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opennurbs_beziervolume.cpp
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opennurbs_beziervolume.cpp
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//
// Copyright (c) 1993-2022 Robert McNeel & Associates. All rights reserved.
// OpenNURBS, Rhinoceros, and Rhino3D are registered trademarks of Robert
// McNeel & Associates.
//
// THIS SOFTWARE IS PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY.
// ALL IMPLIED WARRANTIES OF FITNESS FOR ANY PARTICULAR PURPOSE AND OF
// MERCHANTABILITY ARE HEREBY DISCLAIMED.
//
// For complete openNURBS copyright information see <http://www.opennurbs.org>.
//
////////////////////////////////////////////////////////////////
#include "opennurbs.h"
#if !defined(ON_COMPILING_OPENNURBS)
// This check is included in all opennurbs source .c and .cpp files to insure
// ON_COMPILING_OPENNURBS is defined when opennurbs source is compiled.
// When opennurbs source is being compiled, ON_COMPILING_OPENNURBS is defined
// and the opennurbs .h files alter what is declared and how it is declared.
#error ON_COMPILING_OPENNURBS must be defined when compiling opennurbs
#endif
bool ON_BezierCage::Read(ON_BinaryArchive& archive)
{
Destroy();
int major_version = 0;
int minor_version = 0;
bool rc = archive.BeginRead3dmChunk(TCODE_ANONYMOUS_CHUNK,&major_version,&minor_version);
if ( rc )
{
while(rc)
{
if ( major_version != 1 )
{
ON_ERROR("ON_BezierCage::Read - old code unable to read new version of chunk");
rc = false;
break;
}
int dim=0,order0=0,order1=0,order2=0;
bool is_rat=false;
rc = archive.ReadInt(&dim);
if (!rc)
break;
if (dim < 1 || dim > 10000)
{
ON_ERROR("ON_BezierCage::Read - invalid dim");
rc=false;
break;
}
rc = archive.ReadBool(&is_rat);
if (!rc)
break;
rc = archive.ReadInt(&order0);
if (!rc)
break;
if ( order0 < 2 || order0 > 10000 )
{
ON_ERROR("ON_BezierCage::Read - invalid order0");
rc=false;
break;
}
rc = archive.ReadInt(&order1);
if (!rc)
break;
if ( order1 < 2 || order1 > 10000 )
{
ON_ERROR("ON_BezierCage::Read - invalid order1");
rc=false;
break;
}
rc = archive.ReadInt(&order2);
if (!rc)
break;
if ( order2 < 2 || order2 > 10000 )
{
ON_ERROR("ON_BezierCage::Read - invalid order2");
rc=false;
break;
}
rc = Create(dim,is_rat,order0,order1,order2);
if (!rc)
break;
int i,j,k;
const int cv_dim = m_is_rat?(m_dim+1):m_dim;
for(i = 0; i < order0 && rc; i++)
{
for(j = 0; j < order1 && rc; j++)
{
for ( k = 0; k < order2 && rc; k++)
{
rc = archive.ReadDouble(cv_dim,CV(i,j,k));
}
}
}
break;
}
if ( !archive.EndRead3dmChunk() )
{
rc = false;
}
}
return rc;
}
bool ON_BezierCage::Write(ON_BinaryArchive& archive) const
{
bool rc = archive.BeginWrite3dmChunk(TCODE_ANONYMOUS_CHUNK,1,0);
if (rc)
{
rc = archive.WriteInt(m_dim);
if(rc)
rc = archive.WriteInt(m_is_rat);
if (rc)
rc = archive.WriteInt(m_order[0]);
if (rc)
rc = archive.WriteInt(m_order[1]);
if (rc)
rc = archive.WriteInt(m_order[2]);
int i,j,k;
const int cv_dim = m_is_rat?(m_dim+1):m_dim;
double* bogus_cv = 0;
for(i = 0; i < m_order[0] && rc; i++)
{
for(j = 0; j < m_order[1] && rc; j++)
{
for ( k = 0; k < m_order[2] && rc; k++)
{
const double* cv = CV(i,j,k);
if ( !cv )
{
if ( 0 == bogus_cv )
{
bogus_cv = (double*)onmalloc(cv_dim*sizeof(*bogus_cv));
for ( int n = 0; n < cv_dim; n++ )
bogus_cv[n] = ON_UNSET_VALUE;
}
cv = bogus_cv;
}
rc = archive.WriteDouble(cv_dim,cv);
}
}
}
if ( 0 != bogus_cv )
onfree(bogus_cv);
if ( !archive.EndWrite3dmChunk() )
{
rc = false;
}
}
return rc;
}
ON_BezierCage::ON_BezierCage()
: m_dim(0),m_is_rat(0),m_cv_capacity(0),m_cv(0)
{
m_order[0] = 0;
m_order[1] = 0;
m_order[2] = 0;
m_cv_stride[0] = 0;
m_cv_stride[1] = 0;
m_cv_stride[2] = 0;
}
ON_BezierCage::ON_BezierCage( int dim, bool is_rat, int order0, int order1, int order2 )
: m_dim(0),m_is_rat(0),m_cv_capacity(0),m_cv(0)
{
m_order[0] = 0;
m_order[1] = 0;
m_order[2] = 0;
m_cv_stride[0] = 0;
m_cv_stride[1] = 0;
m_cv_stride[2] = 0;
Create( dim, is_rat, order0, order1, order2 );
}
ON_BezierCage::ON_BezierCage( const ON_BoundingBox& bbox, int order0, int order1, int order2 )
: m_dim(0),m_is_rat(0),m_cv_capacity(0),m_cv(0)
{
Create(bbox,order0,order1,order2);
}
ON_BezierCage::ON_BezierCage( const ON_3dPoint* box_corners, int order0, int order1, int order2 )
: m_dim(0),m_is_rat(0),m_cv_capacity(0),m_cv(0)
{
Create(box_corners,order0,order1,order2);
}
ON_BezierCage::~ON_BezierCage()
{
Destroy();
}
ON_BezierCage::ON_BezierCage(const ON_BezierCage& src)
: m_dim(0),m_is_rat(0),m_cv_capacity(0),m_cv(0)
{
m_order[0] = 0;
m_order[1] = 0;
m_order[2] = 0;
m_cv_stride[0] = 0;
m_cv_stride[1] = 0;
m_cv_stride[2] = 0;
*this = src;
}
ON_BezierCage& ON_BezierCage::operator=(const ON_BezierCage& src)
{
if ( this != &src ) {
if ( Create( src.m_dim, src.m_is_rat,
src.m_order[0], src.m_order[1], src.m_order[2] ) )
{
const int sizeof_cv = src.CVSize()*sizeof(m_cv[0]);
int i, j, k;
for ( i = 0; i < m_order[0]; i++ )
for ( j = 0; j < m_order[1]; j++ )
for ( k = 0; k < m_order[2]; k++ )
{
memcpy( CV(i,j,k), src.CV(i,j,k), sizeof_cv );
}
}
else
{
Destroy();
}
}
return *this;
}
bool ON_BezierCage::IsValid() const
{
if ( m_cv == nullptr )
return false;
if ( m_order[0] < 2 )
return false;
if ( m_order[1] < 2 )
return false;
if ( m_order[2] < 2 )
return false;
if ( m_dim <= 0 )
return false;
if ( m_is_rat != 0 && m_is_rat != 1 )
return false;
const int cvdim = m_is_rat ? (m_dim+1) : m_dim;
if ( m_cv_capacity > 0 && m_cv_capacity < cvdim*m_order[0]*m_order[1]*m_order[2] )
return false;
int i[3];
i[0] = (m_cv_stride[0] <= m_cv_stride[1]) ? 0 : 1;
i[1] = 1-i[0];
if ( m_cv_stride[2] < m_cv_stride[i[0]] )
{
i[2] = i[1];
i[1] = i[0];
i[0] = 2;
}
else if ( m_cv_stride[2] < m_cv_stride[i[1]] )
{
i[2] = i[1];
i[1] = 2;
}
else
{
i[2] = 2;
}
if ( m_cv_stride[i[0]] < cvdim )
return false;
if ( m_cv_stride[i[1]] < m_cv_stride[i[0]]*m_order[i[0]] )
return false;
if ( m_cv_stride[i[2]] < m_cv_stride[i[1]]*m_order[i[1]] )
return false;
return true;
}
void ON_BezierCage::Dump( ON_TextLog& dump ) const
{
dump.Print( "ON_BezierCage dim = %d is_rat = %d\n"
" order = (%d, %d, %d) \n",
m_dim, m_is_rat, m_order[0], m_order[1], m_order[2] );
dump.Print( "Control Points %d %s points\n"
" index value\n",
m_order[0]*m_order[1]*m_order[2],
(m_is_rat) ? "rational" : "non-rational" );
if ( !m_cv )
{
dump.Print(" nullptr cv array\n");
}
else
{
int i,j;
char sPreamble[128] = { 0 };
const size_t sPremable_capacity = sizeof(sPreamble) / sizeof(sPreamble[0]);
for ( i = 0; i < m_order[0]; i++ )
{
for ( j = 0; j < m_order[1]; j++ )
{
if ( i > 0 || j > 0)
dump.Print("\n");
ON_String::FormatIntoBuffer(sPreamble, sPremable_capacity," CV[%2d][%2d]", i, j);
dump.PrintPointList( m_dim, m_is_rat,
m_order[2], m_cv_stride[2],
CV(i,j,0),
sPreamble );
}
if ( i < m_order[0]-1)
dump.Print("\n");
}
}
}
int ON_BezierCage::Dimension() const
{
return m_dim;
}
bool ON_BezierCage::Create( const ON_BoundingBox& bbox, int order0, int order1, int order2 )
{
/*
7______________6
|\ |\
| \ | \
| \ _____________\
| 4 | 5
| | | |
| | | |
3---|----------2 |
\ | \ |
\ |z \ |
y \ | \ |
\0_____________\1
x
*/
ON_3dPoint box_corners[8];
box_corners[0] = bbox.Corner(0,0,0);
box_corners[1] = bbox.Corner(1,0,0);
box_corners[2] = bbox.Corner(1,1,0);
box_corners[3] = bbox.Corner(0,1,0);
box_corners[4] = bbox.Corner(0,0,1);
box_corners[5] = bbox.Corner(1,0,1);
box_corners[6] = bbox.Corner(1,1,1);
box_corners[7] = bbox.Corner(0,1,1);
return Create(box_corners,order0,order1,order2);
}
bool ON_BezierCage::Create( int dim, bool is_rat, int order0, int order1, int order2 )
{
if ( m_cv_capacity < 1 )
m_cv = 0;
m_dim = (dim>0) ? dim : 0;
m_is_rat = is_rat ? 1 : 0;
m_order[0] = (order0 >= 2) ? order0 : 0;
m_order[1] = (order1 >= 2) ? order1 : 0;
m_order[2] = (order2 >= 2) ? order2 : 0;
m_cv_stride[2] = (m_dim > 0) ? m_dim+m_is_rat : 0;
m_cv_stride[1] = m_cv_stride[2]*m_order[2];
m_cv_stride[0] = m_cv_stride[1]*m_order[1];
m_cv_capacity = m_cv_stride[0]*m_order[0];
m_cv = (double*)onrealloc( m_cv, m_cv_capacity*sizeof(m_cv[0]) );
return IsValid() ? true : false;
}
bool ON_BezierCage::Create(
const ON_3dPoint* box_corners,
int order0,
int order1,
int order2
)
{
int i, j, k;
double r,s,t;
if ( 0 == box_corners )
return false;
for( i = 0; i < 8; i++ )
{
if ( !box_corners[i].IsValid() )
return false;
}
// create trilinear "cube" to make it easy
// to calculate CV locations.
ON_BezierCage cube(3,0,2,2,2);
cube.SetCV(0,0,0,box_corners[0]);
cube.SetCV(1,0,0,box_corners[1]);
cube.SetCV(1,1,0,box_corners[2]);
cube.SetCV(0,1,0,box_corners[3]);
cube.SetCV(0,0,1,box_corners[4]);
cube.SetCV(1,0,1,box_corners[5]);
cube.SetCV(1,1,1,box_corners[6]);
cube.SetCV(0,1,1,box_corners[7]);
if ( 2 == order0 && 2 == order1 && 2 == order2 )
{
operator=(cube);
}
else
{
if (!Create(3,0,order0,order1,order2))
return false;
const int d0 = Degree(0);
const int d1 = Degree(1);
const int d2 = Degree(2);
for (i = 0; i <= d0; i++)
{
r = ((double)i)/((double)d0);
for (j = 0; j <= d1; j++)
{
s = ((double)j)/((double)d1);
for (k = 0; k <= d2; k++)
{
t = ((double)k)/((double)d2);
SetCV(i,j,k,cube.PointAt(r,s,t));
}
}
}
}
return IsValid();
}
void ON_BezierCage::Destroy()
{
if ( m_cv && m_cv_capacity > 0 )
onfree(m_cv);
m_cv_capacity = 0;
m_cv_stride[0] = 0;
m_cv_stride[1] = 0;
m_cv_stride[2] = 0;
m_cv = 0;
m_dim = 0;
m_is_rat = 0;
m_order[0] = 0;
m_order[1] = 0;
m_order[2] = 0;
}
void ON_BezierCage::EmergencyDestroy()
{
m_cv_capacity = 0;
m_cv_stride[0] = 0;
m_cv_stride[1] = 0;
m_cv_stride[2] = 0;
m_cv = 0;
m_dim = 0;
m_is_rat = 0;
m_order[0] = 0;
m_order[1] = 0;
m_order[2] = 0;
}
bool ON_BezierCage::GetBBox( // returns true if successful
double* boxmin, // minimum
double* boxmax, // maximum
bool bGrowBox // true means grow box
) const
{
int i, j;
bool rc = (m_order[0] > 0 && m_order[1] > 0 && m_order[2] > 0) ? true : false;
for ( i = 0; rc && i < m_order[0]; i++ )
for ( j = 0; rc && j < m_order[1]; j++ )
{
rc = ON_GetPointListBoundingBox( m_dim, m_is_rat, m_order[2], m_cv_stride[2],
CV(i,j,0), boxmin, boxmax, bGrowBox );
bGrowBox = true;
}
return rc;
}
bool ON_BezierCage::Transform( const ON_Xform& xform )
{
int i,j;
bool rc = (m_order[0] > 0 && m_order[1] > 0 && m_order[2]) ? true : false;
if (rc)
{
if ( 0 == m_is_rat )
{
if ( xform.m_xform[3][0] != 0.0 || xform.m_xform[3][1] != 0.0 || xform.m_xform[3][2] != 0.0 )
{
MakeRational();
}
}
for ( i = 0; rc && i < m_order[0]; i++ )
{
for ( j = 0; rc && j < m_order[1]; j++ )
{
rc = ON_TransformPointList( m_dim, m_is_rat,
m_order[2], m_cv_stride[2],
CV(i,j,0), xform );
}
}
}
return rc;
}
bool ON_BezierCage::Rotate(
double sin_angle, // sin(angle)
double cos_angle, // cos(angle)
const ON_3dVector& axis, // axis of rotation
const ON_3dPoint& center // center of rotation
)
{
ON_Xform rot;
rot.Rotation( sin_angle, cos_angle, axis, center );
return Transform( rot );
}
bool ON_BezierCage::Rotate(
double angle, // angle in radians
const ON_3dVector& axis, // axis of rotation
const ON_3dPoint& center // center of rotation
)
{
return Rotate( sin(angle), cos(angle), axis, center );
}
bool ON_BezierCage::Translate( const ON_3dVector& delta )
{
ON_Xform tr(ON_Xform::TranslationTransformation( delta ));
return Transform( tr );
}
bool ON_BezierCage::Scale( double x )
{
ON_Xform s(ON_Xform::DiagonalTransformation(x));
return Transform( s );
}
ON_Interval ON_BezierCage::Domain(
int // dir - formal parameter intentionally ignored in this virtual function
) const
{
return ON_Interval(0.0,1.0);
}
bool ON_BezierCage::Evaluate( // returns false if unable to evaluate
double r, double s, double t, // evaluation parameter
int der_count, // number of derivatives (>=0)
int v_stride, // array stride (>=Dimension())
double* v // array of length stride*(ndir+1)*(ndir+2)/2
) const
{
const int cvdim = m_is_rat?(m_dim+1):m_dim;
int i,j,k,n;
double Barray[64], vtmparray[10*4], Bi, Bij, Bijk, *Bj, *Bk, *vtmp;
const double* CVi;
const double* CVij;
const double* CVijk;
void* freeme1 = 0;
void* freeme2 = 0;
size_t sz;
if ( der_count > 0 )
{
// TODO - time to add support for derivative evaluation
ON_ERROR("ON_BezierCage::Evaluate does not evaluate derivatives");
}
sz = cvdim*sizeof(*vtmp);
vtmp = m_is_rat
? (sz <= sizeof(vtmparray) ? vtmparray : (double*)(freeme1 = onmalloc(sz)))
: v;
memset(vtmp,0,sz);
// get arrays to hold values of Bernstein basis functions
sz = (m_order[1]+m_order[2])*sizeof(*Bj);
Bj = (sz <= sizeof(Barray))
? Barray
: ((double*)(freeme2=onmalloc( sz ) ));
Bk = Bj + m_order[1];
const int d2 = m_order[2]-1;
for ( k = 0; k <= d2; k++)
{
Bk[k] = ON_EvaluateBernsteinBasis(d2,k,t);
}
const int d1 = m_order[1]-1;
for ( j = 0; j <= d1; j++)
{
Bj[j] = ON_EvaluateBernsteinBasis(d1,j,s);
}
const int d0 = m_order[0]-1;
for ( i = 0; i <= d0; i++ )
{
CVi = m_cv + i*m_cv_stride[0];
Bi = ON_EvaluateBernsteinBasis(d0,i,r);
for ( j = 0; j <= d1; j++ )
{
CVij = CVi + j*m_cv_stride[1];
Bij = Bi*Bj[j];
for ( k = 0; k <= d2; k++ )
{
CVijk = CVij + k*m_cv_stride[2];
Bijk = Bij*Bk[k];
n = cvdim;
while(n--)
{
*vtmp++ += *CVijk++ * Bijk;
}
vtmp -= cvdim;
}
}
}
if ( m_is_rat )
{
Bi = (vtmp[m_dim] != 0.0) ? (1.0/vtmp[m_dim]) : 1.0;
for ( n = 0; n < m_dim; n++ )
{
v[n] = vtmp[n]*Bi;
}
}
if ( 0 != freeme1 )
onfree(freeme1);
if ( 0 != freeme2 )
onfree(freeme2);
return (0 == der_count);
}
ON_3dPoint ON_BezierCage::PointAt(
double r,
double s,
double t
) const
{
ON_3dPoint pt;
if ( m_dim <= 3 )
{
pt.x = 0.0;
pt.y = 0.0;
pt.z = 0.0;
Evaluate(r,s,t,0,3,&pt.x);
}
else
{
double stack_buffer[16];
double* v;
size_t sizeof_buffer = m_dim*sizeof(*v);
v = (sizeof_buffer <= sizeof(stack_buffer)) ? stack_buffer : (double*)onmalloc(sizeof_buffer);
v[0] = 0.0;
v[1] = 0.0;
v[2] = 0.0;
Evaluate(r,s,t,0,m_dim,v);
pt.x = v[0];
pt.y = v[1];
pt.z = v[2];
if ( v != stack_buffer )
onfree(v);
}
return pt;
}
ON_3dPoint ON_BezierCage::PointAt( ON_3dPoint rst ) const
{
ON_3dPoint pt;
if ( m_dim <= 3 )
{
pt.x = 0.0;
pt.y = 0.0;
pt.z = 0.0;
Evaluate(rst.x,rst.y,rst.z,0,3,&pt.x);
}
else
{
double stack_buffer[16];
double* v;
size_t sizeof_buffer = m_dim*sizeof(*v);
v = (sizeof_buffer <= sizeof(stack_buffer)) ? stack_buffer : (double*)onmalloc(sizeof_buffer);
v[0] = 0.0;
v[1] = 0.0;
v[2] = 0.0;
Evaluate(rst.x,rst.y,rst.z,0,m_dim,v);
pt.x = v[0];
pt.y = v[1];
pt.z = v[2];
if ( v != stack_buffer )
onfree(v);
}
return pt;
}
bool ON_BezierCage::IsRational() const
{
return m_is_rat ? true : false;
}
int ON_BezierCage::CVSize() const
{
return ( m_is_rat && m_dim>0 ) ? m_dim+1 : m_dim;
}
int ON_BezierCage::Order( int dir ) const
{
return (dir>=0&&dir<=2) ? m_order[dir] : 0;
}
int ON_BezierCage::Degree(int dir) const
{
int order = Order(dir);
return (order>=2) ? order-1 : 0;
}
double* ON_BezierCage::CV( int i, int j, int k ) const
{
#if defined(ON_DEBUG)
if ( 0 == m_cv )
{
ON_ERROR("ON_BezierCage::CV - nullptr m_cv");
return 0;
}
if ( i < 0 || i >= m_order[0] || j< 0 || j >= m_order[1] || k < 0 || k >= m_order[2])
{
ON_ERROR("ON_BezierCage::CV - (i,j,k) out of range");
return 0;
}
#endif
return (m_cv) ? (m_cv + i*m_cv_stride[0] + j*m_cv_stride[1] + k*m_cv_stride[2]) : 0;
}
ON::point_style ON_BezierCage::CVStyle() const
{
return m_is_rat ? ON::homogeneous_rational : ON::not_rational;
}
double ON_BezierCage::Weight( int i, int j, int k ) const
{
return (m_cv && m_is_rat) ? m_cv[i*m_cv_stride[0] + j*m_cv_stride[1] + k*m_cv_stride[2] + + m_dim] : 1.0;
}
bool ON_BezierCage::SetWeight( int i, int j, int k, double w )
{
bool rc = false;
if ( m_is_rat )
{
double* cv = CV(i,j,k);
if (cv)
{
cv[m_dim] = w;
rc = true;
}
}
else if ( w == 1.0 )
{
rc = true;
}
return rc;
}
bool ON_BezierCage::SetCV( int i, int j, int k, ON::point_style style, const double* Point )
{
bool rc = true;
int n;
double w;
double* cv = CV(i,j,k);
if ( !cv )
return false;
switch ( style ) {
case ON::not_rational: // input Point is not rational
memcpy( cv, Point, m_dim*sizeof(*cv) );
if ( IsRational() ) {
// NURBS surface is rational - set weight to one
cv[m_dim] = 1.0;
}
break;
case ON::homogeneous_rational: // input Point is homogeneous rational
if ( IsRational() ) {
// NURBS surface is rational
memcpy( cv, Point, (m_dim+1)*sizeof(*cv) );
}
else {
// NURBS surface is not rational
w = (Point[m_dim] != 0.0) ? 1.0/Point[m_dim] : 1.0;
for ( n = 0; n < m_dim; n++ ) {
cv[n] = w*Point[n];
}
}
break;
case ON::euclidean_rational: // input Point is euclidean rational
if ( IsRational() ) {
// NURBS surface is rational - convert euclean point to homogeneous form
w = Point[m_dim];
for ( n = 0; n < m_dim; n++ )
cv[i] = w*Point[i];
cv[m_dim] = w;
}
else {
// NURBS surface is not rational
memcpy( cv, Point, m_dim*sizeof(*cv) );
}
break;
case ON::intrinsic_point_style:
n = m_is_rat?m_dim+1:m_dim;
memcpy(cv,Point,n*sizeof(*cv));
break;
default:
rc = false;
break;
}
return rc;
}
bool ON_BezierCage::SetCV( int i, int j, int k, const ON_3dPoint& point )
{
bool rc = false;
double* cv = CV(i,j,k);
if ( cv ) {
cv[0] = point.x;
if ( m_dim > 1 ) {
cv[1] = point.y;
if ( m_dim > 2 )
cv[2] = point.z;
}
if ( m_is_rat ) {
cv[m_dim] = 1.0;
}
rc = true;
}
return rc;
}
bool ON_BezierCage::SetCV( int i, int j, int k, const ON_4dPoint& point )
{
bool rc = false;
double* cv = CV(i,j,k);
if ( cv ) {
if ( m_is_rat ) {
cv[0] = point.x;
if ( m_dim > 1 ) {
cv[1] = point.y;
if ( m_dim > 2 )
cv[2] = point.z;
}
cv[m_dim] = point.w;
rc = true;
}
else {
double w;
if ( point.w != 0.0 ) {
w = 1.0/point.w;
rc = true;
}
else {
w = 1.0;
}
cv[0] = w*point.x;
if ( m_dim > 1 ) {
cv[1] = w*point.y;
if ( m_dim > 2 ) {
cv[2] = w*point.z;
}
}
}
}
return rc;
}
bool ON_BezierCage::GetCV( int i, int j, int k, ON::point_style style, double* Point ) const
{
const double* cv = CV(i,j,k);
if ( !cv )
return false;
int dim = Dimension();
double w = ( IsRational() ) ? cv[dim] : 1.0;
switch(style) {
case ON::euclidean_rational:
Point[dim] = w;
// no break here
case ON::not_rational:
if ( w == 0.0 )
return false;
w = 1.0/w;
while(dim--) *Point++ = *cv++ * w;
break;
case ON::homogeneous_rational:
Point[dim] = w;
memcpy( Point, cv, dim*sizeof(*Point) );
break;
default:
return false;
}
return true;
}
bool ON_BezierCage::GetCV( int i, int j, int k, ON_3dPoint& point ) const
{
bool rc = false;
const double* cv = CV(i,j,k);
if ( cv ) {
if ( m_is_rat ) {
if (cv[m_dim] != 0.0) {
const double w = 1.0/cv[m_dim];
point.x = cv[0]*w;
point.y = (m_dim>1)? cv[1]*w : 0.0;
point.z = (m_dim>2)? cv[2]*w : 0.0;
rc = true;
}
}
else {
point.x = cv[0];
point.y = (m_dim>1)? cv[1] : 0.0;
point.z = (m_dim>2)? cv[2] : 0.0;
rc = true;
}
}
return rc;
}
bool ON_BezierCage::GetCV( int i, int j, int k, ON_4dPoint& point ) const
{
bool rc = false;
const double* cv = CV(i,j,k);
if ( cv ) {
point.x = cv[0];
point.y = (m_dim>1)? cv[1] : 0.0;
point.z = (m_dim>2)? cv[2] : 0.0;
point.w = (m_is_rat) ? cv[m_dim] : 1.0;
rc = true;
}
return rc;
}
bool ON_BezierCage::ZeroCVs()
{
// zeros control vertices and, if rational, sets weights to 1
bool rc = false;
int i,j,k;
if ( m_cv ) {
if ( m_cv_capacity > 0 ) {
memset( m_cv, 0, m_cv_capacity*sizeof(*m_cv) );
if ( m_is_rat ) {
for ( i = 0; i < m_order[0]; i++ ) {
for ( j = 0; j < m_order[1]; j++ ) {
for ( k = 0; k < m_order[2]; k++ ) {
SetWeight( i,j,k, 1.0 );
}
}
}
}
rc = true;
}
else {
double* cv;
int s = CVSize()*sizeof(*cv);
for ( i = 0; i < m_order[0]; i++ ) {
for ( j = 0; j < m_order[1]; j++ ) {
for ( k = 0; k < m_order[2]; k++ ) {
cv = CV(i,j,k);
memset(cv,0,s);
if ( m_is_rat )
cv[m_dim] = 1.0;
}
}
}
rc = (i>0) ? true : false;
}
}
return rc;
}
bool ON_BezierCage::MakeRational()
{