bool ON_Matrix::Invert( double zero_tolerance )
{
ON_Workspace ws;
int i, j, k, ix, jx, rank;
double x;
const int n = MinCount();
if ( n < 1 )
return false;
ON_Matrix I(m_col_count, m_row_count);
int* col = ws.GetIntMemory(n);
I.SetDiagonal(1.0);
rank = 0;
double** this_m = ThisM();
for ( k = 0; k < n; k++ ) {
// find largest value in sub matrix
ix = jx = k;
x = fabs(this_m[ix][jx]);
for ( i = k; i < n; i++ ) {
for ( j = k; j < n; j++ ) {
if ( fabs(this_m[i][j]) > x ) {
ix = i;
jx = j;
x = fabs(this_m[ix][jx]);
}
}
}
SwapRows( k, ix );
I.SwapRows( k, ix );
SwapCols( k, jx );
col[k] = jx;
if ( x <= zero_tolerance ) {
break;
}
x = 1.0/this_m[k][k];
this_m[k][k] = 1.0;
ON_ArrayScale( m_col_count-k-1, x, &this_m[k][k+1], &this_m[k][k+1] );
I.RowScale( k, x );
// zero this_m[!=k][k]'s
for ( i = 0; i < n; i++ ) {
if ( i != k ) {
x = -this_m[i][k];
this_m[i][k] = 0.0;
if ( fabs(x) > zero_tolerance ) {
ON_Array_aA_plus_B( m_col_count-k-1, x, &this_m[k][k+1], &this_m[i][k+1], &this_m[i][k+1] );
I.RowOp( i, x, k );
}
}
}
}
// take care of column swaps
for ( i = k-1; i >= 0; i-- ) {
if ( i != col[i] )
I.SwapRows(i,col[i]);
}
*this = I;
return (k == n) ? true : false;
}
bool ON_BrepExtrude(
ON_Brep& brep,
const ON_Curve& path_curve,
bool bCap
)
{
ON_Workspace ws;
const int vcount0 = brep.m_V.Count();
const int tcount0 = brep.m_T.Count();
const int lcount0 = brep.m_L.Count();
const int ecount0 = brep.m_E.Count();
const int fcount0 = brep.m_F.Count();
const ON_3dPoint PathStart = path_curve.PointAtStart();
ON_3dPoint P = path_curve.PointAtEnd();
if ( !PathStart.IsValid() || !P.IsValid() )
return false;
const ON_3dVector height = P - PathStart;
if ( !height.IsValid() || height.Length() <= ON_ZERO_TOLERANCE )
return false;
ON_Xform tr;
tr.Translation(height);
// count number of new sides
int side_count = 0;
int i, vi, ei, fi;
bool* bSideEdge = (bool*)ws.GetIntMemory(ecount0*sizeof(bSideEdge[0]));
for ( ei = 0; ei < ecount0; ei++ )
{
const ON_BrepEdge& e = brep.m_E[ei];
if ( 1 == e.m_ti.Count() )
{
side_count++;
bSideEdge[ei] = true;
}
else
{
bSideEdge[ei] = false;
}
}
brep.m_V.Reserve( 2*vcount0 );
i = 4*side_count + (bCap?tcount0:0);
brep.m_T.Reserve( tcount0 + i );
brep.m_C2.Reserve( brep.m_C2.Count() + i );
brep.m_L.Reserve( lcount0 + side_count + (bCap?lcount0:0) );
i = side_count + (bCap?ecount0:side_count);
brep.m_E.Reserve( ecount0 + i );
brep.m_C3.Reserve( brep.m_C3.Count() + i );
i = side_count + (bCap?fcount0:0);
brep.m_F.Reserve( fcount0 + i );
brep.m_S.Reserve( brep.m_S.Count() + i );
bool bOK = true;
// build top vertices
int* topvimap = ws.GetIntMemory(vcount0);
memset(topvimap,0,vcount0*sizeof(topvimap[0]));
if ( bCap )
{
for ( vi = 0; vi < vcount0; vi++ )
{
const ON_BrepVertex& bottomv = brep.m_V[vi];
ON_BrepVertex& topv = brep.NewVertex(bottomv.point+height,bottomv.m_tolerance);
topvimap[vi] = topv.m_vertex_index;
}
}
else
{
for ( ei = 0; ei < ecount0; ei++ )
{
if ( bSideEdge[ei] )
{
const ON_BrepEdge& bottome = brep.m_E[ei];
int bottomvi0 = bottome.m_vi[0];
if ( bottomvi0 < 0 || bottomvi0 >= vcount0 )
{
bOK = false;
break;
}
int bottomvi1 = bottome.m_vi[1];
if ( bottomvi1 < 0 || bottomvi1 >= vcount0 )
{
bOK = false;
break;
}
if ( !topvimap[bottomvi0] )
{
const ON_BrepVertex& bottomv = brep.m_V[bottomvi0];
ON_BrepVertex& topv = brep.NewVertex(bottomv.point+height,bottomv.m_tolerance);
topvimap[bottomvi0] = topv.m_vertex_index;
}
if ( !topvimap[bottomvi1] )
{
const ON_BrepVertex& bottomv = brep.m_V[bottomvi1];
ON_BrepVertex& topv = brep.NewVertex(bottomv.point+height,bottomv.m_tolerance);
topvimap[bottomvi1] = topv.m_vertex_index;
}
}
}
}
// build top edges
int* topeimap = ws.GetIntMemory(ecount0);
memset(topeimap,0,ecount0*sizeof(topeimap[0]));
if ( bOK ) for ( ei = 0; ei < ecount0; ei++ )
{
if ( bCap || bSideEdge[ei] )
{
const ON_BrepEdge& bottome = brep.m_E[ei];
ON_BrepVertex& topv0 = brep.m_V[topvimap[bottome.m_vi[0]]];
ON_BrepVertex& topv1 = brep.m_V[topvimap[bottome.m_vi[1]]];
ON_Curve* c3 = bottome.DuplicateCurve();
if ( !c3 )
{
bOK = false;
break;
}
c3->Transform(tr);
int c3i = brep.AddEdgeCurve(c3);
ON_BrepEdge& tope = brep.NewEdge(topv0,topv1,c3i,0,bottome.m_tolerance);
topeimap[ei] = tope.m_edge_index;
}
}
// build side edges
int* sideveimap = ws.GetIntMemory(vcount0);
memset(sideveimap,0,vcount0*sizeof(sideveimap[0]));
if ( bOK ) for ( vi = 0; vi < vcount0; vi++ )
{
ON_BrepVertex& bottomv = brep.m_V[vi];
for ( int vei = 0; vei < bottomv.m_ei.Count(); vei++ )
{
if ( bSideEdge[bottomv.m_ei[vei]] && topvimap[vi] )
{
ON_BrepVertex& topv = brep.m_V[topvimap[vi]];
ON_Curve* c3 = path_curve.DuplicateCurve();
if ( !c3 )
{
bOK = false;
}
else
{
ON_3dVector D = bottomv.point - PathStart;
c3->Translate(D);
int c3i = brep.AddEdgeCurve(c3);
const ON_BrepEdge& e = brep.NewEdge(bottomv,topv,c3i,0,0.0);
sideveimap[vi] = e.m_edge_index;
}
break;
}
}
}
if ( bOK && bCap )
{
// build top faces
for (fi = 0; fi < fcount0; fi++ )
{
const ON_BrepFace& bottomf = brep.m_F[fi];
ON_Surface* srf = bottomf.DuplicateSurface();
if ( !srf )
{
bOK = false;
break;
}
srf->Transform(tr);
int si = brep.AddSurface(srf);
ON_BrepFace& topf = brep.NewFace(si);
topf.m_bRev = !bottomf.m_bRev;
const int loop_count = bottomf.m_li.Count();
topf.m_li.Reserve(loop_count);
for ( int fli = 0; fli < loop_count; fli++ )
{
const ON_BrepLoop& bottoml = brep.m_L[bottomf.m_li[fli]];
ON_BrepLoop& topl = brep.NewLoop(bottoml.m_type,topf);
const int loop_trim_count = bottoml.m_ti.Count();
topl.m_ti.Reserve(loop_trim_count);
for ( int lti = 0; lti < loop_trim_count; lti++ )
{
const ON_BrepTrim& bottomt = brep.m_T[bottoml.m_ti[lti]];
ON_NurbsCurve* c2 = ON_NurbsCurve::New();
if ( !bottomt.GetNurbForm(*c2) )
{
delete c2;
bOK = false;
break;
}
int c2i = brep.AddTrimCurve(c2);
ON_BrepTrim* topt = 0;
if ( bottomt.m_ei >= 0 )
{
ON_BrepEdge& tope = brep.m_E[topeimap[bottomt.m_ei]];
topt = &brep.NewTrim(tope,bottomt.m_bRev3d,topl,c2i);
}
else
{
// singular trim
ON_BrepVertex& topv = brep.m_V[topvimap[bottomt.m_vi[0]]];
topt = &brep.NewSingularTrim(topv,topl,bottomt.m_iso,c2i);
}
topt->m_tolerance[0] = bottomt.m_tolerance[0];
topt->m_tolerance[1] = bottomt.m_tolerance[1];
topt->m_pbox = bottomt.m_pbox;
topt->m_type = bottomt.m_type;
topt->m_iso = bottomt.m_iso;
}
topl.m_pbox = bottoml.m_pbox;
}
}
}
// build sides
int bRev3d[4] = {0,0,1,1};
int vid[4], eid[4];
if( bOK ) for ( ei = 0; ei < ecount0; ei++ )
{
if ( bSideEdge[ei] && topeimap[ei] )
{
ON_BrepEdge& bottome = brep.m_E[ei];
ON_BrepEdge& tope = brep.m_E[topeimap[ei]];
vid[0] = bottome.m_vi[0];
vid[1] = bottome.m_vi[1];
vid[2] = topvimap[vid[1]];
vid[3] = topvimap[vid[0]];
if ( sideveimap[vid[0]] && sideveimap[vid[1]] )
{
ON_BrepEdge& leftedge = brep.m_E[sideveimap[vid[0]]];
ON_BrepEdge& rightedge = brep.m_E[sideveimap[vid[1]]];
ON_Curve* cx = bottome.DuplicateCurve();
if ( !cx )
{
bOK = false;
break;
}
ON_Curve* cy = leftedge.DuplicateCurve();
if ( !cy )
{
delete cx;
bOK = false;
break;
}
ON_SumSurface* srf = new ON_SumSurface();
srf->m_curve[0] = cx;
srf->m_curve[1] = cy;
srf->m_basepoint = srf->m_curve[1]->PointAtStart();
srf->m_basepoint.x = -srf->m_basepoint.x;
srf->m_basepoint.y = -srf->m_basepoint.y;
srf->m_basepoint.z = -srf->m_basepoint.z;
eid[0] = bottome.m_edge_index;
eid[1] = rightedge.m_edge_index;
eid[2] = tope.m_edge_index;
eid[3] = leftedge.m_edge_index;
ON_BrepFace* face = brep.NewFace(srf,vid,eid,bRev3d);
if ( !face )
{
bOK = false;
break;
}
else if ( bottome.m_ti.Count() == 2 )
{
const ON_BrepTrim& trim0 = brep.m_T[bottome.m_ti[0]];
const ON_BrepTrim& trim1 = brep.m_T[bottome.m_ti[1]];
const ON_BrepLoop& loop0 = brep.m_L[trim0.m_li];
const ON_BrepLoop& loop1 = brep.m_L[trim1.m_li];
bool bBottomFaceRev = brep.m_F[(loop0.m_fi != face->m_face_index) ? loop0.m_fi : loop1.m_fi].m_bRev;
bool bSideFaceRev = ( trim0.m_bRev3d != trim1.m_bRev3d )
? bBottomFaceRev
: !bBottomFaceRev;
face->m_bRev = bSideFaceRev;
}
}
}
}
if ( !bOK )
{
for ( vi = brep.m_V.Count(); vi >= vcount0; vi-- )
{
brep.DeleteVertex(brep.m_V[vi]);
}
}
return bOK;
}