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581 | /*
* SmoothCurve.cpp
*
*/
#include "SmoothCurve.hpp"
//#include "SmoothVertex.hpp"
#include "SmoothFace.hpp"
#include <cassert>
#include <iostream>
#include "moab/GeomTopoTool.hpp"
namespace moab
{
SmoothCurve::SmoothCurve( Interface* mb, EntityHandle curve, GeomTopoTool* gTool )
: _mb( mb ), _set( curve ), _gtt( gTool )
{
//_mbOut->create_meshset(MESHSET_ORDERED, _oSet);
/*_cmlEdgeMesher = new CMLEdgeMesher (this, CML::STANDARD);
_cmlEdgeMesher->set_sizing_function(CML::LINEAR_SIZING);*/
_leng = 0; // not initialized
_edgeTag = 0; // not initialized<--- Variable '_edgeTag' is assigned in constructor body. Consider performing initialization in initialization list. [+]When an object of a class is created, the constructors of all member variables are called consecutively in the order the variables are declared, even if you don't explicitly write them to the initialization list. You could avoid assigning '_edgeTag' a value by passing the value to the constructor in the initialization list.
}
SmoothCurve::~SmoothCurve()
{
// TODO Auto-generated destructor stub
}
double SmoothCurve::arc_length()
{
return _leng;
}
//! \brief Get the parametric status of the curve.
//!
//! \return \a true if curve is parametric, \a false otherwise.
bool SmoothCurve::is_parametric()<--- The function 'is_parametric' is never used.
{
return true;
}
//! \brief Get the periodic status of the curve.
//!
//! \param period The period of the curve if periodic.
//!
//! \return \a true if curve is periodic, \a false otherwise.
bool SmoothCurve::is_periodic( double& period )
{
// assert(_ref_edge);
// return _ref_edge->is_periodic( period);
Range vsets;
_mb->get_child_meshsets( _set, vsets ); // num_hops =1
if( vsets.size() == 1 )
{
period = _leng;
return true; // true , especially for ice sheet data
}
return false;
}
//! \brief Get the parameter range of the curve.
//!
//! \param u_start The beginning curve parameter
//! \param u_end The ending curve parameter
//!
//! \note The numerical value of \a u_start may be greater
//! than the numerical value of \a u_end.
void SmoothCurve::get_param_range( double& u_start, double& u_end )
{
// assert(_ref_edge);
u_start = 0;
u_end = 1.;
return;
}
//! Compute the parameter value at a specified distance along the curve.
//!
//! \param u_root The start parameter from which to compute the distance
//! along the curve.
//! \param arc_length The distance to move along the curve.
//!
//! \note For positive values of \a arc_length the distance will be
//! computed in the direction of increasing parameter value along the
//! curve. For negative values of \a arc_length the distance will be
//! computed in the direction of decreasing parameter value along the
//! curve.
//!
//! \return The parametric coordinate u along the curve
double SmoothCurve::u_from_arc_length( double u_root, double arc_leng )<--- The function 'u_from_arc_length' is never used.
{
if( _leng <= 0 ) return 0;
return u_root + arc_leng / _leng;
}
//! \brief Evaluate the curve at a specified parameter value.
//!
//! \param u The parameter at which to evaluate the curve
//! \param x The x coordinate of the evaluated point
//! \param y The y coordinate of the evaluated point
//! \param z The z coordinate of the evaluated point
bool SmoothCurve::position_from_u( double u, double& x, double& y, double& z, double* tg )
{
// _fractions are increasing, so find the
double* ptr = std::lower_bound( &_fractions[0], ( &_fractions[0] ) + _fractions.size(), u );
int index = ptr - &_fractions[0];
double nextFraction = _fractions[index];
double prevFraction = 0;
if( index > 0 )
{
prevFraction = _fractions[index - 1];
}
double t = ( u - prevFraction ) / ( nextFraction - prevFraction );
EntityHandle edge = _entities[index];
CartVect position, tangent;
ErrorCode rval = evaluate_smooth_edge( edge, t, position, tangent );
if( MB_SUCCESS != rval ) return false;
assert( rval == MB_SUCCESS );
x = position[0];
y = position[1];
z = position[2];
if( tg )
{
// we need to do some scaling,
double dtdu = 1 / ( nextFraction - prevFraction );
tg[0] = tangent[0] * dtdu;
tg[1] = tangent[1] * dtdu;
tg[2] = tangent[2] * dtdu;
}
return true;
}
//! \brief Move a point near the curve to the closest point on the curve.
//!
//! \param x The x coordinate of the point
//! \param y The y coordinate of the point
//! \param z The z coordinate of the point
void SmoothCurve::move_to_curve( double& x, double& y, double& z )
{
// find closest point to the curve, and the parametric position
// must be close by, but how close ???
EntityHandle v;
int edgeIndex;
double u = u_from_position( x, y, z, v, edgeIndex );
position_from_u( u, x, y, z );
return;
}
//! Get the u parameter value on the curve closest to x,y,z
//! and the point on the curve.
//!
//! \param x The x coordinate of the point
//! \param y The y coordinate of the point
//! \param z The z coordinate of the point
//!
//! \return The parametric coordinate u on the curve
double SmoothCurve::u_from_position( double x, double y, double z, EntityHandle& v, int& edgeIndex )
{
// this is an iterative process, expensive usually
// get first all nodes , and their positions
// find the closest node (and edge), and from there do some
// iterations up to a point
// do not exaggerate with convergence criteria
v = 0; // we do not have a close by vertex yet
CartVect initialPos( x, y, z );
double u = 0;
int nbNodes = (int)_entities.size() * 2; // the mesh edges are stored
std::vector< EntityHandle > nodesConnec;
nodesConnec.resize( nbNodes );
ErrorCode rval = this->_mb->get_connectivity( &( _entities[0] ), nbNodes / 2, nodesConnec );
if( MB_SUCCESS != rval )
{
std::cout << "error in getting connectivity\n";
return 0;
}
// collapse nodesConnec, nodes should be in order
for( int k = 0; k < nbNodes / 2; k++ )
{
nodesConnec[k + 1] = nodesConnec[2 * k + 1];
}
int numNodes = nbNodes / 2 + 1;
std::vector< CartVect > coordNodes;
coordNodes.resize( numNodes );
rval = _mb->get_coords( &( nodesConnec[0] ), numNodes, (double*)&( coordNodes[0] ) );
if( MB_SUCCESS != rval )
{
std::cout << "error in getting node positions\n";
return 0;
}
// find the closest node, then find the closest edge, based on closest node
int indexNode = 0;
double minDist = 1.e30;
// expensive linear search
for( int i = 0; i < numNodes; i++ )
{
double d1 = ( initialPos - coordNodes[i] ).length();
if( d1 < minDist )
{
indexNode = i;
minDist = d1;
}
}
double tolerance = 0.00001; // what is the unit?
// something reasonable
if( minDist < tolerance )
{
v = nodesConnec[indexNode];
// we are done, just return the proper u (from fractions)
if( indexNode == 0 )
{
return 0; // first node has u = 0
}
else
return _fractions[indexNode - 1]; // fractions[0] > 0!!)
}
// find the mesh edge; could be previous or next edge
edgeIndex = indexNode; // could be the previous one, though!!
if( edgeIndex == numNodes - 1 )
edgeIndex--; // we have one less edge, and do not worry about next edge
else
{
if( edgeIndex > 0 )
{
// could be the previous; decide based on distance to the other
// nodes of the 2 connected edges
CartVect prevNodePos = coordNodes[edgeIndex - 1];
CartVect nextNodePos = coordNodes[edgeIndex + 1];
if( ( prevNodePos - initialPos ).length_squared() < ( nextNodePos - initialPos ).length_squared() )
{
edgeIndex--;
}
}
}
// now, we know for sure that the closest point is somewhere on edgeIndex edge
//
// do newton iteration for local t between 0 and 1
// copy from evaluation method
CartVect P[2]; // P0 and P1
CartVect controlPoints[3]; // edge control points
double t4, t3, t2, one_minus_t, one_minus_t2, one_minus_t3, one_minus_t4;<--- The scope of the variable 't4' can be reduced. [+]The scope of the variable 't4' can be reduced. Warning: Be careful when fixing this message, especially when there are inner loops. Here is an example where cppcheck will write that the scope for 'i' can be reduced:
void f(int x)
{
int i = 0;
if (x) {
// it's safe to move 'int i = 0;' here
for (int n = 0; n < 10; ++n) {
// it is possible but not safe to move 'int i = 0;' here
do_something(&i);
}
}
}
When you see this message it is always safe to reduce the variable scope 1 level. <--- The scope of the variable 't3' can be reduced. [+]The scope of the variable 't3' can be reduced. Warning: Be careful when fixing this message, especially when there are inner loops. Here is an example where cppcheck will write that the scope for 'i' can be reduced:
void f(int x)
{
int i = 0;
if (x) {
// it's safe to move 'int i = 0;' here
for (int n = 0; n < 10; ++n) {
// it is possible but not safe to move 'int i = 0;' here
do_something(&i);
}
}
}
When you see this message it is always safe to reduce the variable scope 1 level. <--- The scope of the variable 't2' can be reduced. [+]The scope of the variable 't2' can be reduced. Warning: Be careful when fixing this message, especially when there are inner loops. Here is an example where cppcheck will write that the scope for 'i' can be reduced:
void f(int x)
{
int i = 0;
if (x) {
// it's safe to move 'int i = 0;' here
for (int n = 0; n < 10; ++n) {
// it is possible but not safe to move 'int i = 0;' here
do_something(&i);
}
}
}
When you see this message it is always safe to reduce the variable scope 1 level. <--- The scope of the variable 'one_minus_t' can be reduced. [+]The scope of the variable 'one_minus_t' can be reduced. Warning: Be careful when fixing this message, especially when there are inner loops. Here is an example where cppcheck will write that the scope for 'i' can be reduced:
void f(int x)
{
int i = 0;
if (x) {
// it's safe to move 'int i = 0;' here
for (int n = 0; n < 10; ++n) {
// it is possible but not safe to move 'int i = 0;' here
do_something(&i);
}
}
}
When you see this message it is always safe to reduce the variable scope 1 level. <--- The scope of the variable 'one_minus_t2' can be reduced. [+]The scope of the variable 'one_minus_t2' can be reduced. Warning: Be careful when fixing this message, especially when there are inner loops. Here is an example where cppcheck will write that the scope for 'i' can be reduced:
void f(int x)
{
int i = 0;
if (x) {
// it's safe to move 'int i = 0;' here
for (int n = 0; n < 10; ++n) {
// it is possible but not safe to move 'int i = 0;' here
do_something(&i);
}
}
}
When you see this message it is always safe to reduce the variable scope 1 level. <--- The scope of the variable 'one_minus_t3' can be reduced. [+]The scope of the variable 'one_minus_t3' can be reduced. Warning: Be careful when fixing this message, especially when there are inner loops. Here is an example where cppcheck will write that the scope for 'i' can be reduced:
void f(int x)
{
int i = 0;
if (x) {
// it's safe to move 'int i = 0;' here
for (int n = 0; n < 10; ++n) {
// it is possible but not safe to move 'int i = 0;' here
do_something(&i);
}
}
}
When you see this message it is always safe to reduce the variable scope 1 level. <--- The scope of the variable 'one_minus_t4' can be reduced. [+]The scope of the variable 'one_minus_t4' can be reduced. Warning: Be careful when fixing this message, especially when there are inner loops. Here is an example where cppcheck will write that the scope for 'i' can be reduced:
void f(int x)
{
int i = 0;
if (x) {
// it's safe to move 'int i = 0;' here
for (int n = 0; n < 10; ++n) {
// it is possible but not safe to move 'int i = 0;' here
do_something(&i);
}
}
}
When you see this message it is always safe to reduce the variable scope 1 level.
P[0] = coordNodes[edgeIndex];
P[1] = coordNodes[edgeIndex + 1];
if( 0 == _edgeTag )
{
rval = _mb->tag_get_handle( "CONTROLEDGE", 9, MB_TYPE_DOUBLE, _edgeTag );
if( rval != MB_SUCCESS ) return 0;
}
rval = _mb->tag_get_data( _edgeTag, &( _entities[edgeIndex] ), 1, (double*)&controlPoints[0] );
if( rval != MB_SUCCESS ) return rval;
// starting point
double tt = 0.5; // between the 2 ends of the edge
int iterations = 0;
// find iteratively a better point
int maxIterations = 10; // not too many
CartVect outv;
// we will solve minimize F = 0.5 * ( ini - r(t) )^2
// so solve F'(t) = 0
// Iteration: t_ -> t - F'(t)/F"(t)
// F'(t) = r'(t) (ini-r(t) )
// F"(t) = r"(t) (ini-r(t) ) - (r'(t))^2
while( iterations < maxIterations )
//
{
t2 = tt * tt;
t3 = t2 * tt;
t4 = t3 * tt;
one_minus_t = 1. - tt;
one_minus_t2 = one_minus_t * one_minus_t;
one_minus_t3 = one_minus_t2 * one_minus_t;
one_minus_t4 = one_minus_t3 * one_minus_t;
outv = one_minus_t4 * P[0] + 4. * one_minus_t3 * tt * controlPoints[0] +
6. * one_minus_t2 * t2 * controlPoints[1] + 4. * one_minus_t * t3 * controlPoints[2] + t4 * P[1];
CartVect out_tangent = -4. * one_minus_t3 * P[0] +
4. * ( one_minus_t3 - 3. * tt * one_minus_t2 ) * controlPoints[0] +
12. * ( tt * one_minus_t2 - t2 * one_minus_t ) * controlPoints[1] +
4. * ( 3. * t2 * one_minus_t - t3 ) * controlPoints[2] + 4. * t3 * P[1];
CartVect second_deriv =
12. * one_minus_t2 * P[0] +
4. * ( -3. * one_minus_t2 - 3. * one_minus_t2 + 6. * tt * one_minus_t ) * controlPoints[0] +
12. * ( one_minus_t2 - 4 * tt * one_minus_t + t2 ) * controlPoints[1] +
4. * ( 6. * tt - 12 * t2 ) * controlPoints[2] + 12. * t2 * P[1];
CartVect diff = outv - initialPos;
double F_d = out_tangent % diff;
double F_dd = second_deriv % diff + out_tangent.length_squared();
if( 0 == F_dd ) break; // get out, we found minimum?
double delta_t = -F_d / F_dd;
if( fabs( delta_t ) < 0.000001 ) break;
tt = tt + delta_t;
if( tt < 0 )
{
tt = 0.;
v = nodesConnec[edgeIndex]; // we are at end of mesh edge
break;
}
if( tt > 1 )
{
tt = 1;
v = nodesConnec[edgeIndex + 1]; // we are at one end
break;
}
iterations++;
}
// so we have t on the segment, convert to u, which should
// be between _fractions[edgeIndex] numbers
double prevFraction = 0;
if( edgeIndex > 0 ) prevFraction = _fractions[edgeIndex - 1];
u = prevFraction + tt * ( _fractions[edgeIndex] - prevFraction );
return u;
}
//! \brief Get the starting point of the curve.
//!
//! \param x The x coordinate of the start point
//! \param y The y coordinate of the start point
//! \param z The z coordinate of the start point
void SmoothCurve::start_coordinates( double& x, double& y, double& z )<--- The function 'start_coordinates' is never used.
{
int nnodes = 0;
const EntityHandle* conn2 = NULL;
_mb->get_connectivity( _entities[0], conn2, nnodes );
double c[3];
_mb->get_coords( conn2, 1, c );
x = c[0];
y = c[1];
z = c[2];
return;
}
//! \brief Get the ending point of the curve.
//!
//! \param x The x coordinate of the start point
//! \param y The y coordinate of the start point
//! \param z The z coordinate of the start point
void SmoothCurve::end_coordinates( double& x, double& y, double& z )<--- The function 'end_coordinates' is never used.
{
int nnodes = 0;
const EntityHandle* conn2 = NULL;
_mb->get_connectivity( _entities[_entities.size() - 1], conn2, nnodes );
double c[3];
// careful, the second node here
_mb->get_coords( &conn2[1], 1, c );
x = c[0];
y = c[1];
z = c[2];
return;
}
// this will recompute the 2 tangents for each edge, considering the geo edge they are into
void SmoothCurve::compute_tangents_for_each_edge()
{
// will retrieve the edges in each set; they are retrieved in order they were put into, because
// these sets are "MESHSET_ORDERED"
// retrieve the tag handle for the tangents; it should have been created already
// this tangents are computed for the chain of edges that form a geometric edge
// some checks should be performed on the vertices, but we trust the correctness of the model
// completely (like the vertices should match in the chain...)
Tag tangentsTag;
ErrorCode rval = _mb->tag_get_handle( "TANGENTS", 6, MB_TYPE_DOUBLE, tangentsTag );
if( rval != MB_SUCCESS ) return; // some error should be thrown
std::vector< EntityHandle > entities;
_mb->get_entities_by_type( _set, MBEDGE, entities ); // no recursion!!
// basically, each tangent at a node will depend on previous tangent
int nbEdges = entities.size();
// now, we can advance in the loop
// the only special problem is if the first node coincides with the last node, then we should
// consider the closed loop; or maybe we should look at angles in that case too?
// also, should we look at the 2 semi-circles case? How to decide if we need to continue the
// "tangents" maybe we can do that later, and we can alter the tangents at the feature nodes, in
// the directions of the loops again, do we need to decide the "closed" loop or not? Not yet...
EntityHandle previousEdge = entities[0]; // this is the first edge in the chain
CartVect TP[2]; // tangents for the previous edge
rval = _mb->tag_get_data( tangentsTag, &previousEdge, 1, &TP[0] ); // tangents for previous edge
if( rval != MB_SUCCESS ) return; // some error should be thrown
CartVect TC[2]; // tangents for the current edge
EntityHandle currentEdge;
for( int i = 1; i < nbEdges; i++ )
{
// current edge will start after first one
currentEdge = entities[i];
rval = _mb->tag_get_data( tangentsTag, ¤tEdge, 1, &TC[0] ); //
if( rval != MB_SUCCESS ) return; // some error should be thrown
// now compute the new tangent at common vertex; reset tangents for previous edge and
// current edge a little bit of CPU and memory waste, but this is life
CartVect T = 0.5 * TC[0] + 0.5 * TP[1]; //
T.normalize();
TP[1] = T;
rval = _mb->tag_set_data( tangentsTag, &previousEdge, 1, &TP[0] ); //
if( rval != MB_SUCCESS ) return; // some error should be thrown
TC[0] = T;
rval = _mb->tag_set_data( tangentsTag, ¤tEdge, 1, &TC[0] ); //
if( rval != MB_SUCCESS ) return; // some error should be thrown
// now set the next edge
previousEdge = currentEdge;
TP[0] = TC[0];
TP[1] = TC[1];
}
return;
}
void SmoothCurve::compute_control_points_on_boundary_edges( double,
std::map< EntityHandle, SmoothFace* >& mapSurfaces,
Tag controlPointsTag,
Tag markTag )
{
// these points really need the surfaces they belong to, because the control points on edges
// depend on the normals on surfaces
// the control points are averaged from different surfaces, by simple mean average
// the surfaces have
// do we really need min_dot here?
// first of all, find out the SmoothFace for each surface set that is adjacent here
// GeomTopoTool gTopoTool(_mb);
std::vector< EntityHandle > faces;
std::vector< int > senses;
ErrorCode rval = _gtt->get_senses( _set, faces, senses );
if( MB_SUCCESS != rval ) return;
// need to find the smooth face attached
unsigned int numSurfacesAdjacent = faces.size();
// get the edges, and then get the
// std::vector<EntityHandle> entities;
_mb->get_entities_by_type( _set, MBEDGE, _entities ); // no recursion!!
// each edge has the tangent computed already
Tag tangentsTag;
rval = _mb->tag_get_handle( "TANGENTS", 6, MB_TYPE_DOUBLE, tangentsTag );
if( rval != MB_SUCCESS ) return; // some error should be thrown
// we do not want to search every time
std::vector< SmoothFace* > smoothFaceArray;
unsigned int i = 0;
for( i = 0; i < numSurfacesAdjacent; i++ )
{
SmoothFace* sms = mapSurfaces[faces[i]];
smoothFaceArray.push_back( sms );
}
unsigned int e = 0;
for( e = 0; e < _entities.size(); e++ )
{
CartVect zero( 0. );
CartVect ctrlP[3] = { zero, zero, zero }; // null positions initially
// the control points are averaged from connected faces
EntityHandle edge = _entities[e]; // the edge in the chain
int nnodes;
const EntityHandle* conn2;
rval = _mb->get_connectivity( edge, conn2, nnodes );
if( rval != MB_SUCCESS || 2 != nnodes ) return; // or continue or return error
// double coords[6]; // store the coordinates for the nodes
CartVect P[2];
// ErrorCode rval = _mb->get_coords(conn2, 2, coords);
rval = _mb->get_coords( conn2, 2, (double*)&P[0] );
if( rval != MB_SUCCESS ) return;
CartVect chord = P[1] - P[0];
_leng += chord.length();
_fractions.push_back( _leng );
CartVect N[2];
// MBCartVect N0(&normalVec[0]);
// MBCartVect N3(&normalVec[3]);
CartVect T[2]; // T0, T3
// if (edge->num_adj_facets() <= 1) {
// stat = compute_curve_tangent(edge, min_dot, T0, T3);
// if (stat != CUBIT_SUCCESS)
// return stat;
//} else {
//}
rval = _mb->tag_get_data( tangentsTag, &edge, 1, &T[0] );
if( rval != MB_SUCCESS ) return;
for( i = 0; i < numSurfacesAdjacent; i++ )
{
CartVect controlForEdge[3];
rval = smoothFaceArray[i]->get_normals_for_vertices( conn2, N );
if( rval != MB_SUCCESS ) return;
rval = smoothFaceArray[i]->init_edge_control_points( P[0], P[1], N[0], N[1], T[0], T[1], controlForEdge );
if( rval != MB_SUCCESS ) return;
// accumulate those over faces!!!
for( int j = 0; j < 3; j++ )
{
ctrlP[j] += controlForEdge[j];
}
}
// now divide them for the average position!
for( int j = 0; j < 3; j++ )
{
ctrlP[j] /= numSurfacesAdjacent;
}
// we are done, set the control points now!
// edge->control_points(ctrl_pts, 4);
rval = _mb->tag_set_data( controlPointsTag, &edge, 1, &ctrlP[0] );
if( rval != MB_SUCCESS ) return;
this->_edgeTag = controlPointsTag; // this is a tag that will be stored with the edge
// is that a waste of memory or not...
// also mark the edge for later on
unsigned char used = 1;
_mb->tag_set_data( markTag, &edge, 1, &used );
}
// now divide fractions, to make them vary from 0 to 1
assert( _leng > 0. );
for( e = 0; e < _entities.size(); e++ )
_fractions[e] /= _leng;
}
ErrorCode SmoothCurve::evaluate_smooth_edge( EntityHandle eh, double& tt, CartVect& outv, CartVect& out_tangent )
{
CartVect P[2]; // P0 and P1
CartVect controlPoints[3]; // edge control points
double t4, t3, t2, one_minus_t, one_minus_t2, one_minus_t3, one_minus_t4;
// project the position to the linear edge
// t is from 0 to 1 only!!
// double tt = (t + 1) * 0.5;
if( tt <= 0.0 ) tt = 0.0;
if( tt >= 1.0 ) tt = 1.0;
int nnodes = 0;
const EntityHandle* conn2 = NULL;
ErrorCode rval = _mb->get_connectivity( eh, conn2, nnodes );
if( rval != MB_SUCCESS ) return rval;
rval = _mb->get_coords( conn2, 2, (double*)&P[0] );
if( rval != MB_SUCCESS ) return rval;
if( 0 == _edgeTag )
{
rval = _mb->tag_get_handle( "CONTROLEDGE", 9, MB_TYPE_DOUBLE, _edgeTag );
if( rval != MB_SUCCESS ) return rval;
}
rval = _mb->tag_get_data( _edgeTag, &eh, 1, (double*)&controlPoints[0] );
if( rval != MB_SUCCESS ) return rval;
t2 = tt * tt;
t3 = t2 * tt;
t4 = t3 * tt;
one_minus_t = 1. - tt;
one_minus_t2 = one_minus_t * one_minus_t;
one_minus_t3 = one_minus_t2 * one_minus_t;
one_minus_t4 = one_minus_t3 * one_minus_t;
outv = one_minus_t4 * P[0] + 4. * one_minus_t3 * tt * controlPoints[0] + 6. * one_minus_t2 * t2 * controlPoints[1] +
4. * one_minus_t * t3 * controlPoints[2] + t4 * P[1];
out_tangent = -4. * one_minus_t3 * P[0] + 4. * ( one_minus_t3 - 3. * tt * one_minus_t2 ) * controlPoints[0] +
12. * ( tt * one_minus_t2 - t2 * one_minus_t ) * controlPoints[1] +
4. * ( 3. * t2 * one_minus_t - t3 ) * controlPoints[2] + 4. * t3 * P[1];
return MB_SUCCESS;
}
} // namespace moab
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