * (w - r);
dNdr[6] = -4 * q;
dNdr[7] = 4 * p;
dNdr[8] = 4 * q;
dNdr[9] = 0;
}
/*==========================================================================*/
void TetrahedralCell::updateInterpolationFunctions( const kvs::Vec3& local ) const
{
KVS_ASSERT( this->containsLocalPoint( local ) );
const float p = local.x();
const float q = local.y();
const float r = local.z();
kvs::Real32* N = BaseClass::interpolationFunctions();
N[0] = p;
N[1] = q;
N[2] = r;
N[3] = 1.0f - p - q - r;
}
bool StreamlineBase::isTerminatedByVectorLength( const kvs::Vec3& vector )
{
if ( m_enable_vector_length_condition )
{
return vector.length() < m_vector_length_threshold;
}
return false;
}
/*===========================================================================*/
const kvs::RGBColor Streamline::calculate_color( const kvs::Vec3& direction )
{
const kvs::Real64 min_length = BaseClass::volume()->minValue();
const kvs::Real64 max_length = BaseClass::volume()->maxValue();
const kvs::Real64 diff = direction.length() - min_length;
const kvs::Real64 interval = max_length - min_length;
const kvs::UInt8 level = kvs::UInt8( 255.0 * diff / interval );
return BaseClass::transferFunction().colorMap()[level];
}
void GridBase::updateDifferentialFunctions( const kvs::Vec3& local )
{
const float p = local.x();
const float q = local.y();
const float r = local.z();
const float pq = p * q;
const float qr = q * r;
const float rp = r * p;
const size_t nnodes = m_nnodes;
kvs::Real32* dN = m_differential_functions;
kvs::Real32* dNdp = dN;
kvs::Real32* dNdq = dNdp + nnodes;
kvs::Real32* dNdr = dNdq + nnodes;
dNdp[0] = - 1.0f + q +r - qr;
dNdp[1] = 1.0f - q - r + qr;
dNdp[2] = q - qr;
dNdp[3] = - q + qr;
dNdp[4] = - r + qr;
dNdp[5] = r - qr;
dNdp[6] = qr;
dNdp[7] = - qr;
dNdq[0] = - 1.0f + p + r - rp;
dNdq[1] = - p + rp;
dNdq[2] = p - rp;
dNdq[3] = 1.0f - p - r + rp;
dNdq[4] = - r + rp;
dNdq[5] = - rp;
dNdq[6] = rp;
dNdq[7] = r - rp;
dNdr[0] = - 1.0f + q + p - pq;
dNdr[1] = - p + pq;
dNdr[2] = - pq;
dNdr[3] = - q + pq;
dNdr[4] = 1.0f - q - p + pq;
dNdr[5] = p - pq;
dNdr[6] = pq;
dNdr[7] = q - pq;
}
/*==========================================================================*/
void QuadraticTetrahedralCell::updateInterpolationFunctions( const kvs::Vec3& local ) const
{
KVS_ASSERT( BaseClass::containsLocalPoint( local ) );
const float p = local.x();
const float q = local.y();
const float r = local.z();
const float w = 1 - p - q - r;
kvs::Real32* N = BaseClass::interpolationFunctions();
N[0] = w * (2 * w - 1); // (0, 0, 0)
N[1] = p * (2 * p - 1); // (1, 0, 0)
N[2] = r * (2 * r - 1); // (0, 0, 1)
N[3] = q * (2 * q - 1); // (0, 1, 0)
N[4] = 4 * p * w; // (1/2, 0, 0)
N[5] = 4 * r * w; // ( 0, 0, 1/2)
N[6] = 4 * q * w; // ( 0, 1/2, 0)
N[7] = 4 * r * p; // (1/2, 0, 1/2)
N[8] = 4 * q * r; // ( 0, 1/2, 1/2)
N[9] = 4 * p * q; // (1/2, 1/2, 0)
}
void GridBase::updateInterpolationFunctions( const kvs::Vec3& local )
{
const float p = local.x();
const float q = local.y();
const float r = local.z();
const float pq = p * q;
const float qr = q * r;
const float rp = r * p;
const float pqr = pq * r;
kvs::Real32* N = m_interpolation_functions;
N[0] = 1.0f - p - q - r + pq + qr + rp - pqr;
N[1] = p - pq - rp + pqr;
N[2] = pq - pqr;
N[3] = q - pq - qr + pqr;
N[4] = r - rp - qr + pqr;
N[5] = rp - pqr;
N[6] = pqr;
N[7] = qr - pqr;
}
/*===========================================================================*/
bool CellBase::containsLocalPoint( const kvs::Vec3& local ) const
{
if ( local.x() < 0 || 1 < local.x() ) { return false; }
if ( local.y() < 0 || 1 < local.y() ) { return false; }
if ( local.z() < 0 || 1 < local.z() ) { return false; }
return true;
}
kvs::Vec3 PrismCell::globalToLocal( const kvs::Vec3 point )
{
const kvs::Vec3 X( point );
const float TinyValue = static_cast<float>( 1.e-6 );
const size_t MaxLoop = 100;
kvs::Vec3 x0( 0.3f, 0.3f, 0.5f );
for ( size_t i = 0; i < MaxLoop; i++ )
{
this->setLocalPoint( x0 );
const kvs::Vec3 X0( this->localToGlobal( x0 ) );
const kvs::Vec3 dX( X - X0 );
const kvs::Mat3 J( this->JacobiMatrix() );
const kvs::Vec3 dx = J.transposed().inverted() * dX;
if ( dx.length() < TinyValue ) break; // Converged.
x0 += dx;
}
return x0;
}
/*===========================================================================*/
const kvs::Vec3 CellBase::globalToLocal( const kvs::Vec3& global ) const
{
const kvs::Vec3 X( global );
// Calculate the coordinate of 'global' in the local coordinate
// by using Newton-Raphson method.
const float TinyValue = static_cast<float>( 1.e-6 );
const size_t MaxLoop = 100;
kvs::Vec3 x0( 0.25f, 0.25f, 0.25f ); // Initial point in local coordinate.
for ( size_t i = 0; i < MaxLoop; i++ )
{
const kvs::Vec3 X0( this->localToGlobal( x0 ) );
const kvs::Vec3 dX( X - X0 );
const kvs::Mat3 J( this->JacobiMatrix() );
const kvs::Vec3 dx = J.transposed().inverted() * dX;
if ( dx.length() < TinyValue ) break; // Converged.
x0 += dx;
}
return x0;
}
/*===========================================================================*/
bool StreamlineBase::integrate_by_runge_kutta_4th(
const kvs::Vec3& current_vertex,
const kvs::Vec3& current_direction,
kvs::Vec3* next_vertex )
{
if ( m_enable_boundary_condition )
{
if ( !this->check_for_inside_volume( current_vertex ) ) return false;
}
// Calculate integration interval.
const float integration_direction = static_cast<float>( m_integration_direction );
const kvs::Vec3 k1 = current_direction.normalized() * integration_direction;
// Interpolate vector from vertex of cell.
const kvs::Vec3 vertex2 = current_vertex + 0.5f * m_integration_interval * k1;
if ( m_enable_boundary_condition )
{
if ( !this->check_for_inside_volume( vertex2 ) ) return false;
}
const kvs::Vec3 direction2 = this->interpolate_vector( vertex2, current_direction );
const kvs::Vec3 k2 = direction2.normalized() * integration_direction;
// Interpolate vector from vertex of cell.
const kvs::Vec3 vertex3 = current_vertex + 0.5f * m_integration_interval * k2;
if ( m_enable_boundary_condition )
{
if ( !this->check_for_inside_volume( vertex3 ) ) return false;
}
const kvs::Vec3 direction3 = this->interpolate_vector( vertex3, current_direction );
const kvs::Vec3 k3 = direction3.normalized() * integration_direction;
// Interpolate vector from vertex of cell.
const kvs::Vec3 vertex4 = current_vertex + m_integration_interval * k3;
if ( m_enable_boundary_condition )
{
if ( !this->check_for_inside_volume( vertex4 ) ) return false;
}
const kvs::Vec3 direction4 = this->interpolate_vector( vertex4, current_direction );
const kvs::Vec3 k4 = direction4.normalized() * integration_direction;
*next_vertex = current_vertex + integration_direction * ( k1 + 2.0f * ( k2 + k3 ) + k4 ) / 6.0f;
return true;
}
/*===========================================================================*/
const Quaternion Quaternion::RotationQuaternion(
kvs::Vec3 v0,
kvs::Vec3 v1 )
{
Quaternion q;
v0.normalize();
v1.normalize();
kvs::Vec3 c = v0.cross( v1 );
float d = v0.x() * v1.x() + v0.y() * v1.y() + v0.z() * v1.z();
double s = std::sqrt( double( ( 1 + d ) * 2.0 ) );
q.x() = float( c.x() / s );
q.y() = float( c.y() / s );
q.z() = float( c.z() / s );
q.w() = float( s / 2.0 );
return q;
}
/*===========================================================================*/
bool StreamlineBase::integrate_by_euler(
const kvs::Vec3& current_vertex,
const kvs::Vec3& current_direction,
kvs::Vec3* next_vertex )
{
if ( m_enable_boundary_condition )
{
if ( !this->check_for_inside_volume( current_vertex ) ) return false;
}
const float integration_direction = static_cast<float>( m_integration_direction );
const kvs::Vec3 k1 = current_direction.normalized() * integration_direction;
*next_vertex = current_vertex + m_integration_interval * k1;
return true;
}
/*===========================================================================*/
bool StreamlineBase::calculate_one_side(
std::vector<kvs::Real32>* coords,
std::vector<kvs::UInt8>* colors,
const kvs::Vec3& seed_point,
const kvs::Vec3& seed_vector )
{
// Register the seed point.
kvs::Vec3 current_vertex = seed_point;
kvs::Vec3 next_vertex = seed_point;
coords->push_back( seed_point.x() );
coords->push_back( seed_point.y() );
coords->push_back( seed_point.z() );
// Register the vector on the seed point.
kvs::Vec3 current_vector = seed_vector;
kvs::Vec3 previous_vector = seed_vector;
// Set the color of seed point.
kvs::RGBColor col = this->calculate_color( current_vector );
colors->push_back( col.r() );
colors->push_back( col.g() );
colors->push_back( col.b() );
size_t integral_times = 0;
for ( ; ; )
{
// Calculate the next vertex.
if ( !this->calculate_next_vertex(
current_vertex,
current_vector,
&next_vertex ) )
{
return true;
}
// Check the termination.
if ( this->check_for_termination(
current_vertex,
current_vector,
integral_times,
next_vertex ) )
{
return true;
}
// Update the vertex and vector.
current_vertex = next_vertex;
previous_vector = current_vector;
coords->push_back( current_vertex.x() );
coords->push_back( current_vertex.y() );
coords->push_back( current_vertex.z() );
// Interpolate vector from vertex of cell.
current_vector = this->interpolate_vector( current_vertex, previous_vector );
// Set color of vertex.
kvs::RGBColor col = this->calculate_color( current_vector );
colors->push_back( col.r() );
colors->push_back( col.g() );
colors->push_back( col.b() );
integral_times++;
}
}
/*===========================================================================*/
kvs::Vec3 TetrahedralCell::globalToLocal( const kvs::Vec3& global ) const
{
const kvs::Vec3 v3( BaseClass::coord(3) );
const kvs::Vec3 v03( BaseClass::coord(0) - v3 );
const kvs::Vec3 v13( BaseClass::coord(1) - v3 );
const kvs::Vec3 v23( BaseClass::coord(2) - v3 );
const kvs::Mat3 M(
v03.x(), v13.x(), v23.x(),
v03.y(), v13.y(), v23.y(),
v03.z(), v13.z(), v23.z() );
return M.inverted() * ( global - v3 );
}
/*===========================================================================*/
kvs::Vec3 TetrahedralCell::globalPoint() const
{
const kvs::Vec3 v3( BaseClass::coord(3) );
const kvs::Vec3 v03( BaseClass::coord(0) - v3 );
const kvs::Vec3 v13( BaseClass::coord(1) - v3 );
const kvs::Vec3 v23( BaseClass::coord(2) - v3 );
const kvs::Mat3 M(
v03.x(), v13.x(), v23.x(),
v03.y(), v13.y(), v23.y(),
v03.z(), v13.z(), v23.z() );
return M * BaseClass::localPoint() + v3;
}
/*===========================================================================*/
bool StreamlineBase::check_for_inside_volume( const kvs::Vec3& point )
{
switch ( BaseClass::volume()->volumeType() )
{
case kvs::VolumeObjectBase::Structured:
{
const kvs::StructuredVolumeObject* structured_volume =
kvs::StructuredVolumeObject::DownCast( BaseClass::volume() );
switch ( structured_volume->gridType() )
{
case kvs::StructuredVolumeObject::Uniform:
{
const float dimx = static_cast<float>( structured_volume->resolution().x() - 1 );
const float dimy = static_cast<float>( structured_volume->resolution().y() - 1 );
const float dimz = static_cast<float>( structured_volume->resolution().z() - 1 );
if ( point.x() < 0.0f || dimx < point.x() ) return false;
if ( point.y() < 0.0f || dimy < point.y() ) return false;
if ( point.z() < 0.0f || dimz < point.z() ) return false;
return true;
}
case kvs::StructuredVolumeObject::Rectilinear:
{
const kvs::Vec3& min_obj = structured_volume->minObjectCoord();
const kvs::Vec3& max_obj = structured_volume->maxObjectCoord();
if ( point.x() < min_obj.x() || max_obj.x() < point.x() ) return false;
if ( point.y() < min_obj.y() || max_obj.y() < point.y() ) return false;
if ( point.z() < min_obj.z() || max_obj.z() < point.z() ) return false;
return true;
}
default: break;
}
break;
}
default: break;
}
return false;
}
/*===========================================================================*/
const kvs::Vec3 Streamline::interpolate_vector(
const kvs::Vec3& vertex,
const kvs::Vec3& previous_vector )
{
kvs::IgnoreUnusedVariable( previous_vector );
const size_t cell_x = static_cast<size_t>( vertex.x() );
const size_t cell_y = static_cast<size_t>( vertex.y() );
const size_t cell_z = static_cast<size_t>( vertex.z() );
const kvs::StructuredVolumeObject* volume = kvs::StructuredVolumeObject::DownCast( BaseClass::volume() );
const size_t resolution_x = static_cast<size_t>( volume->resolution().x() );
const size_t resolution_y = static_cast<size_t>( volume->resolution().y() );
// const size_t resolution_z = static_cast<size_t>( volume->resolution().z() );
size_t vertex_id[8];
vertex_id[0] = cell_z * resolution_x * resolution_y + cell_y * resolution_x + cell_x;
vertex_id[1] = vertex_id[0] + 1;
vertex_id[2] = vertex_id[1] + resolution_x;
vertex_id[3] = vertex_id[2] - 1;
vertex_id[4] = vertex_id[0] + resolution_x * resolution_y;
vertex_id[5] = vertex_id[4] + 1;
vertex_id[6] = vertex_id[5] + resolution_x;
vertex_id[7] = vertex_id[6] - 1;
// Weight.
const kvs::Vec3 local_coord(
2.0f * ( vertex.x() - cell_x ) - 1.0f,
2.0f * ( vertex.y() - cell_y ) - 1.0f,
2.0f * ( vertex.z() - cell_z ) - 1.0f );
const float x_min = local_coord.x() - 1.0f;
const float x_max = local_coord.x() + 1.0f;
const float y_min = local_coord.y() - 1.0f;
const float y_max = local_coord.y() + 1.0f;
const float z_min = local_coord.z() - 1.0f;
const float z_max = local_coord.z() + 1.0f;
const float weight[8] = {
-x_min * y_min * z_min * 0.125f,
x_max * y_min * z_min * 0.125f,
-x_max * y_max * z_min * 0.125f,
x_min * y_max * z_min * 0.125f,
x_min * y_min * z_max * 0.125f,
-x_max * y_min * z_max * 0.125f,
x_max * y_max * z_max * 0.125f,
-x_min * y_max * z_max * 0.125f };
// Interpolate.
const std::type_info& type = BaseClass::volume()->values().typeInfo()->type();
if ( type == typeid( kvs::Int8 ) ) return ::GetInterpolatedVector<kvs::Int8>( vertex_id, weight, BaseClass::volume() );
else if ( type == typeid( kvs::Int16 ) ) return ::GetInterpolatedVector<kvs::Int16>( vertex_id, weight, BaseClass::volume() );
else if ( type == typeid( kvs::Int32 ) ) return ::GetInterpolatedVector<kvs::Int32>( vertex_id, weight, BaseClass::volume() );
else if ( type == typeid( kvs::Int64 ) ) return ::GetInterpolatedVector<kvs::Int64>( vertex_id, weight, BaseClass::volume() );
else if ( type == typeid( kvs::UInt8 ) ) return ::GetInterpolatedVector<kvs::UInt8>( vertex_id, weight, BaseClass::volume() );
else if ( type == typeid( kvs::UInt16 ) ) return ::GetInterpolatedVector<kvs::UInt16>( vertex_id, weight, BaseClass::volume() );
else if ( type == typeid( kvs::UInt32 ) ) return ::GetInterpolatedVector<kvs::UInt32>( vertex_id, weight, BaseClass::volume() );
else if ( type == typeid( kvs::UInt64 ) ) return ::GetInterpolatedVector<kvs::UInt64>( vertex_id, weight, BaseClass::volume() );
else if ( type == typeid( kvs::Real32 ) ) return ::GetInterpolatedVector<kvs::Real32>( vertex_id, weight, BaseClass::volume() );
else if ( type == typeid( kvs::Real64 ) ) return ::GetInterpolatedVector<kvs::Real64>( vertex_id, weight, BaseClass::volume() );
return kvs::Vec3( 0.0f, 0.0f, 0.0f );
}
/*===========================================================================*/
bool StreamlineBase::check_for_vector_length( const kvs::Vec3& direction )
{
return direction.length() < m_vector_length_threshold;
}
kvs::Mat3 PrismCell::localGradient()
{
const kvs::Real32 p = m_local.x();
const kvs::Real32 q = m_local.y();
const kvs::Real32 r = m_local.z();
KVS_ASSERT( 0.0f <= p && p <= 1.0f );
KVS_ASSERT( 0.0f <= q && q <= 1.0f );
KVS_ASSERT( 0.0f <= r && r <= 1.0f );
KVS_ASSERT( p + q <= 1.0f );
const kvs::Vec3 v02 = ::Mix( this->value(0), this->value(2), q );
const kvs::Vec3 v35 = ::Mix( this->value(3), this->value(5), q );
const kvs::Vec3 v12 = ::Mix( this->value(1), this->value(2), q );
const kvs::Vec3 v45 = ::Mix( this->value(4), this->value(5), q );
const kvs::Vec3 x0 = ::Mix( v02, v35, r );
const kvs::Vec3 x1 = ::Mix( v12, v45, r );
const kvs::Vec3 v01 = ::Mix( this->value(0), this->value(1), p );
const kvs::Vec3 v34 = ::Mix( this->value(3), this->value(4), p );
const kvs::Vec3 v21 = ::Mix( this->value(2), this->value(1), p );
const kvs::Vec3 v54 = ::Mix( this->value(5), this->value(4), p );
const kvs::Vec3 y0 = ::Mix( v01, v34, r );
const kvs::Vec3 y1 = ::Mix( v21, v54, r );
const kvs::Real32 ratio = kvs::Math::IsZero( 1 - q ) ? 0.0f : p / ( 1 - q );
const kvs::Vec3 z0 = ::Mix( v02, v12, ratio );
const kvs::Vec3 z1 = ::Mix( v35, v45, ratio );
const kvs::Real32 dx = 1 - q;
const kvs::Real32 dy = 1 - p;
const kvs::Real32 dz = 1;
const kvs::Real32 dudx = ( x1.x() - x0.x() ) / dx;
const kvs::Real32 dudy = ( y1.x() - y0.x() ) / dy;
const kvs::Real32 dudz = ( z1.x() - z0.x() ) / dz;
const kvs::Real32 dvdx = ( x1.y() - x0.y() ) / dx;
const kvs::Real32 dvdy = ( y1.y() - y0.y() ) / dy;
const kvs::Real32 dvdz = ( z1.y() - z0.y() ) / dz;
const kvs::Real32 dwdx = ( x1.z() - x0.z() ) / dx;
const kvs::Real32 dwdy = ( y1.z() - y0.z() ) / dy;
const kvs::Real32 dwdz = ( z1.z() - z0.z() ) / dz;
return kvs::Mat3(
dudx, dvdx, dwdx,
dudy, dvdy, dwdy,
dudz, dvdz, dwdz );
}
kvs::RGBColor StreamlineBase::interpolatedColor( const kvs::Vec3& value )
{
return BaseClass::transferFunction().colorMap().at( value.length() );
}
/*===========================================================================*/
bool CellBase::containsInBounds( const kvs::Vec3& global ) const
{
kvs::Vec3 min_coord = this->coords()[0];
kvs::Vec3 max_coord = this->coords()[0];
const size_t nnodes = this->numberOfCellNodes();
for ( size_t i = 0; i < nnodes; i++ )
{
const kvs::Vec3 v = this->coords()[i];
min_coord.x() = kvs::Math::Min( min_coord.x(), v.x() );
min_coord.y() = kvs::Math::Min( min_coord.y(), v.y() );
min_coord.z() = kvs::Math::Min( min_coord.z(), v.z() );
max_coord.x() = kvs::Math::Max( max_coord.x(), v.x() );
max_coord.y() = kvs::Math::Max( max_coord.y(), v.y() );
max_coord.z() = kvs::Math::Max( max_coord.z(), v.z() );
}
if ( global.x() < min_coord.x() || global.x() > max_coord.x() ) { return false; }
if ( global.y() < min_coord.y() || global.y() > max_coord.y() ) { return false; }
if ( global.z() < min_coord.z() || global.z() > max_coord.z() ) { return false; }
return true;
}