mirror of https://github.com/CGAL/cgal
Improved readability of weighted point-related functors (no real changes)
Fixed indentation, trailing whitespace, english, etc.
This commit is contained in:
Mael Rouxel-Labbé
parent
046058fabe
commit
1223f5f5a0
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@ -418,12 +418,11 @@ scaled_distance_to_lineC2( const FT &px, const FT &py,
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return determinant<FT>(px-rx, py-ry, qx-rx, qy-ry);
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return determinant<FT>(px-rx, py-ry, qx-rx, qy-ry);
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}
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}
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template < class RT >
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template < class RT >
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void
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void
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weighted_circumcenter_translateC2(const RT &dqx, const RT &dqy, const RT &dqw,
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weighted_circumcenter_translateC2(const RT &dqx, const RT &dqy, const RT &dqw,
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const RT &drx, const RT &dry, const RT &drw,
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const RT &drx, const RT &dry, const RT &drw,
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RT &dcx, RT &dcy)
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RT &dcx, RT &dcy)
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{
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{
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// Given 3 points P, Q, R, this function takes as input:
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// Given 3 points P, Q, R, this function takes as input:
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// qx-px, qy-py,qw-pw, rx-px, ry-py, rw-pw. And returns cx-px, cy-py,
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// qx-px, qy-py,qw-pw, rx-px, ry-py, rw-pw. And returns cx-px, cy-py,
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@ -449,30 +448,29 @@ weighted_circumcenter_translateC2(const RT &dqx, const RT &dqy, const RT &dqw,
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template < class RT, class We>
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template < class RT, class We>
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void
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void
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weighted_circumcenterC2( const RT &px, const RT &py, const We &pw,
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weighted_circumcenterC2( const RT &px, const RT &py, const We &pw,
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const RT &qx, const RT &qy, const We &qw,
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const RT &qx, const RT &qy, const We &qw,
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const RT &rx, const RT &ry, const We &rw,
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const RT &rx, const RT &ry, const We &rw,
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RT &x, RT &y )
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RT &x, RT &y )
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{
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{
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RT dqw = RT(qw-pw);
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RT dqw = RT(qw-pw);
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RT drw = RT(rw-pw);
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RT drw = RT(rw-pw);
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weighted_circumcenter_translateC2(qx-px, qy-py, dqw,rx-px, ry-py,drw,x, y);
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weighted_circumcenter_translateC2(qx-px, qy-py, dqw,rx-px, ry-py,drw,x, y);
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x += px;
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x += px;
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y += py;
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y += py;
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}
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}
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template < class RT , class We>
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template < class RT , class We>
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void
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void
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radical_axisC2(const RT &px, const RT &py, const We &pw,
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radical_axisC2(const RT &px, const RT &py, const We &pw,
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const RT &qx, const RT &qy, const We &qw,
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const RT &qx, const RT &qy, const We &qw,
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RT &a, RT &b, RT& c )
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RT &a, RT &b, RT& c )
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{
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{
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a = RT(2)*(px - qx);
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a = RT(2)*(px - qx);
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b = RT(2)*(py - qy);
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b = RT(2)*(py - qy);
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c = - CGAL_NTS square(px) - CGAL_NTS square(py)
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c = - CGAL_NTS square(px) - CGAL_NTS square(py)
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+ CGAL_NTS square(qx) + CGAL_NTS square(qy)
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+ CGAL_NTS square(qx) + CGAL_NTS square(qy)
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+RT(pw) - RT(qw);
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+ RT(pw) - RT(qw);
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}
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}
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template< class FT >
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template< class FT >
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@ -1,4 +1,4 @@
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// Copyright (c) 2000
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// Copyright (c) 2000
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// Utrecht University (The Netherlands),
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// Utrecht University (The Netherlands),
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// ETH Zurich (Switzerland),
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// ETH Zurich (Switzerland),
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// INRIA Sophia-Antipolis (France),
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// INRIA Sophia-Antipolis (France),
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@ -403,113 +403,109 @@ squared_areaC3(const FT &px, const FT &py, const FT &pz,
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return (CGAL_NTS square(vx) + CGAL_NTS square(vy) + CGAL_NTS square(vz))/4;
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return (CGAL_NTS square(vx) + CGAL_NTS square(vy) + CGAL_NTS square(vz))/4;
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}
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}
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template <class FT>
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template <class FT>
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void
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void
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determinants_for_weighted_circumcenterC3(
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determinants_for_weighted_circumcenterC3(
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const FT &px, const FT &py, const FT &pz, const FT &pw,
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const FT &px, const FT &py, const FT &pz, const FT &pw,
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const FT &qx, const FT &qy, const FT &qz, const FT &qw,
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const FT &qx, const FT &qy, const FT &qz, const FT &qw,
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const FT &rx, const FT &ry, const FT &rz, const FT &rw,
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const FT &rx, const FT &ry, const FT &rz, const FT &rw,
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const FT &sx, const FT &sy, const FT &sz, const FT &sw,
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const FT &sx, const FT &sy, const FT &sz, const FT &sw,
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FT &num_x, FT &num_y, FT &num_z, FT& den)
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FT &num_x, FT &num_y, FT &num_z, FT& den)
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{
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{
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// translate origin to p
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// translate origin to p
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// and compute determinants for weighted_circumcenter and
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// and compute determinants for weighted_circumcenter and
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// circumradius
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// circumradius
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FT qpx = qx-px;
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FT qpx = qx - px;
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FT qpy = qy-py;
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FT qpy = qy - py;
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FT qpz = qz-pz;
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FT qpz = qz - pz;
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FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
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FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
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CGAL_NTS square(qpz) - qw + pw;
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CGAL_NTS square(qpz) - qw + pw;
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FT rpx = rx-px;
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FT rpx = rx - px;
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FT rpy = ry-py;
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FT rpy = ry - py;
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FT rpz = rz-pz;
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FT rpz = rz - pz;
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FT rp2 = CGAL_NTS square(rpx) + CGAL_NTS square(rpy) +
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FT rp2 = CGAL_NTS square(rpx) + CGAL_NTS square(rpy) +
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CGAL_NTS square(rpz) - rw + pw;
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CGAL_NTS square(rpz) - rw + pw;
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FT spx = sx-px;
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FT spx = sx - px;
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FT spy = sy-py;
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FT spy = sy - py;
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FT spz = sz-pz;
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FT spz = sz - pz;
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FT sp2 = CGAL_NTS square(spx) + CGAL_NTS square(spy) +
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FT sp2 = CGAL_NTS square(spx) + CGAL_NTS square(spy) +
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CGAL_NTS square(spz) - sw + pw;
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CGAL_NTS square(spz) - sw + pw;
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num_x = determinant(qpy,qpz,qp2,
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num_x = determinant(qpy,qpz,qp2,
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rpy,rpz,rp2,
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rpy,rpz,rp2,
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spy,spz,sp2);
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spy,spz,sp2);
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num_y = determinant(qpx,qpz,qp2,
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num_y = determinant(qpx,qpz,qp2,
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rpx,rpz,rp2,
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rpx,rpz,rp2,
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spx,spz,sp2);
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spx,spz,sp2);
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num_z = determinant(qpx,qpy,qp2,
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num_z = determinant(qpx,qpy,qp2,
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rpx,rpy,rp2,
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rpx,rpy,rp2,
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spx,spy,sp2);
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spx,spy,sp2);
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den = determinant(qpx,qpy,qpz,
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den = determinant(qpx,qpy,qpz,
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rpx,rpy,rpz,
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rpx,rpy,rpz,
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spx,spy,spz);
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spx,spy,spz);
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}
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}
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template <class FT>
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template <class FT>
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void
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void
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determinants_for_circumcenterC3(
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determinants_for_circumcenterC3(const FT &px, const FT &py, const FT &pz,
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const FT &px, const FT &py, const FT &pz,
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const FT &qx, const FT &qy, const FT &qz,
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const FT &qx, const FT &qy, const FT &qz,
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const FT &rx, const FT &ry, const FT &rz,
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const FT &rx, const FT &ry, const FT &rz,
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const FT &sx, const FT &sy, const FT &sz,
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const FT &sx, const FT &sy, const FT &sz,
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FT &num_x, FT &num_y, FT &num_z, FT& den)
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FT &num_x, FT &num_y, FT &num_z, FT& den)
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{
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{
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// translate origin to p
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// translate origin to p
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// and compute determinants for weighted_circumcenter and
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// and compute determinants for weighted_circumcenter and
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// circumradius
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// circumradius
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FT qpx = qx-px;
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FT qpx = qx - px;
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FT qpy = qy-py;
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FT qpy = qy - py;
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FT qpz = qz-pz;
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FT qpz = qz - pz;
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FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
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FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
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CGAL_NTS square(qpz);
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CGAL_NTS square(qpz);
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FT rpx = rx-px;
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FT rpx = rx - px;
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FT rpy = ry-py;
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FT rpy = ry - py;
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FT rpz = rz-pz;
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FT rpz = rz - pz;
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FT rp2 = CGAL_NTS square(rpx) + CGAL_NTS square(rpy) +
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FT rp2 = CGAL_NTS square(rpx) + CGAL_NTS square(rpy) +
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CGAL_NTS square(rpz);
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CGAL_NTS square(rpz);
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FT spx = sx-px;
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FT spx = sx - px;
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FT spy = sy-py;
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FT spy = sy - py;
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FT spz = sz-pz;
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FT spz = sz - pz;
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FT sp2 = CGAL_NTS square(spx) + CGAL_NTS square(spy) +
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FT sp2 = CGAL_NTS square(spx) + CGAL_NTS square(spy) +
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CGAL_NTS square(spz);
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CGAL_NTS square(spz);
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num_x = determinant(qpy,qpz,qp2,
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num_x = determinant(qpy,qpz,qp2,
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rpy,rpz,rp2,
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rpy,rpz,rp2,
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spy,spz,sp2);
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spy,spz,sp2);
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num_y = determinant(qpx,qpz,qp2,
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num_y = determinant(qpx,qpz,qp2,
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rpx,rpz,rp2,
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rpx,rpz,rp2,
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spx,spz,sp2);
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spx,spz,sp2);
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num_z = determinant(qpx,qpy,qp2,
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num_z = determinant(qpx,qpy,qp2,
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rpx,rpy,rp2,
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rpx,rpy,rp2,
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spx,spy,sp2);
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spx,spy,sp2);
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den = determinant(qpx,qpy,qpz,
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den = determinant(qpx,qpy,qpz,
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rpx,rpy,rpz,
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rpx,rpy,rpz,
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spx,spy,spz);
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spx,spy,spz);
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}
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}
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template < class FT>
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template < class FT>
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void
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void
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weighted_circumcenterC3(
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weighted_circumcenterC3(const FT &px, const FT &py, const FT &pz, const FT &pw,
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const FT &px, const FT &py, const FT &pz, const FT &pw,
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const FT &qx, const FT &qy, const FT &qz, const FT &qw,
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const FT &qx, const FT &qy, const FT &qz, const FT &qw,
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const FT &rx, const FT &ry, const FT &rz, const FT &rw,
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const FT &rx, const FT &ry, const FT &rz, const FT &rw,
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const FT &sx, const FT &sy, const FT &sz, const FT &sw,
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const FT &sx, const FT &sy, const FT &sz, const FT &sw,
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FT &x, FT &y, FT &z)
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FT &x, FT &y, FT &z)
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{
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{
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// this function compute the weighted circumcenter point only
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// this function computes the weighted circumcenter point only
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// Translate p to origin and compute determinants
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// Translate p to origin and compute determinants
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FT num_x, num_y, num_z, den;
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FT num_x, num_y, num_z, den;
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determinants_for_weighted_circumcenterC3(px, py, pz, pw,
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determinants_for_weighted_circumcenterC3(px, py, pz, pw,
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qx, qy, qz, qw,
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qx, qy, qz, qw,
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rx, ry, rz, rw,
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rx, ry, rz, rw,
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sx, sy, sz, sw,
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sx, sy, sz, sw,
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num_x, num_y, num_z,den);
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num_x, num_y, num_z,den);
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CGAL_assertion( ! CGAL_NTS is_zero(den) );
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CGAL_assertion( ! CGAL_NTS is_zero(den) );
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FT inv = FT(1)/(FT(2) * den);
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FT inv = FT(1)/(FT(2) * den);
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x = px + num_x*inv;
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x = px + num_x*inv;
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y = py - num_y*inv;
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y = py - num_y*inv;
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@ -518,248 +514,231 @@ weighted_circumcenterC3(
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template < class FT>
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template < class FT>
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void
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void
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weighted_circumcenterC3(
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weighted_circumcenterC3(const FT &px, const FT &py, const FT &pz, const FT &pw,
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const FT &px, const FT &py, const FT &pz, const FT &pw,
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const FT &qx, const FT &qy, const FT &qz, const FT &qw,
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const FT &qx, const FT &qy, const FT &qz, const FT &qw,
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const FT &rx, const FT &ry, const FT &rz, const FT &rw,
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const FT &rx, const FT &ry, const FT &rz, const FT &rw,
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const FT &sx, const FT &sy, const FT &sz, const FT &sw,
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const FT &sx, const FT &sy, const FT &sz, const FT &sw,
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FT &x, FT &y, FT &z, FT &w)
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FT &x, FT &y, FT &z, FT &w)
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{
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{
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// this function compute the weighted circumcenter point
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// this function computes the weighted circumcenter point
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// and the squared weighted circumradius
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// and the squared weighted circumradius
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// Translate p to origin and compute determinants
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// Translate p to origin and compute determinants
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FT num_x, num_y, num_z, den;
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FT num_x, num_y, num_z, den;
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determinants_for_weighted_circumcenterC3(px, py, pz, pw,
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determinants_for_weighted_circumcenterC3(px, py, pz, pw,
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qx, qy, qz, qw,
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qx, qy, qz, qw,
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rx, ry, rz, rw,
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rx, ry, rz, rw,
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sx, sy, sz, sw,
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sx, sy, sz, sw,
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num_x, num_y, num_z, den);
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num_x, num_y, num_z, den);
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CGAL_assertion( ! CGAL_NTS is_zero(den) );
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CGAL_assertion( ! CGAL_NTS is_zero(den) );
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FT inv = FT(1)/(FT(2) * den);
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FT inv = FT(1)/(FT(2) * den);
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x = px + num_x*inv;
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x = px + num_x*inv;
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y = py - num_y*inv;
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y = py - num_y*inv;
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z = pz + num_z*inv;
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z = pz + num_z*inv;
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w = (CGAL_NTS square(num_x)+CGAL_NTS square(num_y)+CGAL_NTS square(num_z))
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w = (CGAL_NTS square(num_x) + CGAL_NTS square(num_y) + CGAL_NTS square(num_z))
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*CGAL_NTS square(inv) - pw;
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* CGAL_NTS square(inv) - pw;
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}
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}
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template< class FT >
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template< class FT >
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FT
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FT
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squared_radius_orthogonal_sphereC3(
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squared_radius_orthogonal_sphereC3(
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const FT &px, const FT &py, const FT &pz, const FT &pw,
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const FT &px, const FT &py, const FT &pz, const FT &pw,
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const FT &qx, const FT &qy, const FT &qz, const FT &qw,
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const FT &qx, const FT &qy, const FT &qz, const FT &qw,
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const FT &rx, const FT &ry, const FT &rz, const FT &rw,
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const FT &rx, const FT &ry, const FT &rz, const FT &rw,
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const FT &sx, const FT &sy, const FT &sz, const FT &sw)
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const FT &sx, const FT &sy, const FT &sz, const FT &sw)
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{
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{
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// this function computes the squared weighted circumradius only
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// this function compute the squared weighted circumradius only
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// Translate p to origin and compute determinants
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// Translate p to origin and compute determinants
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FT num_x, num_y, num_z, den;
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FT num_x, num_y, num_z, den;
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determinants_for_weighted_circumcenterC3(px, py, pz, pw,
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determinants_for_weighted_circumcenterC3(px, py, pz, pw,
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qx, qy, qz, qw,
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qx, qy, qz, qw,
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rx, ry, rz, rw,
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rx, ry, rz, rw,
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sx, sy, sz, sw,
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sx, sy, sz, sw,
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num_x, num_y, num_z,den);
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num_x, num_y, num_z,den);
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CGAL_assertion( ! CGAL_NTS is_zero(den) );
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CGAL_assertion( ! CGAL_NTS is_zero(den) );
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FT inv = FT(1)/(FT(2) * den);
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FT inv = FT(1)/(FT(2) * den);
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return
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return (CGAL_NTS square(num_x) + CGAL_NTS square(num_y) + CGAL_NTS square(num_z))
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(CGAL_NTS square(num_x)+CGAL_NTS square(num_y)+CGAL_NTS square(num_z))
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* CGAL_NTS square(inv) - pw;
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*CGAL_NTS square(inv) - pw;
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}
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}
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template <class FT>
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template <class FT>
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void
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void
|
||||||
determinants_for_weighted_circumcenterC3(
|
determinants_for_weighted_circumcenterC3(
|
||||||
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
||||||
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
||||||
const FT &rx, const FT &ry, const FT &rz, const FT &rw,
|
const FT &rx, const FT &ry, const FT &rz, const FT &rw,
|
||||||
FT &num_x, FT &num_y, FT &num_z, FT &den)
|
FT &num_x, FT &num_y, FT &num_z, FT &den)
|
||||||
{
|
{
|
||||||
// translate origin to p
|
// translate origin to p and compute determinants for weighted_circumcenter
|
||||||
// and compute determinants for weighted_circumcenter and
|
// and circumradius
|
||||||
// circumradius
|
|
||||||
|
|
||||||
// Translate s to origin to simplify the expression.
|
// Translate s to origin to simplify the expression.
|
||||||
FT qpx = qx-px;
|
FT qpx = qx - px;
|
||||||
FT qpy = qy-py;
|
FT qpy = qy - py;
|
||||||
FT qpz = qz-pz;
|
FT qpz = qz - pz;
|
||||||
FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
|
FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
|
||||||
CGAL_NTS square(qpz) - qw + pw;
|
CGAL_NTS square(qpz) - qw + pw;
|
||||||
FT rpx = rx-px;
|
FT rpx = rx - px;
|
||||||
FT rpy = ry-py;
|
FT rpy = ry - py;
|
||||||
FT rpz = rz-pz;
|
FT rpz = rz - pz;
|
||||||
FT rp2 = CGAL_NTS square(rpx) + CGAL_NTS square(rpy) +
|
FT rp2 = CGAL_NTS square(rpx) + CGAL_NTS square(rpy) +
|
||||||
CGAL_NTS square(rpz) - rw + pw;
|
CGAL_NTS square(rpz) - rw + pw;
|
||||||
|
|
||||||
FT sx = qpy*rpz-qpz*rpy;
|
FT sx = qpy*rpz - qpz*rpy;
|
||||||
FT sy = qpz*rpx-qpx*rpz;
|
FT sy = qpz*rpx - qpx*rpz;
|
||||||
FT sz = qpx*rpy-qpy*rpx;
|
FT sz = qpx*rpy - qpy*rpx;
|
||||||
|
|
||||||
// The following determinants can be developped and simplified.
|
// The following determinants can be developped and simplified.
|
||||||
//
|
//
|
||||||
// FT num_x = determinant(qpy,qpz,qp2,
|
// FT num_x = determinant(qpy,qpz,qp2,
|
||||||
// rpy,rpz,rp2,
|
// rpy,rpz,rp2,
|
||||||
// sy,sz,FT(0));
|
// sy,sz,FT(0));
|
||||||
// FT num_y = determinant(qpx,qpz,qp2,
|
// FT num_y = determinant(qpx,qpz,qp2,
|
||||||
// rpx,rpz,rp2,
|
// rpx,rpz,rp2,
|
||||||
// sx,sz,FT(0));
|
// sx,sz,FT(0));
|
||||||
// FT num_z = determinant(qpx,qpy,qp2,
|
// FT num_z = determinant(qpx,qpy,qp2,
|
||||||
// rpx,rpy,rp2,
|
// rpx,rpy,rp2,
|
||||||
// sx,sy,FT(0));
|
// sx,sy,FT(0));
|
||||||
|
|
||||||
num_x = qp2 * determinant(rpy,rpz,sy,sz)
|
num_x = qp2 * determinant(rpy,rpz,sy,sz)
|
||||||
- rp2 * determinant(qpy,qpz,sy,sz);
|
- rp2 * determinant(qpy,qpz,sy,sz);
|
||||||
|
|
||||||
num_y = qp2 * determinant(rpx,rpz,sx,sz)
|
num_y = qp2 * determinant(rpx,rpz,sx,sz)
|
||||||
- rp2 * determinant(qpx,qpz,sx,sz);
|
- rp2 * determinant(qpx,qpz,sx,sz);
|
||||||
|
|
||||||
num_z = qp2 * determinant(rpx,rpy,sx,sy)
|
num_z = qp2 * determinant(rpx,rpy,sx,sy)
|
||||||
- rp2 * determinant(qpx,qpy,sx,sy);
|
- rp2 * determinant(qpx,qpy,sx,sy);
|
||||||
|
|
||||||
den = determinant(qpx,qpy,qpz,
|
den = determinant(qpx,qpy,qpz,
|
||||||
rpx,rpy,rpz,
|
rpx,rpy,rpz,
|
||||||
sx,sy,sz);
|
sx,sy,sz);
|
||||||
}
|
}
|
||||||
|
|
||||||
template < class FT >
|
template < class FT >
|
||||||
void
|
void
|
||||||
weighted_circumcenterC3(
|
weighted_circumcenterC3(const FT &px, const FT &py, const FT &pz, const FT &pw,
|
||||||
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
||||||
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
const FT &rx, const FT &ry, const FT &rz, const FT &rw,
|
||||||
const FT &rx, const FT &ry, const FT &rz, const FT &rw,
|
FT &x, FT &y, FT &z)
|
||||||
FT &x, FT &y, FT &z)
|
|
||||||
{
|
{
|
||||||
// this function compute the weighted circumcenter point only
|
// this function computes the weighted circumcenter point only
|
||||||
|
|
||||||
// Translate p to origin and compute determinants
|
// Translate p to origin and compute determinants
|
||||||
FT num_x, num_y, num_z, den;
|
FT num_x, num_y, num_z, den;
|
||||||
determinants_for_weighted_circumcenterC3(px, py, pz, pw,
|
determinants_for_weighted_circumcenterC3(px, py, pz, pw,
|
||||||
qx, qy, qz, qw,
|
qx, qy, qz, qw,
|
||||||
rx, ry, rz, rw,
|
rx, ry, rz, rw,
|
||||||
num_x, num_y, num_z, den);
|
num_x, num_y, num_z, den);
|
||||||
|
|
||||||
CGAL_assertion( den != FT(0) );
|
CGAL_assertion( den != FT(0) );
|
||||||
FT inv = FT(1)/(FT(2) * den);
|
FT inv = FT(1) / (FT(2) * den);
|
||||||
|
|
||||||
x = px + num_x*inv;
|
x = px + num_x*inv;
|
||||||
y = py - num_y*inv;
|
y = py - num_y*inv;
|
||||||
z = pz + num_z*inv;
|
z = pz + num_z*inv;
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|
||||||
template < class FT >
|
template < class FT >
|
||||||
void
|
void
|
||||||
weighted_circumcenterC3(
|
weighted_circumcenterC3(const FT &px, const FT &py, const FT &pz, const FT &pw,
|
||||||
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
||||||
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
const FT &rx, const FT &ry, const FT &rz, const FT &rw,
|
||||||
const FT &rx, const FT &ry, const FT &rz, const FT &rw,
|
FT &x, FT &y, FT &z, FT &w)
|
||||||
FT &x, FT &y, FT &z, FT &w)
|
|
||||||
{
|
{
|
||||||
// this function compute the weighted circumcenter and
|
// this function computes the weighted circumcenter and
|
||||||
// the weighted squared circumradius
|
// the weighted squared circumradius
|
||||||
|
|
||||||
// Translate p to origin and compute determinants
|
// Translate p to origin and compute determinants
|
||||||
FT num_x, num_y, num_z, den;
|
FT num_x, num_y, num_z, den;
|
||||||
determinants_for_weighted_circumcenterC3(px, py, pz, pw,
|
determinants_for_weighted_circumcenterC3(px, py, pz, pw,
|
||||||
qx, qy, qz, qw,
|
qx, qy, qz, qw,
|
||||||
rx, ry, rz, rw,
|
rx, ry, rz, rw,
|
||||||
num_x, num_y, num_z, den);
|
num_x, num_y, num_z, den);
|
||||||
|
|
||||||
CGAL_assertion( den != FT(0) );
|
CGAL_assertion( den != FT(0) );
|
||||||
FT inv = FT(1)/(FT(2) * den);
|
FT inv = FT(1) / (FT(2) * den);
|
||||||
|
|
||||||
x = px + num_x*inv;
|
x = px + num_x*inv;
|
||||||
y = py - num_y*inv;
|
y = py - num_y*inv;
|
||||||
z = pz + num_z*inv;
|
z = pz + num_z*inv;
|
||||||
|
|
||||||
w = (CGAL_NTS square(num_x)+CGAL_NTS square(num_y)+CGAL_NTS square(num_z))
|
w = (CGAL_NTS square(num_x) + CGAL_NTS square(num_y) + CGAL_NTS square(num_z))
|
||||||
*CGAL_NTS square(inv) - pw;
|
*CGAL_NTS square(inv) - pw;
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|
||||||
template< class FT >
|
template< class FT >
|
||||||
CGAL_MEDIUM_INLINE
|
CGAL_MEDIUM_INLINE
|
||||||
FT
|
FT
|
||||||
squared_radius_smallest_orthogonal_sphereC3(
|
squared_radius_smallest_orthogonal_sphereC3(
|
||||||
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
||||||
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
||||||
const FT &rx, const FT &ry, const FT &rz, const FT &rw)
|
const FT &rx, const FT &ry, const FT &rz, const FT &rw)
|
||||||
{
|
{
|
||||||
// this function compute the weighted squared circumradius only
|
// this function computes the weighted squared circumradius only
|
||||||
|
|
||||||
// Translate p to origin and compute determinants
|
// Translate p to origin and compute determinants
|
||||||
FT num_x, num_y, num_z, den;
|
FT num_x, num_y, num_z, den;
|
||||||
determinants_for_weighted_circumcenterC3(px, py, pz, pw,
|
determinants_for_weighted_circumcenterC3(px, py, pz, pw,
|
||||||
qx, qy, qz, qw,
|
qx, qy, qz, qw,
|
||||||
rx, ry, rz, rw,
|
rx, ry, rz, rw,
|
||||||
num_x, num_y, num_z, den);
|
num_x, num_y, num_z, den);
|
||||||
|
|
||||||
CGAL_assertion( den != FT(0) );
|
CGAL_assertion( den != FT(0) );
|
||||||
FT inv = FT(1)/(FT(2) * den);
|
FT inv = FT(1)/(FT(2) * den);
|
||||||
|
|
||||||
return
|
return (CGAL_NTS square(num_x) + CGAL_NTS square(num_y) + CGAL_NTS square(num_z))
|
||||||
(CGAL_NTS square(num_x)+CGAL_NTS square(num_y)+CGAL_NTS square(num_z))
|
* CGAL_NTS square(inv) - pw;
|
||||||
*CGAL_NTS square(inv) - pw;
|
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
template < class FT >
|
template < class FT >
|
||||||
void
|
void
|
||||||
weighted_circumcenterC3(
|
weighted_circumcenterC3(const FT &px, const FT &py, const FT &pz, const FT &pw,
|
||||||
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
||||||
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
FT &x, FT &y, FT &z)
|
||||||
FT &x, FT &y, FT &z)
|
|
||||||
{
|
{
|
||||||
// this function compute the weighted circumcenter point only
|
// this function computes the weighted circumcenter point only
|
||||||
FT qpx = qx-px;
|
FT qpx = qx - px;
|
||||||
FT qpy = qy-py;
|
FT qpy = qy - py;
|
||||||
FT qpz = qz-pz;
|
FT qpz = qz - pz;
|
||||||
FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
|
FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
|
||||||
CGAL_NTS square(qpz);
|
CGAL_NTS square(qpz);
|
||||||
FT inv = FT(1)/(FT(2)*qp2);
|
FT inv = FT(1) / (FT(2) * qp2);
|
||||||
FT alpha = 1/FT(2) + (pw-qw)*inv;
|
FT alpha = 1 / FT(2) + (pw-qw) * inv;
|
||||||
|
|
||||||
x = px + alpha * qpx;
|
x = px + alpha * qpx;
|
||||||
y = py + alpha * qpy;
|
y = py + alpha * qpy;
|
||||||
z = pz + alpha * qpz;
|
z = pz + alpha * qpz;
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|
||||||
template < class FT >
|
template < class FT >
|
||||||
void
|
void
|
||||||
weighted_circumcenterC3(
|
weighted_circumcenterC3(const FT &px, const FT &py, const FT &pz, const FT &pw,
|
||||||
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
||||||
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
FT &x, FT &y, FT &z, FT &w)
|
||||||
FT &x, FT &y, FT &z, FT &w)
|
|
||||||
{
|
{
|
||||||
// this function compute the weighted circumcenter point and
|
// this function computes the weighted circumcenter point and
|
||||||
// the weighted circumradius
|
// the weighted circumradius
|
||||||
FT qpx = qx-px;
|
FT qpx = qx - px;
|
||||||
FT qpy = qy-py;
|
FT qpy = qy - py;
|
||||||
FT qpz = qz-pz;
|
FT qpz = qz - pz;
|
||||||
FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
|
FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
|
||||||
CGAL_NTS square(qpz);
|
CGAL_NTS square(qpz);
|
||||||
FT inv = FT(1)/(FT(2)*qp2);
|
FT inv = FT(1) / (FT(2) * qp2);
|
||||||
FT alpha = 1/FT(2) + (pw-qw)*inv;
|
FT alpha = 1 / FT(2) + (pw-qw) * inv;
|
||||||
|
|
||||||
x = px + alpha * qpx;
|
x = px + alpha * qpx;
|
||||||
y = py + alpha * qpy;
|
y = py + alpha * qpy;
|
||||||
z = pz + alpha * qpz;
|
z = pz + alpha * qpz;
|
||||||
|
|
||||||
w = CGAL_NTS square(alpha)*qp2 - pw;
|
w = CGAL_NTS square(alpha) * qp2 - pw;
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|
||||||
template< class FT >
|
template< class FT >
|
||||||
CGAL_MEDIUM_INLINE
|
CGAL_MEDIUM_INLINE
|
||||||
FT
|
FT
|
||||||
|
|
@ -767,30 +746,27 @@ squared_radius_smallest_orthogonal_sphereC3(
|
||||||
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
||||||
const FT &qx, const FT &qy, const FT &qz, const FT &qw)
|
const FT &qx, const FT &qy, const FT &qz, const FT &qw)
|
||||||
{
|
{
|
||||||
// this function computes
|
// this function computes the weighted circumradius only
|
||||||
// the weighted circumradius only
|
FT qpx = qx - px;
|
||||||
FT qpx = qx-px;
|
FT qpy = qy - py;
|
||||||
FT qpy = qy-py;
|
FT qpz = qz - pz;
|
||||||
FT qpz = qz-pz;
|
|
||||||
FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
|
FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
|
||||||
CGAL_NTS square(qpz);
|
CGAL_NTS square(qpz);
|
||||||
FT inv = FT(1)/(FT(2)*qp2);
|
FT inv = FT(1) / (FT(2) * qp2);
|
||||||
FT alpha = 1/FT(2) + (pw-qw)*inv;
|
FT alpha = 1 / FT(2) + (pw-qw) * inv;
|
||||||
|
|
||||||
return CGAL_NTS square(alpha)*qp2 - pw;
|
return CGAL_NTS square(alpha)*qp2 - pw;
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|
||||||
template< class FT >
|
template< class FT >
|
||||||
FT
|
FT
|
||||||
power_productC3(
|
power_productC3(const FT &px, const FT &py, const FT &pz, const FT &pw,
|
||||||
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
const FT &qx, const FT &qy, const FT &qz, const FT &qw)
|
||||||
const FT &qx, const FT &qy, const FT &qz, const FT &qw)
|
|
||||||
{
|
{
|
||||||
// computes the power product of two weighted points
|
// computes the power product of two weighted points
|
||||||
FT qpx = qx-px;
|
FT qpx = qx - px;
|
||||||
FT qpy = qy-py;
|
FT qpy = qy - py;
|
||||||
FT qpz = qz-pz;
|
FT qpz = qz - pz;
|
||||||
FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
|
FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy) +
|
||||||
CGAL_NTS square(qpz);
|
CGAL_NTS square(qpz);
|
||||||
return qp2 - pw - qw ;
|
return qp2 - pw - qw ;
|
||||||
|
|
@ -799,17 +775,17 @@ power_productC3(
|
||||||
template < class RT , class We>
|
template < class RT , class We>
|
||||||
void
|
void
|
||||||
radical_axisC3(const RT &px, const RT &py, const RT &pz, const We & /* pw */,
|
radical_axisC3(const RT &px, const RT &py, const RT &pz, const We & /* pw */,
|
||||||
const RT &qx, const RT &qy, const RT &qz, const We & /* qw */,
|
const RT &qx, const RT &qy, const RT &qz, const We & /* qw */,
|
||||||
const RT &rx, const RT &ry, const RT &rz, const We & /* rw */,
|
const RT &rx, const RT &ry, const RT &rz, const We & /* rw */,
|
||||||
RT &a, RT &b, RT& c )
|
RT &a, RT &b, RT& c )
|
||||||
{
|
{
|
||||||
RT dqx=qx-px, dqy=qy-py, dqz=qz-pz, drx=rx-px, dry=ry-py, drz=rz-pz;
|
RT dqx=qx-px, dqy=qy-py, dqz=qz-pz, drx=rx-px, dry=ry-py, drz=rz-pz;
|
||||||
|
|
||||||
//il manque des tests...
|
//il manque des tests...
|
||||||
|
|
||||||
a= RT(1)*determinant(dqy, dqz, dry, drz);
|
a = RT(1)*determinant(dqy, dqz, dry, drz);
|
||||||
b= - RT(1)*determinant(dqx, dqz, drx, drz);
|
b = - RT(1)*determinant(dqx, dqz, drx, drz);
|
||||||
c= RT(1)*determinant(dqx, dqy, drx, dry);
|
c = RT(1)*determinant(dqx, dqy, drx, dry);
|
||||||
}
|
}
|
||||||
|
|
||||||
// function used in critical_squared_radiusC3
|
// function used in critical_squared_radiusC3
|
||||||
|
|
@ -817,77 +793,69 @@ radical_axisC3(const RT &px, const RT &py, const RT &pz, const We & /* pw */,
|
||||||
// circle orthogonal (p,pw), (q,qw), (r,rw), (s,sw)
|
// circle orthogonal (p,pw), (q,qw), (r,rw), (s,sw)
|
||||||
template < class FT>
|
template < class FT>
|
||||||
FT
|
FT
|
||||||
power_to_orthogonal_sphereC3(
|
power_to_orthogonal_sphereC3(const FT &px, const FT &py, const FT &pz, const FT &pw,
|
||||||
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
||||||
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
const FT &rx, const FT &ry, const FT &rz, const FT &rw,
|
||||||
const FT &rx, const FT &ry, const FT &rz, const FT &rw,
|
const FT &sx, const FT &sy, const FT &sz, const FT &sw,
|
||||||
const FT &sx, const FT &sy, const FT &sz, const FT &sw,
|
const FT &tx, const FT &ty, const FT &tz, const FT &tw)
|
||||||
const FT &tx, const FT &ty, const FT &tz, const FT &tw)
|
|
||||||
{
|
{
|
||||||
//to get the value of the determinant
|
//to get the value of the determinant
|
||||||
// We translate the points so that t becomes the origin.
|
// We translate the points so that t becomes the origin.
|
||||||
FT dpx = px - tx;
|
FT dpx = px - tx;
|
||||||
FT dpy = py - ty;
|
FT dpy = py - ty;
|
||||||
FT dpz = pz - tz;
|
FT dpz = pz - tz;
|
||||||
FT dpt = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) +
|
FT dpt = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) +
|
||||||
CGAL_NTS square(dpz) - pw + tw ;
|
CGAL_NTS square(dpz) - pw + tw ;
|
||||||
FT dqx = qx - tx;
|
FT dqx = qx - tx;
|
||||||
FT dqy = qy - ty;
|
FT dqy = qy - ty;
|
||||||
FT dqz = qz - tz;
|
FT dqz = qz - tz;
|
||||||
FT dqt = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) +
|
FT dqt = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) +
|
||||||
CGAL_NTS square(dqz) - qw + tw;
|
CGAL_NTS square(dqz) - qw + tw;
|
||||||
FT drx = rx - tx;
|
FT drx = rx - tx;
|
||||||
FT dry = ry - ty;
|
FT dry = ry - ty;
|
||||||
FT drz = rz - tz;
|
FT drz = rz - tz;
|
||||||
FT drt = CGAL_NTS square(drx) + CGAL_NTS square(dry) +
|
FT drt = CGAL_NTS square(drx) + CGAL_NTS square(dry) +
|
||||||
CGAL_NTS square(drz) - rw + tw;
|
CGAL_NTS square(drz) - rw + tw;
|
||||||
FT dsx = sx - tx;
|
FT dsx = sx - tx;
|
||||||
FT dsy = sy - ty;
|
FT dsy = sy - ty;
|
||||||
FT dsz = sz - tz;
|
FT dsz = sz - tz;
|
||||||
FT dst = CGAL_NTS square(dsx) + CGAL_NTS square(dsy) +
|
FT dst = CGAL_NTS square(dsx) + CGAL_NTS square(dsy) +
|
||||||
CGAL_NTS square(dsz) - sw + tw;
|
CGAL_NTS square(dsz) - sw + tw;
|
||||||
|
|
||||||
return determinant(dpx, dpy, dpz, dpt,
|
|
||||||
dqx, dqy, dqz, dqt,
|
|
||||||
drx, dry, drz, drt,
|
|
||||||
dsx, dsy, dsz, dst);
|
|
||||||
|
|
||||||
|
return determinant(dpx, dpy, dpz, dpt,
|
||||||
|
dqx, dqy, dqz, dqt,
|
||||||
|
drx, dry, drz, drt,
|
||||||
|
dsx, dsy, dsz, dst);
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
// compute the critical weight tw
|
// compute the critical weight tw
|
||||||
// where weighted point t is orthogonal to weighted points p, q,r,s
|
// where weighted point t is orthogonal to weighted points p, q,r,s
|
||||||
template < class FT>
|
template < class FT>
|
||||||
FT
|
FT
|
||||||
power_distance_to_power_sphereC3(
|
power_distance_to_power_sphereC3(const FT &px, const FT &py, const FT &pz, const FT &pw,
|
||||||
const FT &px, const FT &py, const FT &pz, const FT &pw,
|
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
||||||
const FT &qx, const FT &qy, const FT &qz, const FT &qw,
|
const FT &rx, const FT &ry, const FT &rz, const FT &rw,
|
||||||
const FT &rx, const FT &ry, const FT &rz, const FT &rw,
|
const FT &sx, const FT &sy, const FT &sz, const FT &sw,
|
||||||
const FT &sx, const FT &sy, const FT &sz, const FT &sw,
|
const FT &tx, const FT &ty, const FT &tz, const FT & )
|
||||||
const FT &tx, const FT &ty, const FT &tz, const FT & )
|
|
||||||
{
|
{
|
||||||
// the 5x5 det is a linear function of tw ff(tw)= ff(0) + tw ff(1)
|
// the 5x5 det is a linear function of tw ff(tw)= ff(0) + tw ff(1)
|
||||||
// the critical value for tw is - ff(0)/( ff(1) - ff(0))
|
// the critical value for tw is - ff(0)/( ff(1) - ff(0))
|
||||||
|
|
||||||
|
FT ff0 = power_to_orthogonal_sphereC3(px, py, pz, pw,
|
||||||
|
qx, qy, qz, qw,
|
||||||
|
rx, ry, rz, rw,
|
||||||
|
sx, sy, sz, sw,
|
||||||
|
tx, ty, tz, FT(0));
|
||||||
|
|
||||||
FT ff0 = power_to_orthogonal_sphereC3(px, py, pz, pw,
|
FT ff1 = power_to_orthogonal_sphereC3(px, py, pz, pw,
|
||||||
qx, qy, qz, qw,
|
qx, qy, qz, qw,
|
||||||
rx, ry, rz, rw,
|
rx, ry, rz, rw,
|
||||||
sx, sy, sz, sw,
|
sx, sy, sz, sw,
|
||||||
tx, ty, tz, FT(0));
|
tx, ty, tz, FT(1));
|
||||||
|
|
||||||
FT ff1 = power_to_orthogonal_sphereC3(px, py, pz, pw,
|
return -ff0/(ff1 - ff0);
|
||||||
qx, qy, qz, qw,
|
|
||||||
rx, ry, rz, rw,
|
|
||||||
sx, sy, sz, sw,
|
|
||||||
tx, ty, tz, FT(1));
|
|
||||||
|
|
||||||
return -ff0/(ff1 - ff0);
|
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
// I will use this to test if the radial axis of three spheres
|
// I will use this to test if the radial axis of three spheres
|
||||||
// intersect the triangle formed by the centers.
|
// intersect the triangle formed by the centers.
|
||||||
// // resolution of the system (where we note c the center)
|
// // resolution of the system (where we note c the center)
|
||||||
|
|
@ -913,9 +881,7 @@ power_distance_to_power_sphereC3(
|
||||||
// FT Mu = (dqq*dp-dpp*dpdq)/denom;
|
// FT Mu = (dqq*dp-dpp*dpdq)/denom;
|
||||||
|
|
||||||
// return (CGAL_NTS square(Lambda)*dp+CGAL_NTS square(Mu)*dq
|
// return (CGAL_NTS square(Lambda)*dp+CGAL_NTS square(Mu)*dq
|
||||||
// +FT2*Lambda*Mu*dpdq - rw);
|
// + FT2*Lambda*Mu*dpdq - rw);
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
} //namespace CGAL
|
} //namespace CGAL
|
||||||
|
|
||||||
|
|
|
||||||
|
|
@ -635,12 +635,11 @@ side_of_oriented_lineC2(const FT &a, const FT &b, const FT &c,
|
||||||
return CGAL_NTS sign(a*x+b*y+c);
|
return CGAL_NTS sign(a*x+b*y+c);
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|
||||||
template <class FT>
|
template <class FT>
|
||||||
Comparison_result
|
Comparison_result
|
||||||
compare_power_distanceC2(const FT& px, const FT& py, const FT& pwt,
|
compare_power_distanceC2(const FT& px, const FT& py, const FT& pwt,
|
||||||
const FT& qx, const FT& qy, const FT& qwt,
|
const FT& qx, const FT& qy, const FT& qwt,
|
||||||
const FT& rx, const FT& ry)
|
const FT& rx, const FT& ry)
|
||||||
{
|
{
|
||||||
// returns SMALLER if r is closer to p w.r.t. the power metric
|
// returns SMALLER if r is closer to p w.r.t. the power metric
|
||||||
FT d1 = CGAL_NTS square(rx - px) + CGAL_NTS square(ry - py) - pwt;
|
FT d1 = CGAL_NTS square(rx - px) + CGAL_NTS square(ry - py) - pwt;
|
||||||
|
|
@ -648,7 +647,6 @@ compare_power_distanceC2(const FT& px, const FT& py, const FT& pwt,
|
||||||
return CGAL_NTS compare(d1, d2);
|
return CGAL_NTS compare(d1, d2);
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|
||||||
template <class FT>
|
template <class FT>
|
||||||
Oriented_side
|
Oriented_side
|
||||||
power_side_of_oriented_power_circleC2( const FT &px, const FT &py, const FT &pwt,
|
power_side_of_oriented_power_circleC2( const FT &px, const FT &py, const FT &pwt,
|
||||||
|
|
@ -699,7 +697,6 @@ power_side_of_oriented_power_circleC2( const FT &px, const FT &py, const FT &pwt
|
||||||
return cmpy * sign_of_determinant(dpy, dpz, dqy, dqz);
|
return cmpy * sign_of_determinant(dpy, dpz, dqy, dqz);
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|
||||||
} //namespace CGAL
|
} //namespace CGAL
|
||||||
|
|
||||||
#endif // CGAL_PREDICATES_KERNEL_FTC2_H
|
#endif // CGAL_PREDICATES_KERNEL_FTC2_H
|
||||||
|
|
|
||||||
|
|
@ -301,7 +301,6 @@ namespace CommonKernelFunctors {
|
||||||
}
|
}
|
||||||
};
|
};
|
||||||
|
|
||||||
|
|
||||||
template < typename K >
|
template < typename K >
|
||||||
class Compare_power_distance_3
|
class Compare_power_distance_3
|
||||||
{
|
{
|
||||||
|
|
@ -310,407 +309,373 @@ namespace CommonKernelFunctors {
|
||||||
typedef typename K::Point_3 Point_3;
|
typedef typename K::Point_3 Point_3;
|
||||||
typedef typename K::Comparison_result Comparison_result;
|
typedef typename K::Comparison_result Comparison_result;
|
||||||
|
|
||||||
typedef Comparison_result result_type;
|
typedef Comparison_result result_type;
|
||||||
|
|
||||||
Comparison_result operator() ( const Point_3 & p,
|
Comparison_result operator()(const Point_3 & p,
|
||||||
const Weighted_point_3 & q,
|
const Weighted_point_3 & q,
|
||||||
const Weighted_point_3 & r) const
|
const Weighted_point_3 & r) const
|
||||||
{
|
{
|
||||||
return compare_power_distanceC3(p.x(), p.y(), p.z(),
|
return compare_power_distanceC3(p.x(), p.y(), p.z(),
|
||||||
q.x(), q.y(), q.z(), q.weight(),
|
q.x(), q.y(), q.z(), q.weight(),
|
||||||
r.x(), r.y(), r.z(), r.weight());
|
r.x(), r.y(), r.z(), r.weight());
|
||||||
}
|
}
|
||||||
};
|
};
|
||||||
|
|
||||||
|
template < typename K >
|
||||||
|
class Construct_weighted_circumcenter_3
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
typedef typename K::Weighted_point_3 Weighted_point_3;
|
||||||
|
typedef typename K::Point_3 Point_3;
|
||||||
|
typedef typename K::FT FT;
|
||||||
|
|
||||||
|
typedef Point_3 result_type;
|
||||||
|
|
||||||
template < typename K >
|
Point_3 operator()(const Weighted_point_3 & p,
|
||||||
class Construct_weighted_circumcenter_3
|
const Weighted_point_3 & q,
|
||||||
{
|
const Weighted_point_3 & r,
|
||||||
public:
|
const Weighted_point_3 & s) const
|
||||||
typedef typename K::Weighted_point_3 Weighted_point_3;
|
|
||||||
typedef typename K::Point_3 Point_3;
|
|
||||||
typedef typename K::FT FT;
|
|
||||||
|
|
||||||
typedef Point_3 result_type;
|
|
||||||
|
|
||||||
Point_3 operator() ( const Weighted_point_3 & p,
|
|
||||||
const Weighted_point_3 & q,
|
|
||||||
const Weighted_point_3 & r,
|
|
||||||
const Weighted_point_3 & s) const
|
|
||||||
{
|
{
|
||||||
FT x, y, z;
|
FT x, y, z;
|
||||||
weighted_circumcenterC3(p.x(), p.y(), p.z(), p.weight(),
|
weighted_circumcenterC3(p.x(), p.y(), p.z(), p.weight(),
|
||||||
q.x(), q.y(), q.z(), q.weight(),
|
q.x(), q.y(), q.z(), q.weight(),
|
||||||
r.x(), r.y(), r.z(), r.weight(),
|
r.x(), r.y(), r.z(), r.weight(),
|
||||||
s.x(), s.y(), s.z(), s.weight(),
|
s.x(), s.y(), s.z(), s.weight(),
|
||||||
x,y,z);
|
x,y,z);
|
||||||
return Point_3(x,y,z);
|
return Point_3(x,y,z);
|
||||||
}
|
}
|
||||||
|
|
||||||
Point_3 operator() ( const Weighted_point_3 & p,
|
Point_3 operator()(const Weighted_point_3 & p,
|
||||||
const Weighted_point_3 & q,
|
const Weighted_point_3 & q,
|
||||||
const Weighted_point_3 & r) const
|
const Weighted_point_3 & r) const
|
||||||
{
|
{
|
||||||
FT x, y, z;
|
FT x, y, z;
|
||||||
weighted_circumcenterC3(p.x(), p.y(), p.z(), p.weight(),
|
weighted_circumcenterC3(p.x(), p.y(), p.z(), p.weight(),
|
||||||
q.x(), q.y(), q.z(), q.weight(),
|
q.x(), q.y(), q.z(), q.weight(),
|
||||||
r.x(), r.y(), r.z(), r.weight(),
|
r.x(), r.y(), r.z(), r.weight(),
|
||||||
x,y,z);
|
x,y,z);
|
||||||
return Point_3(x,y,z);
|
return Point_3(x,y,z);
|
||||||
}
|
}
|
||||||
|
|
||||||
Point_3 operator() ( const Weighted_point_3 & p,
|
Point_3 operator()(const Weighted_point_3 & p,
|
||||||
const Weighted_point_3 & q) const
|
const Weighted_point_3 & q) const
|
||||||
{
|
{
|
||||||
FT x, y, z;
|
FT x, y, z;
|
||||||
weighted_circumcenterC3(p.x(), p.y(), p.z(), p.weight(),
|
weighted_circumcenterC3(p.x(), p.y(), p.z(), p.weight(),
|
||||||
q.x(), q.y(), q.z(), q.weight(),
|
q.x(), q.y(), q.z(), q.weight(),
|
||||||
x,y,z);
|
x,y,z);
|
||||||
return Point_3(x,y,z);
|
return Point_3(x,y,z);
|
||||||
}
|
}
|
||||||
};
|
};
|
||||||
|
|
||||||
//////////////////////
|
// operator ()
|
||||||
|
// return the sign of the power test of last weighted point
|
||||||
// operator ()
|
// with respect to the smallest sphere orthogonal to the others
|
||||||
// return the sign of the power test of last weighted point
|
template< typename K >
|
||||||
// with respect to the smallest sphere orthogonal to the others
|
class Power_side_of_bounded_power_sphere_3
|
||||||
template< typename K >
|
|
||||||
class Power_side_of_bounded_power_sphere_3
|
|
||||||
{
|
|
||||||
public:
|
|
||||||
typedef typename K::Weighted_point_3 Weighted_point_3;
|
|
||||||
typedef typename K::Sign Sign;
|
|
||||||
|
|
||||||
typedef Bounded_side result_type;
|
|
||||||
|
|
||||||
Bounded_side operator() (const Weighted_point_3 & p,
|
|
||||||
const Weighted_point_3 & q,
|
|
||||||
const Weighted_point_3 & r,
|
|
||||||
const Weighted_point_3 & s,
|
|
||||||
const Weighted_point_3 & t) const
|
|
||||||
{
|
{
|
||||||
K traits;
|
public:
|
||||||
typename K::Orientation_3 orientation = traits.orientation_3_object();
|
typedef typename K::Weighted_point_3 Weighted_point_3;
|
||||||
typename K::Power_side_of_oriented_power_sphere_3 power_test = traits.power_side_of_oriented_power_sphere_3_object();
|
typedef typename K::Sign Sign;
|
||||||
typename K::Orientation o = orientation(p,q,r,s);
|
|
||||||
typename K::Oriented_side os = power_test(p,q,r,s,t);
|
|
||||||
// power_test_3
|
|
||||||
// returns in fact minus the 5x5 determinant of lifted (p,q,r,s.t)
|
|
||||||
CGAL_assertion(o != COPLANAR);
|
|
||||||
return enum_cast<Bounded_side>(o * os);
|
|
||||||
}
|
|
||||||
|
|
||||||
Bounded_side operator() (const Weighted_point_3 & p,
|
typedef Bounded_side result_type;
|
||||||
const Weighted_point_3 & q,
|
|
||||||
const Weighted_point_3 & r,
|
|
||||||
const Weighted_point_3 & s) const
|
|
||||||
{
|
|
||||||
return power_side_of_bounded_power_sphereC3(
|
|
||||||
p.x(), p.y(), p.z(), p.weight(),
|
|
||||||
q.x(), q.y(), q.z(), q.weight(),
|
|
||||||
r.x(), r.y(), r.z(), r.weight(),
|
|
||||||
s.x(), s.y(), s.z(), s.weight());
|
|
||||||
}
|
|
||||||
|
|
||||||
Bounded_side operator() (const Weighted_point_3 & p,
|
Bounded_side operator()(const Weighted_point_3 & p,
|
||||||
const Weighted_point_3 & q,
|
const Weighted_point_3 & q,
|
||||||
const Weighted_point_3 & r) const
|
const Weighted_point_3 & r,
|
||||||
{
|
const Weighted_point_3 & s,
|
||||||
return power_side_of_bounded_power_sphereC3(
|
const Weighted_point_3 & t) const
|
||||||
p.x(), p.y(), p.z(), p.weight(),
|
|
||||||
q.x(), q.y(), q.z(), q.weight(),
|
|
||||||
r.x(), r.y(), r.z(), r.weight());
|
|
||||||
}
|
|
||||||
|
|
||||||
Bounded_side operator() (const Weighted_point_3 & p,
|
|
||||||
const Weighted_point_3 & q) const
|
|
||||||
{
|
|
||||||
return enum_cast<Bounded_side>(
|
|
||||||
- CGAL_NTS sign( CGAL_NTS square(p.x()-q.x()) +
|
|
||||||
CGAL_NTS square(p.y()-q.y()) +
|
|
||||||
CGAL_NTS square(p.z()-q.z()) +
|
|
||||||
p.weight() - q.weight()));
|
|
||||||
}
|
|
||||||
|
|
||||||
};
|
|
||||||
|
|
||||||
template < typename K >
|
|
||||||
class Power_side_of_oriented_power_sphere_3
|
|
||||||
{
|
|
||||||
public:
|
|
||||||
typedef typename K::Weighted_point_3 Weighted_point_3;
|
|
||||||
typedef typename K::Oriented_side Oriented_side;
|
|
||||||
|
|
||||||
typedef Oriented_side result_type;
|
|
||||||
|
|
||||||
Oriented_side operator() ( const Weighted_point_3 & p,
|
|
||||||
const Weighted_point_3 & q,
|
|
||||||
const Weighted_point_3 & r,
|
|
||||||
const Weighted_point_3 & s,
|
|
||||||
const Weighted_point_3 & t) const
|
|
||||||
{
|
{
|
||||||
return power_side_of_oriented_power_sphereC3(p.x(), p.y(), p.z(), p.weight(),
|
K traits;
|
||||||
q.x(), q.y(), q.z(), q.weight(),
|
typename K::Orientation_3 orientation = traits.orientation_3_object();
|
||||||
r.x(), r.y(), r.z(), r.weight(),
|
typename K::Power_side_of_oriented_power_sphere_3 power_test = traits.power_side_of_oriented_power_sphere_3_object();
|
||||||
s.x(), s.y(), s.z(), s.weight(),
|
typename K::Orientation o = orientation(p,q,r,s);
|
||||||
t.x(), t.y(), t.z(), t.weight());
|
typename K::Oriented_side os = power_test(p,q,r,s,t);
|
||||||
|
// power_test_3
|
||||||
|
// returns in fact minus the 5x5 determinant of lifted (p,q,r,s.t)
|
||||||
|
CGAL_assertion(o != COPLANAR);
|
||||||
|
return enum_cast<Bounded_side>(o * os);
|
||||||
}
|
}
|
||||||
|
|
||||||
Oriented_side operator() ( const Weighted_point_3 & p,
|
Bounded_side operator()(const Weighted_point_3 & p,
|
||||||
const Weighted_point_3 & q,
|
const Weighted_point_3 & q,
|
||||||
const Weighted_point_3 & r,
|
const Weighted_point_3 & r,
|
||||||
const Weighted_point_3 & s) const
|
const Weighted_point_3 & s) const
|
||||||
{
|
{
|
||||||
return power_side_of_oriented_power_sphereC3(p.x(), p.y(), p.z(), p.weight(),
|
return power_side_of_bounded_power_sphereC3(
|
||||||
q.x(), q.y(), q.z(), q.weight(),
|
p.x(), p.y(), p.z(), p.weight(),
|
||||||
r.x(), r.y(), r.z(), r.weight(),
|
q.x(), q.y(), q.z(), q.weight(),
|
||||||
s.x(), s.y(), s.z(), s.weight());
|
r.x(), r.y(), r.z(), r.weight(),
|
||||||
|
s.x(), s.y(), s.z(), s.weight());
|
||||||
}
|
}
|
||||||
|
|
||||||
Oriented_side operator() ( const Weighted_point_3 & p,
|
Bounded_side operator()(const Weighted_point_3 & p,
|
||||||
const Weighted_point_3 & q,
|
const Weighted_point_3 & q,
|
||||||
const Weighted_point_3 & r) const
|
const Weighted_point_3 & r) const
|
||||||
{
|
{
|
||||||
return power_side_of_oriented_power_sphereC3(p.x(), p.y(), p.z(), p.weight(),
|
return power_side_of_bounded_power_sphereC3(
|
||||||
q.x(), q.y(), q.z(), q.weight(),
|
p.x(), p.y(), p.z(), p.weight(),
|
||||||
r.x(), r.y(), r.z(), r.weight());
|
q.x(), q.y(), q.z(), q.weight(),
|
||||||
|
r.x(), r.y(), r.z(), r.weight());
|
||||||
}
|
}
|
||||||
|
|
||||||
Oriented_side operator() ( const Weighted_point_3 & p,
|
Bounded_side operator()(const Weighted_point_3 & p,
|
||||||
const Weighted_point_3 & q) const
|
const Weighted_point_3 & q) const
|
||||||
|
{
|
||||||
|
return enum_cast<Bounded_side>(
|
||||||
|
- CGAL_NTS sign( CGAL_NTS square(p.x()-q.x()) +
|
||||||
|
CGAL_NTS square(p.y()-q.y()) +
|
||||||
|
CGAL_NTS square(p.z()-q.z()) +
|
||||||
|
p.weight() - q.weight()));
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
template < typename K >
|
||||||
|
class Power_side_of_oriented_power_sphere_3
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
typedef typename K::Weighted_point_3 Weighted_point_3;
|
||||||
|
typedef typename K::Oriented_side Oriented_side;
|
||||||
|
|
||||||
|
typedef Oriented_side result_type;
|
||||||
|
|
||||||
|
Oriented_side operator()(const Weighted_point_3 & p,
|
||||||
|
const Weighted_point_3 & q,
|
||||||
|
const Weighted_point_3 & r,
|
||||||
|
const Weighted_point_3 & s,
|
||||||
|
const Weighted_point_3 & t) const
|
||||||
|
{
|
||||||
|
return power_side_of_oriented_power_sphereC3(p.x(), p.y(), p.z(), p.weight(),
|
||||||
|
q.x(), q.y(), q.z(), q.weight(),
|
||||||
|
r.x(), r.y(), r.z(), r.weight(),
|
||||||
|
s.x(), s.y(), s.z(), s.weight(),
|
||||||
|
t.x(), t.y(), t.z(), t.weight());
|
||||||
|
}
|
||||||
|
|
||||||
|
Oriented_side operator()(const Weighted_point_3 & p,
|
||||||
|
const Weighted_point_3 & q,
|
||||||
|
const Weighted_point_3 & r,
|
||||||
|
const Weighted_point_3 & s) const
|
||||||
|
{
|
||||||
|
return power_side_of_oriented_power_sphereC3(p.x(), p.y(), p.z(), p.weight(),
|
||||||
|
q.x(), q.y(), q.z(), q.weight(),
|
||||||
|
r.x(), r.y(), r.z(), r.weight(),
|
||||||
|
s.x(), s.y(), s.z(), s.weight());
|
||||||
|
}
|
||||||
|
|
||||||
|
Oriented_side operator()(const Weighted_point_3 & p,
|
||||||
|
const Weighted_point_3 & q,
|
||||||
|
const Weighted_point_3 & r) const
|
||||||
|
{
|
||||||
|
return power_side_of_oriented_power_sphereC3(p.x(), p.y(), p.z(), p.weight(),
|
||||||
|
q.x(), q.y(), q.z(), q.weight(),
|
||||||
|
r.x(), r.y(), r.z(), r.weight());
|
||||||
|
}
|
||||||
|
|
||||||
|
Oriented_side operator()(const Weighted_point_3 & p,
|
||||||
|
const Weighted_point_3 & q) const
|
||||||
{
|
{
|
||||||
return power_side_of_oriented_power_sphereC3(p.weight(),q.weight());
|
return power_side_of_oriented_power_sphereC3(p.weight(),q.weight());
|
||||||
}
|
}
|
||||||
};
|
};
|
||||||
|
|
||||||
template < typename K >
|
template < typename K >
|
||||||
class Compute_weight_2
|
class Compute_weight_2
|
||||||
{
|
|
||||||
public:
|
|
||||||
typedef typename K::Weighted_point_2 Weighted_point_2;
|
|
||||||
typedef typename K::FT Weight;
|
|
||||||
|
|
||||||
typedef const Weight& result_type;
|
|
||||||
|
|
||||||
const Weight& operator()(const Weighted_point_2 & p) const
|
|
||||||
{
|
{
|
||||||
return p.rep().weight();
|
public:
|
||||||
}
|
typedef typename K::Weighted_point_2 Weighted_point_2;
|
||||||
};
|
typedef typename K::FT Weight;
|
||||||
|
|
||||||
|
typedef const Weight& result_type;
|
||||||
|
|
||||||
template < typename K >
|
const Weight& operator()(const Weighted_point_2 & p) const
|
||||||
class Compute_weight_3
|
|
||||||
{
|
|
||||||
public:
|
|
||||||
typedef typename K::Weighted_point_3 Weighted_point_3;
|
|
||||||
typedef typename K::FT Weight;
|
|
||||||
|
|
||||||
typedef const Weight& result_type;
|
|
||||||
|
|
||||||
const Weight& operator()(const Weighted_point_3 & p) const
|
|
||||||
{
|
|
||||||
return p.rep().weight();
|
|
||||||
}
|
|
||||||
};
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
template < typename K >
|
|
||||||
class Compute_power_product_3
|
|
||||||
{
|
|
||||||
public:
|
|
||||||
typedef typename K::Weighted_point_3 Weighted_point_3;
|
|
||||||
typedef typename K::FT FT;
|
|
||||||
|
|
||||||
typedef FT result_type;
|
|
||||||
|
|
||||||
FT operator() (const Weighted_point_3 & p,
|
|
||||||
const Weighted_point_3 & q) const
|
|
||||||
{
|
|
||||||
return power_productC3(p.x(), p.y(), p.z(), p.weight(),
|
|
||||||
q.x(), q.y(), q.z(), q.weight());
|
|
||||||
}
|
|
||||||
};
|
|
||||||
|
|
||||||
|
|
||||||
template < typename K >
|
|
||||||
class Compute_squared_radius_smallest_orthogonal_circle_2
|
|
||||||
{
|
|
||||||
public:
|
|
||||||
typedef typename K::Weighted_point_2 Weighted_point_2;
|
|
||||||
typedef typename K::FT FT;
|
|
||||||
|
|
||||||
typedef FT result_type;
|
|
||||||
|
|
||||||
FT operator()(const Weighted_point_2& p,
|
|
||||||
const Weighted_point_2& q,
|
|
||||||
const Weighted_point_2& r) const
|
|
||||||
{
|
|
||||||
return squared_radius_orthogonal_circleC2(p.x(), p.y(), p.weight(),
|
|
||||||
q.x(), q.y(), q.weight(),
|
|
||||||
r.x(), r.y(), r.weight());
|
|
||||||
}
|
|
||||||
|
|
||||||
FT operator()(const Weighted_point_2& p,
|
|
||||||
const Weighted_point_2& q) const
|
|
||||||
{
|
|
||||||
return squared_radius_smallest_orthogonal_circleC2(p.x(), p.y(), p.weight(),
|
|
||||||
q.x(), q.y(), q.weight());
|
|
||||||
}
|
|
||||||
|
|
||||||
FT operator()(const Weighted_point_2& p) const
|
|
||||||
{
|
|
||||||
return - p.weight();
|
|
||||||
}
|
|
||||||
};
|
|
||||||
|
|
||||||
template < typename K >
|
|
||||||
class Compute_squared_radius_smallest_orthogonal_sphere_3
|
|
||||||
{
|
|
||||||
public:
|
|
||||||
typedef typename K::Weighted_point_3 Weighted_point_3;
|
|
||||||
typedef typename K::FT FT;
|
|
||||||
|
|
||||||
typedef FT result_type;
|
|
||||||
|
|
||||||
FT operator() ( const Weighted_point_3 & p,
|
|
||||||
const Weighted_point_3 & q,
|
|
||||||
const Weighted_point_3 & r,
|
|
||||||
const Weighted_point_3 & s) const
|
|
||||||
{
|
{
|
||||||
return squared_radius_orthogonal_sphereC3(
|
return p.rep().weight();
|
||||||
p.x(), p.y(), p.z(), p.weight(),
|
}
|
||||||
q.x(), q.y(), q.z(), q.weight(),
|
};
|
||||||
r.x(), r.y(), r.z(), r.weight(),
|
|
||||||
s.x(), s.y(), s.z(), s.weight());
|
template < typename K >
|
||||||
|
class Compute_weight_3
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
typedef typename K::Weighted_point_3 Weighted_point_3;
|
||||||
|
typedef typename K::FT Weight;
|
||||||
|
|
||||||
|
typedef const Weight& result_type;
|
||||||
|
|
||||||
|
const Weight& operator()(const Weighted_point_3 & p) const
|
||||||
|
{
|
||||||
|
return p.rep().weight();
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
template < typename K >
|
||||||
|
class Compute_power_product_3
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
typedef typename K::Weighted_point_3 Weighted_point_3;
|
||||||
|
typedef typename K::FT FT;
|
||||||
|
|
||||||
|
typedef FT result_type;
|
||||||
|
|
||||||
|
FT operator()(const Weighted_point_3 & p,
|
||||||
|
const Weighted_point_3 & q) const
|
||||||
|
{
|
||||||
|
return power_productC3(p.x(), p.y(), p.z(), p.weight(),
|
||||||
|
q.x(), q.y(), q.z(), q.weight());
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
template < typename K >
|
||||||
|
class Compute_squared_radius_smallest_orthogonal_circle_2
|
||||||
|
{
|
||||||
|
public:
|
||||||
|
typedef typename K::Weighted_point_2 Weighted_point_2;
|
||||||
|
typedef typename K::FT FT;
|
||||||
|
|
||||||
|
typedef FT result_type;
|
||||||
|
|
||||||
|
FT operator()(const Weighted_point_2& p,
|
||||||
|
const Weighted_point_2& q,
|
||||||
|
const Weighted_point_2& r) const
|
||||||
|
{
|
||||||
|
return squared_radius_orthogonal_circleC2(p.x(), p.y(), p.weight(),
|
||||||
|
q.x(), q.y(), q.weight(),
|
||||||
|
r.x(), r.y(), r.weight());
|
||||||
}
|
}
|
||||||
|
|
||||||
FT operator() ( const Weighted_point_3 & p,
|
FT operator()(const Weighted_point_2& p,
|
||||||
const Weighted_point_3 & q,
|
const Weighted_point_2& q) const
|
||||||
const Weighted_point_3 & r) const
|
|
||||||
{
|
{
|
||||||
return squared_radius_smallest_orthogonal_sphereC3(
|
return squared_radius_smallest_orthogonal_circleC2(p.x(), p.y(), p.weight(),
|
||||||
p.x(), p.y(), p.z(), p.weight(),
|
q.x(), q.y(), q.weight());
|
||||||
q.x(), q.y(), q.z(), q.weight(),
|
|
||||||
r.x(), r.y(), r.z(), r.weight());
|
|
||||||
}
|
}
|
||||||
|
|
||||||
FT operator() (const Weighted_point_3 & p,
|
FT operator()(const Weighted_point_2& p) const
|
||||||
const Weighted_point_3 & q) const
|
{
|
||||||
|
return - p.weight();
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
template < typename K >
|
||||||
|
class Compute_squared_radius_smallest_orthogonal_sphere_3
|
||||||
{
|
{
|
||||||
return squared_radius_smallest_orthogonal_sphereC3(
|
public:
|
||||||
p.x(), p.y(), p.z(), p.weight(),
|
typedef typename K::Weighted_point_3 Weighted_point_3;
|
||||||
q.x(), q.y(), q.z(), q.weight());
|
typedef typename K::FT FT;
|
||||||
}
|
|
||||||
|
typedef FT result_type;
|
||||||
FT operator() (const Weighted_point_3 & p) const
|
|
||||||
|
FT operator()(const Weighted_point_3 & p,
|
||||||
|
const Weighted_point_3 & q,
|
||||||
|
const Weighted_point_3 & r,
|
||||||
|
const Weighted_point_3 & s) const
|
||||||
|
{
|
||||||
|
return squared_radius_orthogonal_sphereC3(p.x(), p.y(), p.z(), p.weight(),
|
||||||
|
q.x(), q.y(), q.z(), q.weight(),
|
||||||
|
r.x(), r.y(), r.z(), r.weight(),
|
||||||
|
s.x(), s.y(), s.z(), s.weight());
|
||||||
|
}
|
||||||
|
|
||||||
|
FT operator()(const Weighted_point_3 & p,
|
||||||
|
const Weighted_point_3 & q,
|
||||||
|
const Weighted_point_3 & r) const
|
||||||
|
{
|
||||||
|
return squared_radius_smallest_orthogonal_sphereC3(p.x(), p.y(), p.z(), p.weight(),
|
||||||
|
q.x(), q.y(), q.z(), q.weight(),
|
||||||
|
r.x(), r.y(), r.z(), r.weight());
|
||||||
|
}
|
||||||
|
|
||||||
|
FT operator()(const Weighted_point_3 & p,
|
||||||
|
const Weighted_point_3 & q) const
|
||||||
|
{
|
||||||
|
return squared_radius_smallest_orthogonal_sphereC3(p.x(), p.y(), p.z(), p.weight(),
|
||||||
|
q.x(), q.y(), q.z(), q.weight());
|
||||||
|
}
|
||||||
|
|
||||||
|
FT operator()(const Weighted_point_3 & p) const
|
||||||
|
{
|
||||||
|
return - p.weight();
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
// Compute the square radius of the sphere centered in t
|
||||||
|
// and orthogonal to the sphere orthogonal to p,q,r,s
|
||||||
|
template< typename K>
|
||||||
|
class Compute_power_distance_to_power_sphere_3
|
||||||
{
|
{
|
||||||
return -p.weight();
|
public:
|
||||||
}
|
typedef typename K::Weighted_point_3 Weighted_point_3;
|
||||||
|
typedef typename K::FT FT;
|
||||||
};
|
|
||||||
|
|
||||||
|
typedef FT result_type;
|
||||||
|
|
||||||
// Compute the square radius of the sphere centered in t
|
result_type operator()(const Weighted_point_3 & p,
|
||||||
// and orthogonal to the sphere orthogonal to p,q,r,s
|
const Weighted_point_3 & q,
|
||||||
template< typename K>
|
const Weighted_point_3 & r,
|
||||||
class Compute_power_distance_to_power_sphere_3
|
const Weighted_point_3 & s,
|
||||||
{
|
const Weighted_point_3 & t) const
|
||||||
public:
|
{
|
||||||
typedef typename K::Weighted_point_3 Weighted_point_3;
|
return power_distance_to_power_sphereC3 (p.x(),p.y(),p.z(),FT(p.weight()),
|
||||||
typedef typename K::FT FT;
|
q.x(),q.y(),q.z(),FT(q.weight()),
|
||||||
|
r.x(),r.y(),r.z(),FT(r.weight()),
|
||||||
|
s.x(),s.y(),s.z(),FT(s.weight()),
|
||||||
|
t.x(),t.y(),t.z(),FT(t.weight()));
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
typedef FT result_type;
|
template <typename K>
|
||||||
|
class Compare_weighted_squared_radius_3
|
||||||
result_type operator() (const Weighted_point_3 & p,
|
|
||||||
const Weighted_point_3 & q,
|
|
||||||
const Weighted_point_3 & r,
|
|
||||||
const Weighted_point_3 & s,
|
|
||||||
const Weighted_point_3 & t) const
|
|
||||||
{
|
{
|
||||||
return power_distance_to_power_sphereC3 (p.x(),p.y(),p.z(),FT(p.weight()),
|
public:
|
||||||
q.x(),q.y(),q.z(),FT(q.weight()),
|
typedef typename K::Weighted_point_3 Weighted_point_3;
|
||||||
r.x(),r.y(),r.z(),FT(r.weight()),
|
typedef typename K::Comparison_result Comparison_result;
|
||||||
s.x(),s.y(),s.z(),FT(s.weight()),
|
typedef typename K::FT FT;
|
||||||
t.x(),t.y(),t.z(),FT(t.weight()));
|
|
||||||
}
|
|
||||||
};
|
|
||||||
|
|
||||||
|
typedef Comparison_result result_type;
|
||||||
|
|
||||||
|
result_type operator()(const Weighted_point_3 & p,
|
||||||
|
const Weighted_point_3 & q,
|
||||||
|
const Weighted_point_3 & r,
|
||||||
|
const Weighted_point_3 & s,
|
||||||
|
const FT& w) const
|
||||||
|
{
|
||||||
|
return CGAL::compare(squared_radius_orthogonal_sphereC3(
|
||||||
|
p.x(),p.y(),p.z(),p.weight(),
|
||||||
|
q.x(),q.y(),q.z(),q.weight(),
|
||||||
|
r.x(),r.y(),r.z(),r.weight(),
|
||||||
|
s.x(),s.y(),s.z(),s.weight()),
|
||||||
|
w);
|
||||||
|
}
|
||||||
|
|
||||||
template <typename K>
|
result_type operator()(const Weighted_point_3 & p,
|
||||||
class Compare_weighted_squared_radius_3
|
const Weighted_point_3 & q,
|
||||||
{
|
const Weighted_point_3 & r,
|
||||||
|
const FT& w) const
|
||||||
typedef typename K::Weighted_point_3 Weighted_point_3;
|
{
|
||||||
typedef typename K::Comparison_result Comparison_result;
|
return CGAL::compare(squared_radius_smallest_orthogonal_sphereC3(
|
||||||
typedef typename K::FT FT;
|
p.x(),p.y(),p.z(),p.weight(),
|
||||||
|
q.x(),q.y(),q.z(),q.weight(),
|
||||||
public:
|
r.x(),r.y(),r.z(),r.weight()),
|
||||||
typedef Comparison_result result_type;
|
w);
|
||||||
|
}
|
||||||
|
|
||||||
result_type operator() (
|
|
||||||
const Weighted_point_3 & p,
|
|
||||||
const Weighted_point_3 & q,
|
|
||||||
const Weighted_point_3 & r,
|
|
||||||
const Weighted_point_3 & s,
|
|
||||||
const FT& w) const
|
|
||||||
{
|
|
||||||
return CGAL::compare(
|
|
||||||
squared_radius_orthogonal_sphereC3(
|
|
||||||
p.x(),p.y(),p.z(),p.weight(),
|
|
||||||
q.x(),q.y(),q.z(),q.weight(),
|
|
||||||
r.x(),r.y(),r.z(),r.weight(),
|
|
||||||
s.x(),s.y(),s.z(),s.weight() ),
|
|
||||||
w);
|
|
||||||
}
|
|
||||||
|
|
||||||
result_type operator() (
|
|
||||||
const Weighted_point_3 & p,
|
|
||||||
const Weighted_point_3 & q,
|
|
||||||
const Weighted_point_3 & r,
|
|
||||||
const FT& w) const
|
|
||||||
{
|
|
||||||
return CGAL::compare(
|
|
||||||
squared_radius_smallest_orthogonal_sphereC3(
|
|
||||||
p.x(),p.y(),p.z(),p.weight(),
|
|
||||||
q.x(),q.y(),q.z(),q.weight(),
|
|
||||||
r.x(),r.y(),r.z(),r.weight() ),
|
|
||||||
w);
|
|
||||||
}
|
|
||||||
|
|
||||||
result_type operator() (
|
|
||||||
const Weighted_point_3 & p,
|
|
||||||
const Weighted_point_3 & q,
|
|
||||||
const FT& w) const
|
|
||||||
{
|
|
||||||
return CGAL::compare(
|
|
||||||
squared_radius_smallest_orthogonal_sphereC3(
|
|
||||||
p.x(),p.y(),p.z(),p.weight(),
|
|
||||||
q.x(),q.y(),q.z(),q.weight() ),
|
|
||||||
w);
|
|
||||||
}
|
|
||||||
|
|
||||||
result_type operator() (
|
|
||||||
const Weighted_point_3 & p,
|
|
||||||
const FT& w) const
|
|
||||||
{
|
|
||||||
return CGAL::compare(-p.weight(),w);
|
|
||||||
}
|
|
||||||
};
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
//////////////////////
|
|
||||||
|
|
||||||
|
result_type operator()(const Weighted_point_3 & p,
|
||||||
|
const Weighted_point_3 & q,
|
||||||
|
const FT& w) const
|
||||||
|
{
|
||||||
|
return CGAL::compare(squared_radius_smallest_orthogonal_sphereC3(
|
||||||
|
p.x(),p.y(),p.z(),p.weight(),
|
||||||
|
q.x(),q.y(),q.z(),q.weight()),
|
||||||
|
w);
|
||||||
|
}
|
||||||
|
|
||||||
|
result_type operator()(const Weighted_point_3 & p,
|
||||||
|
const FT& w) const
|
||||||
|
{
|
||||||
|
return CGAL::compare(-p.weight(), w);
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
template <typename K>
|
template <typename K>
|
||||||
class Compare_squared_distance_2
|
class Compare_squared_distance_2
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue