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Rename the following functions: 

det2x2_by_formula
  det3x3_by_formula
  det4x4_by_formula
  det5x5_by_formula
  det6x6_by_formula
to:
  determinant

How cute...  a name independent of the dimension, and even readable !
This commit is contained in:
Sylvain Pion 2008-04-09 13:35:34 +00:00
parent af5ffdecae
commit 1d8779b171
45 changed files with 286 additions and 286 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

6
Alpha_shapes_2/include/CGAL/constructions/squared_radius_smallest_orthogonalcircle_ftC2.h
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@ -44,11 +44,11 @@ squared_radius_orthogonalcircleC2(
FT dpp = CGAL_NTS square(dpx)+CGAL_NTS square(dpy)-pw+rw;
FT dqq = CGAL_NTS square(dqx)+CGAL_NTS square(dqy)-qw+rw;
FT det0 = det2x2_by_formula(dpx, dpy, dqx, dqy);
FT det0 = determinant(dpx, dpy, dqx, dqy);
FT det1 = det2x2_by_formula(dpp, dpy, dqq, dqy);
FT det1 = determinant(dpp, dpy, dqq, dqy);
FT det2 = det2x2_by_formula(dpx, dpp, dqx, dqq);
FT det2 = determinant(dpx, dpp, dqx, dqq);
return
(CGAL_NTS square(det1)+CGAL_NTS square(det2))/

12
Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Constructions_ftC2.h
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@ -65,9 +65,9 @@ w_plane_tangent_line_2(const FT &x1, const FT &y1, const FT &w1,
FT Dv = v2 - v3;
FT Dr = r2 - r3;
FT Duv = det2x2_by_formula(u2, v2, u3, v3);
FT Dur = det2x2_by_formula(u2, r2, u3, r3);
FT Dvr = det2x2_by_formula(v2, r2, v3, r3);
FT Duv = determinant(u2, v2, u3, v3);
FT Dur = determinant(u2, r2, u3, r3);
FT Dvr = determinant(v2, r2, v3, r3);
FT D1 = CGAL::square(Du) + CGAL::square(Dv);
FT D1inv = FT(1) / D1;
@ -162,9 +162,9 @@ ad_left_bitangent_lineC2(const FT &x1, const FT &y1, const FT &w1,
FT dy = y1 - y2;
FT dw = w1 - w2;
FT dxw = det2x2_by_formula(x1, w1, x2, w2);
FT dyw = det2x2_by_formula(y1, w1, y2, w2);
FT dxy = det2x2_by_formula(x1, y1, x2, y2);
FT dxw = determinant(x1, w1, x2, w2);
FT dyw = determinant(y1, w1, y2, w2);
FT dxy = determinant(x1, y1, x2, y2);
FT D1 = CGAL::square(dx) + CGAL::square(dy);
FT invD1 = FT(1) / D1;

12
Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Incircle8_C2.h
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@ -101,13 +101,13 @@ public:
FT pk = CGAL::square(xk) + CGAL::square(yk) - CGAL::square(rk);
FT pl = CGAL::square(xl) + CGAL::square(yl) - CGAL::square(rl);
FT Exp = det2x2_by_formula(xj, pj, xk, pk);
FT Eyp = det2x2_by_formula(yj, pj, yk, pk);
FT Erp = det2x2_by_formula(rj, pj, rk, pk);
FT Exp = determinant(xj, pj, xk, pk);
FT Eyp = determinant(yj, pj, yk, pk);
FT Erp = determinant(rj, pj, rk, pk);
FT Exy = det2x2_by_formula(xj, yj, xk, yk);
FT Exr = det2x2_by_formula(xj, rj, xk, rk);
FT Eyr = det2x2_by_formula(yj, rj, yk, rk);
FT Exy = determinant(xj, yj, xk, yk);
FT Exr = determinant(xj, rj, xk, rk);
FT Eyr = determinant(yj, rj, yk, rk);
FT Exyp = xl * Eyp - yl * Exp + pl * Exy;
FT Exrp = xl * Erp - rl * Exp + pl * Exr;

2
Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Infinite_edge_test_C2.h
View File

@ -155,7 +155,7 @@ public:
const FT& D, const FT& P) const
{
FT sigma = a * A + b * B;
FT delta = det2x2_by_formula(a, b, A, B);
FT delta = determinant(a, b, A, B);
Sign sign_sigma = CGAL::sign(sigma);
Sign sign_delta = CGAL::sign(delta);

28
Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Orientation8_C2.h
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@ -118,15 +118,15 @@ public:
FT pj = CGAL::square(xj) + CGAL::square(yj) - CGAL::square(rj);
FT pk = CGAL::square(xk) + CGAL::square(yk) - CGAL::square(rk);
FT Exp = det2x2_by_formula(xj, pj, xk, pk);
FT Eyp = det2x2_by_formula(yj, pj, yk, pk);
FT Erp = det2x2_by_formula(rj, pj, rk, pk);
FT Exp = determinant(xj, pj, xk, pk);
FT Eyp = determinant(yj, pj, yk, pk);
FT Erp = determinant(rj, pj, rk, pk);
FT Exy = det2x2_by_formula(xj, yj, xk, yk);
FT Exr = det2x2_by_formula(xj, rj, xk, rk);
FT Eyr = det2x2_by_formula(yj, rj, yk, rk);
FT Exy = determinant(xj, yj, xk, yk);
FT Exr = determinant(xj, rj, xk, rk);
FT Eyr = determinant(yj, rj, yk, rk);
FT Exy2 = 2 * det2x2_by_formula(xl, yl, xm, ym);
FT Exy2 = 2 * determinant(xl, yl, xm, ym);
FT A = (Exp * Exr + Eyp * Eyr) * Exy2 + (Eyp * dx - Exp * dy) * Erp;
FT B = Exy * Exy2 - Exp * dx - Eyp * dy;
@ -194,13 +194,13 @@ public:
pj = nj - CGAL::square(rj);
pk = nk - CGAL::square(rk);
Exp = det2x2_by_formula(xj, pj, xk, pk);
Eyp = det2x2_by_formula(yj, pj, yk, pk);
Erp = det2x2_by_formula(rj, pj, rk, pk);
Exp = determinant(xj, pj, xk, pk);
Eyp = determinant(yj, pj, yk, pk);
Erp = determinant(rj, pj, rk, pk);
Exy = det2x2_by_formula(xj, yj, xk, yk);
Exr = det2x2_by_formula(xj, rj, xk, rk);
Eyr = det2x2_by_formula(yj, rj, yk, rk);
Exy = determinant(xj, yj, xk, yk);
Exr = determinant(xj, rj, xk, rk);
Eyr = determinant(yj, rj, yk, rk);
A1 = Exp * Exr + Eyp * Eyr;
@ -284,7 +284,7 @@ private:
FT dx = xl - xm;
FT dy = yl - ym;
FT Exy2 = 2 * det2x2_by_formula(xl, yl, xm, ym);
FT Exy2 = 2 * determinant(xl, yl, xm, ym);
FT A = A1 * Exy2 + (Eyp * dx - Exp * dy) * Erp;
FT B = Exy * Exy2 - Exp * dx - Eyp * dy;

4
Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Orientation_2.h
View File

@ -62,7 +62,7 @@ private:
FT b = vc.b1() + vc.b2() * CGAL::sqrt(vc.delta());
FT det1 = a * (p2.y() - p1.y()) - b * (p2.x() - p1.x());
FT c = vc.c1() + vc.c2() * CGAL::sqrt(vc.delta());
FT det2 = det2x2_by_formula(p1.x() - sp1.x(), p1.y() - sp1.y(),
FT det2 = determinant(p1.x() - sp1.x(), p1.y() - sp1.y(),
p2.x() - sp1.x(), p2.y() - sp1.y());
return CGAL::sign(det1 + FT(2) * c * det2);
}
@ -73,7 +73,7 @@ private:
{
FT dx = p2.x() - p1.x();
FT dy = p2.y() - p1.y();
FT det1 = det2x2_by_formula(p1.x() - sp1.x(), p1.y() - sp1.y(),
FT det1 = determinant(p1.x() - sp1.x(), p1.y() - sp1.y(),
p2.x() - sp1.x(), p2.y() - sp1.y());
FT A = vc.a1() * dy - vc.b1() * dx + FT(2) * vc.c1() * det1;
FT B = vc.a2() * dy - vc.b2() * dx + FT(2) * vc.c2() * det1;

42
Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Predicate_constructions_C2.h
View File

@ -100,12 +100,12 @@ public:
Voronoi_radius_2(const Inverted_weighted_point& u1,
const Inverted_weighted_point& u2)
{
FT dxp = det2x2_by_formula(u1.x(), u1.p(), u2.x(), u2.p());
FT dyp = det2x2_by_formula(u1.y(), u1.p(), u2.y(), u2.p());
FT dwp = det2x2_by_formula(u1.weight(), u1.p(), u2.weight(), u2.p());
FT dxy = det2x2_by_formula(u1.x(), u1.y(), u2.x(), u2.y());
FT dxw = det2x2_by_formula(u1.x(), u1.weight(), u2.x(), u2.weight());
FT dyw = det2x2_by_formula(u1.y(), u1.weight(), u2.y(), u2.weight());
FT dxp = determinant(u1.x(), u1.p(), u2.x(), u2.p());
FT dyp = determinant(u1.y(), u1.p(), u2.y(), u2.p());
FT dwp = determinant(u1.weight(), u1.p(), u2.weight(), u2.p());
FT dxy = determinant(u1.x(), u1.y(), u2.x(), u2.y());
FT dxw = determinant(u1.x(), u1.weight(), u2.x(), u2.weight());
FT dyw = determinant(u1.y(), u1.weight(), u2.y(), u2.weight());
_a = CGAL::square(dxp) + CGAL::square(dyp);
_b = dxp * dxw + dyp * dyw;
@ -193,9 +193,9 @@ public:
FT dx = p1.x() - p2.x();
FT dy = p1.y() - p2.y();
FT dw = p1.weight() - p2.weight();
FT dxy = det2x2_by_formula(p1.x(), p1.y(), p2.x(), p2.y());
FT dxw = det2x2_by_formula(p1.x(), p1.weight(), p2.x(), p2.weight());
FT dyw = det2x2_by_formula(p1.y(), p1.weight(), p2.y(), p2.weight());
FT dxy = determinant(p1.x(), p1.y(), p2.x(), p2.y());
FT dxw = determinant(p1.x(), p1.weight(), p2.x(), p2.weight());
FT dyw = determinant(p1.y(), p1.weight(), p2.y(), p2.weight());
store(dx, dy, dw, dxy, dxw, dyw);
}
@ -204,12 +204,12 @@ public:
Bitangent_line_2(const Inverted_weighted_point& u1,
const Inverted_weighted_point& u2)
{
FT dxp = det2x2_by_formula(u1.x(), u1.p(), u2.x(), u2.p());
FT dyp = det2x2_by_formula(u1.y(), u1.p(), u2.y(), u2.p());
FT dwp = det2x2_by_formula(u1.weight(), u1.p(), u2.weight(), u2.p());
FT dxy = det2x2_by_formula(u1.x(), u1.y(), u2.x(), u2.y());
FT dxw = det2x2_by_formula(u1.x(), u1.weight(), u2.x(), u2.weight());
FT dyw = det2x2_by_formula(u1.y(), u1.weight(), u2.y(), u2.weight());
FT dxp = determinant(u1.x(), u1.p(), u2.x(), u2.p());
FT dyp = determinant(u1.y(), u1.p(), u2.y(), u2.p());
FT dwp = determinant(u1.weight(), u1.p(), u2.weight(), u2.p());
FT dxy = determinant(u1.x(), u1.y(), u2.x(), u2.y());
FT dxw = determinant(u1.x(), u1.weight(), u2.x(), u2.weight());
FT dyw = determinant(u1.y(), u1.weight(), u2.y(), u2.weight());
store(dxp, dyp, dwp, dxy, dxw, dyw);
}
@ -315,13 +315,13 @@ public:
const Inverted_weighted_point& u2,
const Inverted_weighted_point& u3) const
{
FT dx1 = det2x2_by_formula(u2.x(), u2.p(), u1.x(), u1.p());
FT dy1 = det2x2_by_formula(u2.y(), u2.p(), u1.y(), u1.p());
FT dw1 = det2x2_by_formula(u2.weight(), u2.p(), u1.weight(), u1.p());
FT dx1 = determinant(u2.x(), u2.p(), u1.x(), u1.p());
FT dy1 = determinant(u2.y(), u2.p(), u1.y(), u1.p());
FT dw1 = determinant(u2.weight(), u2.p(), u1.weight(), u1.p());
FT dx3 = det2x2_by_formula(u3.x(), u3.p(), u2.x(), u2.p());
FT dy3 = det2x2_by_formula(u3.y(), u3.p(), u2.y(), u2.p());
FT dw3 = det2x2_by_formula(u3.weight(), u3.p(), u2.weight(), u2.p());
FT dx3 = determinant(u3.x(), u3.p(), u2.x(), u2.p());
FT dy3 = determinant(u3.y(), u3.p(), u2.y(), u2.p());
FT dw3 = determinant(u3.weight(), u3.p(), u2.weight(), u2.p());
FT u2Pv2 = CGAL::square(u2.x()) + CGAL::square(u2.y());
FT u2Mv2 = CGAL::square(u2.x()) - CGAL::square(u2.y());

14
Apollonius_graph_2/include/CGAL/Apollonius_graph_2/new_traits/Conflict_2.h
View File

@ -58,15 +58,15 @@ protected:
const Inverted_weighted_point &p3, int i) const
{
Sign s = CGAL::sign(
CGAL::square(det3x3_by_formula<RT>(
CGAL::square(determinant<RT>(
p1.p(), p1.weight(), p1.y(),
p2.p(), p2.weight(), p2.y(),
p3.p(), p3.weight(), p3.y()))
+ CGAL::square(det3x3_by_formula<RT>(
+ CGAL::square(determinant<RT>(
p1.p(), p1.x(), p1.weight(),
p2.p(), p2.x(), p2.weight(),
p3.p(), p3.x(), p3.weight()))
- CGAL::square(det3x3_by_formula<RT>(
- CGAL::square(determinant<RT>(
p1.p(), p1.x(), p1.y(),
p2.p(), p2.x(), p2.y(),
p3.p(), p3.x(), p3.y())));
@ -91,17 +91,17 @@ protected:
CGAL_assertion(i == -1 || i == 1 || i == 2 || i == 3);
Sign s = -CGAL::sign(
det2x2_by_formula<RT>(
determinant<RT>(
p1.p(), p1.x(),
p2.p(), p2.x())
* det3x3_by_formula<RT>(
* determinant<RT>(
p1.p(), p1.weight(), p1.x(),
p2.p(), p2.weight(), p2.x(),
p3.p(), p3.weight(), p3.x())
+ det2x2_by_formula<RT>(
+ determinant<RT>(
p1.p(), p1.y(),
p2.p(), p2.y())
* det3x3_by_formula<RT>(
* determinant<RT>(
p1.p(), p1.weight(), p1.y(),
p2.p(), p2.weight(), p2.y(),
p3.p(), p3.weight(), p3.y()));

2
Apollonius_graph_2/include/CGAL/Hyperbola_2.h
View File

@ -159,7 +159,7 @@ protected:
bool right(const Point_2& p) const
{
return
CGAL::is_negative( det3x3_by_formula<FT>(f1.x(), f1.y(), 1,
CGAL::is_negative( determinant<FT>(f1.x(), f1.y(), 1,
f2.x(), f2.y(), 1,
p.x(), p.y(), 1) );
}

2
Apollonius_graph_2/include/CGAL/Parabola_2.h
View File

@ -191,7 +191,7 @@ protected:
bool right(const Point_2& p) const
{
return
CGAL::is_positive( det3x3_by_formula<FT>(c.x(), c.y(), FT(1),
CGAL::is_positive( determinant<FT>(c.x(), c.y(), FT(1),
o.x(), o.y(), FT(1),
p.x(), p.y(), FT(1)) );
}

26
Cartesian_kernel/include/CGAL/Cartesian/Aff_transformation_rep_3.h
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@ -206,22 +206,22 @@ typename Aff_transformation_repC3<R>::Aff_transformation_3
Aff_transformation_repC3<R>::inverse() const // FIXME : construction
{
return Aff_transformation_3(
det2x2_by_formula( t22, t23, t32, t33), // i 11
-det2x2_by_formula( t12, t13, t32, t33), // i 12
det2x2_by_formula( t12, t13, t22, t23), // i 13
-det3x3_by_formula( t12, t13, t14, t22, t23, t24, t32, t33, t34 ),
determinant( t22, t23, t32, t33), // i 11
-determinant( t12, t13, t32, t33), // i 12
determinant( t12, t13, t22, t23), // i 13
-determinant( t12, t13, t14, t22, t23, t24, t32, t33, t34 ),
-det2x2_by_formula( t21, t23, t31, t33), // i 21
det2x2_by_formula( t11, t13, t31, t33), // i 22
-det2x2_by_formula( t11, t13, t21, t23), // i 23
det3x3_by_formula( t11, t13, t14, t21, t23, t24, t31, t33, t34 ),
-determinant( t21, t23, t31, t33), // i 21
determinant( t11, t13, t31, t33), // i 22
-determinant( t11, t13, t21, t23), // i 23
determinant( t11, t13, t14, t21, t23, t24, t31, t33, t34 ),
det2x2_by_formula( t21, t22, t31, t32), // i 31
-det2x2_by_formula( t11, t12, t31, t32), // i 32
det2x2_by_formula( t11, t12, t21, t22), // i 33
-det3x3_by_formula( t11, t12, t14, t21, t22, t24, t31, t32, t34 ),
determinant( t21, t22, t31, t32), // i 31
-determinant( t11, t12, t31, t32), // i 32
determinant( t11, t12, t21, t22), // i 33
-determinant( t11, t12, t14, t21, t22, t24, t31, t32, t34 ),
det3x3_by_formula( t11, t12, t13, t21, t22, t23, t31, t32, t33 ));
determinant( t11, t12, t13, t21, t22, t23, t31, t32, t33 ));
}
template < class R >

56
Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
View File

@ -769,7 +769,7 @@ namespace CartesianKernelFunctors {
FT v1y = q.y() - p.y();
FT v2x = r.x() - p.x();
FT v2y = r.y() - p.y();
return det2x2_by_formula(v1x, v1y, v2x, v2y)/2;
return determinant(v1x, v1y, v2x, v2y)/2;
}
result_type
@ -793,7 +793,7 @@ namespace CartesianKernelFunctors {
result_type
operator()(const Vector_2& v, const Vector_2& w) const
{
return det2x2_by_formula(v.x(), v.y(), w.x(), w.y());
return determinant(v.x(), v.y(), w.x(), w.y());
}
};
@ -809,7 +809,7 @@ namespace CartesianKernelFunctors {
result_type
operator()(const Vector_3& v, const Vector_3& w, const Vector_3& t) const
{
return det3x3_by_formula(v.x(), v.y(), v.z(),
return determinant(v.x(), v.y(), v.z(),
w.x(), w.y(), w.z(),
t.x(), t.y(), t.z());
}
@ -984,7 +984,7 @@ namespace CartesianKernelFunctors {
operator()(const Point_3& p0, const Point_3& p1,
const Point_3& p2, const Point_3& p3) const
{
return det3x3_by_formula<FT>(p1.x()-p0.x(), p1.y()-p0.y(), p1.z()-p0.z(),
return determinant<FT>(p1.x()-p0.x(), p1.y()-p0.y(), p1.z()-p0.z(),
p2.x()-p0.x(), p2.y()-p0.y(), p2.z()-p0.z(),
p3.x()-p0.x(), p3.y()-p0.y(), p3.z()-p0.z())/6;
}
@ -1846,24 +1846,24 @@ namespace CartesianKernelFunctors {
// The following determinants can be developped and simplified.
//
// FT num_x = det3x3_by_formula(psy,psz,ps2,
// FT num_x = determinant(psy,psz,ps2,
// qsy,qsz,qs2,
// rsy,rsz,0);
// FT num_y = det3x3_by_formula(psx,psz,ps2,
// FT num_y = determinant(psx,psz,ps2,
// qsx,qsz,qs2,
// rsx,rsz,0);
// FT num_z = det3x3_by_formula(psx,psy,ps2,
// FT num_z = determinant(psx,psy,ps2,
// qsx,qsy,qs2,
// rsx,rsy,0);
FT num_x = ps2 * det2x2_by_formula(qsy,qsz,rsy,rsz)
- qs2 * det2x2_by_formula(psy,psz,rsy,rsz);
FT num_y = ps2 * det2x2_by_formula(qsx,qsz,rsx,rsz)
- qs2 * det2x2_by_formula(psx,psz,rsx,rsz);
FT num_z = ps2 * det2x2_by_formula(qsx,qsy,rsx,rsy)
- qs2 * det2x2_by_formula(psx,psy,rsx,rsy);
FT num_x = ps2 * determinant(qsy,qsz,rsy,rsz)
- qs2 * determinant(psy,psz,rsy,rsz);
FT num_y = ps2 * determinant(qsx,qsz,rsx,rsz)
- qs2 * determinant(psx,psz,rsx,rsz);
FT num_z = ps2 * determinant(qsx,qsy,rsx,rsy)
- qs2 * determinant(psx,psy,rsx,rsy);
FT den = det3x3_by_formula(psx,psy,psz,
FT den = determinant(psx,psy,psz,
qsx,qsy,qsz,
rsx,rsy,rsz);
@ -1901,16 +1901,16 @@ namespace CartesianKernelFunctors {
FT spz = s.z()-p.z();
FT sp2 = CGAL_NTS square(spx) + CGAL_NTS square(spy) + CGAL_NTS square(spz);
FT num_x = det3x3_by_formula(qpy,qpz,qp2,
FT num_x = determinant(qpy,qpz,qp2,
rpy,rpz,rp2,
spy,spz,sp2);
FT num_y = det3x3_by_formula(qpx,qpz,qp2,
FT num_y = determinant(qpx,qpz,qp2,
rpx,rpz,rp2,
spx,spz,sp2);
FT num_z = det3x3_by_formula(qpx,qpy,qp2,
FT num_z = determinant(qpx,qpy,qp2,
rpx,rpy,rp2,
spx,spy,sp2);
FT den = det3x3_by_formula(qpx,qpy,qpz,
FT den = determinant(qpx,qpy,qpz,
rpx,rpy,rpz,
spx,spy,spz);
CGAL_kernel_assertion( ! CGAL_NTS is_zero(den) );
@ -2149,24 +2149,24 @@ namespace CartesianKernelFunctors {
// The following determinants can be developped and simplified.
//
// FT num_x = det3x3_by_formula(psy,psz,ps2,
// FT num_x = determinant(psy,psz,ps2,
// qsy,qsz,qs2,
// rsy,rsz,0);
// FT num_y = det3x3_by_formula(psx,psz,ps2,
// FT num_y = determinant(psx,psz,ps2,
// qsx,qsz,qs2,
// rsx,rsz,0);
// FT num_z = det3x3_by_formula(psx,psy,ps2,
// FT num_z = determinant(psx,psy,ps2,
// qsx,qsy,qs2,
// rsx,rsy,0);
FT num_x = ps2 * det2x2_by_formula(qsy,qsz,rsy,rsz)
- qs2 * det2x2_by_formula(psy,psz,rsy,rsz);
FT num_y = ps2 * det2x2_by_formula(qsx,qsz,rsx,rsz)
- qs2 * det2x2_by_formula(psx,psz,rsx,rsz);
FT num_z = ps2 * det2x2_by_formula(qsx,qsy,rsx,rsy)
- qs2 * det2x2_by_formula(psx,psy,rsx,rsy);
FT num_x = ps2 * determinant(qsy,qsz,rsy,rsz)
- qs2 * determinant(psy,psz,rsy,rsz);
FT num_y = ps2 * determinant(qsx,qsz,rsx,rsz)
- qs2 * determinant(psx,psz,rsx,rsz);
FT num_z = ps2 * determinant(qsx,qsy,rsx,rsy)
- qs2 * determinant(psx,psy,rsx,rsy);
FT den = det3x3_by_formula(psx,psy,psz,
FT den = determinant(psx,psy,psz,
qsx,qsy,qsz,
rsx,rsy,rsz);

8
Cartesian_kernel/include/CGAL/constructions/kernel_ftC2.h
View File

@ -53,7 +53,7 @@ circumcenter_translateC2(const FT &dqx, const FT &dqy,
// What we do is intersect the bisectors.
FT r2 = CGAL_NTS square(drx) + CGAL_NTS square(dry);
FT q2 = CGAL_NTS square(dqx) + CGAL_NTS square(dqy);
FT den = 2 * det2x2_by_formula(dqx, dqy, drx, dry);
FT den = 2 * determinant(dqx, dqy, drx, dry);
// The 3 points aren't collinear.
// Hopefully, this is already checked at the upper level.
@ -61,8 +61,8 @@ circumcenter_translateC2(const FT &dqx, const FT &dqy,
// One possible optimization here is to precompute 1/den, to avoid one
// division. However, we loose precision, and it's maybe not worth it (?).
dcx = det2x2_by_formula (dry, dqy, r2, q2) / den;
dcy = - det2x2_by_formula (drx, dqx, r2, q2) / den;
dcx = determinant (dry, dqy, r2, q2) / den;
dcy = - determinant (drx, dqx, r2, q2) / den;
}
template < class FT >
@ -338,7 +338,7 @@ scaled_distance_to_lineC2( const FT &px, const FT &py,
const FT &qx, const FT &qy,
const FT &rx, const FT &ry)
{
return det2x2_by_formula<FT>(px-rx, py-ry, qx-rx, qy-ry);
return determinant<FT>(px-rx, py-ry, qx-rx, qy-ry);
}
CGAL_END_NAMESPACE

24
Cartesian_kernel/include/CGAL/constructions/kernel_ftC3.h
View File

@ -87,16 +87,16 @@ squared_radiusC3(const FT &px, const FT &py, const FT &pz,
FT spz = sz-pz;
FT sp2 = CGAL_NTS square(spx) + CGAL_NTS square(spy) + CGAL_NTS square(spz);
FT num_x = det3x3_by_formula(qpy,qpz,qp2,
FT num_x = determinant(qpy,qpz,qp2,
rpy,rpz,rp2,
spy,spz,sp2);
FT num_y = det3x3_by_formula(qpx,qpz,qp2,
FT num_y = determinant(qpx,qpz,qp2,
rpx,rpz,rp2,
spx,spz,sp2);
FT num_z = det3x3_by_formula(qpx,qpy,qp2,
FT num_z = determinant(qpx,qpy,qp2,
rpx,rpy,rp2,
spx,spy,sp2);
FT den = det3x3_by_formula(qpx,qpy,qpz,
FT den = determinant(qpx,qpy,qpz,
rpx,rpy,rpz,
spx,spy,spz);
CGAL_kernel_assertion( ! CGAL_NTS is_zero(den) );
@ -125,14 +125,14 @@ squared_radiusC3(const FT &px, const FT &py, const FT &pz,
FT rsy = psz*qsx-psx*qsz;
FT rsz = psx*qsy-psy*qsx;
FT num_x = ps2 * det2x2_by_formula(qsy,qsz,rsy,rsz)
- qs2 * det2x2_by_formula(psy,psz,rsy,rsz);
FT num_y = ps2 * det2x2_by_formula(qsx,qsz,rsx,rsz)
- qs2 * det2x2_by_formula(psx,psz,rsx,rsz);
FT num_z = ps2 * det2x2_by_formula(qsx,qsy,rsx,rsy)
- qs2 * det2x2_by_formula(psx,psy,rsx,rsy);
FT num_x = ps2 * determinant(qsy,qsz,rsy,rsz)
- qs2 * determinant(psy,psz,rsy,rsz);
FT num_y = ps2 * determinant(qsx,qsz,rsx,rsz)
- qs2 * determinant(psx,psz,rsx,rsz);
FT num_z = ps2 * determinant(qsx,qsy,rsx,rsy)
- qs2 * determinant(psx,psy,rsx,rsy);
FT den = det3x3_by_formula(psx,psy,psz,
FT den = determinant(psx,psy,psz,
qsx,qsy,qsz,
rsx,rsy,rsz);
@ -254,7 +254,7 @@ scaled_distance_to_planeC3(
const FT &prx, const FT &pry, const FT &prz,
const FT &px, const FT &py, const FT &pz)
{
return det3x3_by_formula(ppx-px,ppy-py,ppz-pz,
return determinant(ppx-px,ppy-py,ppz-pz,
pqx-px,pqy-py,pqz-pz,
prx-px,pry-py,prz-pz);
}

36
Cartesian_kernel/include/CGAL/predicates/kernel_ftC2.h
View File

@ -75,8 +75,8 @@ compare_xC2(const FT &px,
const FT &ha, const FT &hb, const FT &hc)
{
// The abscissa of the intersection point is num/den.
FT num = det2x2_by_formula( lb, lc, hb, hc);
FT den = det2x2_by_formula( la, lb, ha, hb);
FT num = determinant( lb, lc, hb, hc);
FT den = determinant( la, lb, ha, hb);
typename Sgn<FT>::result_type s = CGAL_NTS sign(den);
CGAL_kernel_assertion( s != ZERO );
return s * CGAL_NTS compare(px * den, num);
@ -90,20 +90,20 @@ compare_xC2(const FT &la, const FT &lb, const FT &lc,
const FT &h2a, const FT &h2b, const FT &h2c)
{
/*
FT num1 = det2x2_by_formula( lb, lc, h1b, h1c);
FT den1 = det2x2_by_formula( la, lb, h1a, h1b);
FT num2 = det2x2_by_formula( lb, lc, h2b, h2c);
FT den2 = det2x2_by_formula( la, lb, h2a, h2b);
FT num1 = determinant( lb, lc, h1b, h1c);
FT den1 = determinant( la, lb, h1a, h1b);
FT num2 = determinant( lb, lc, h2b, h2c);
FT den2 = determinant( la, lb, h2a, h2b);
Sign s = Sign (CGAL_NTS sign(den1) * CGAL_NTS sign(den2));
CGAL_kernel_assertion( s != ZERO );
return s * sign_of_determinant(num1, num2, den1, den2);
*/
FT num1 = det2x2_by_formula( la, lc, h1a, h1c);
FT num2 = det2x2_by_formula( la, lc, h2a, h2c);
FT num = det2x2_by_formula(h1a,h1c,h2a,h2c)*lb
+ det2x2_by_formula(num1,num2,h1b,h2b);
FT den1 = det2x2_by_formula( la, lb, h1a, h1b);
FT den2 = det2x2_by_formula( la, lb, h2a, h2b);
FT num1 = determinant( la, lc, h1a, h1c);
FT num2 = determinant( la, lc, h2a, h2c);
FT num = determinant(h1a,h1c,h2a,h2c)*lb
+ determinant(num1,num2,h1b,h2b);
FT den1 = determinant( la, lb, h1a, h1b);
FT den2 = determinant( la, lb, h2a, h2b);
return CGAL_NTS sign(lb) *
CGAL_NTS sign(num) *
CGAL_NTS sign(den1) *
@ -118,10 +118,10 @@ compare_xC2(const FT &l1a, const FT &l1b, const FT &l1c,
const FT &l2a, const FT &l2b, const FT &l2c,
const FT &h2a, const FT &h2b, const FT &h2c)
{
FT num1 = det2x2_by_formula( l1b, l1c, h1b, h1c);
FT den1 = det2x2_by_formula( l1a, l1b, h1a, h1b);
FT num2 = det2x2_by_formula( l2b, l2c, h2b, h2c);
FT den2 = det2x2_by_formula( l2a, l2b, h2a, h2b);
FT num1 = determinant( l1b, l1c, h1b, h1c);
FT den1 = determinant( l1a, l1b, h1a, h1b);
FT num2 = determinant( l2b, l2c, h2b, h2c);
FT den2 = determinant( l2a, l2b, h2a, h2b);
typename Sgn<FT>::result_type s = CGAL_NTS sign(den1) * CGAL_NTS sign(den2);
CGAL_kernel_assertion( s != ZERO );
return s * sign_of_determinant(num1, num2, den1, den2);
@ -175,8 +175,8 @@ compare_y_at_xC2(const FT &l1a, const FT &l1b, const FT &l1c,
const FT &h2a, const FT &h2b, const FT &h2c)
{
// The abscissa of the intersection point is num/den.
FT num = det2x2_by_formula( l1b, l1c, l2b, l2c);
FT den = det2x2_by_formula( l1a, l1b, l2a, l2b);
FT num = determinant( l1b, l1c, l2b, l2c);
FT den = determinant( l1a, l1b, l2a, l2b);
typename Sgn<FT>::result_type s = CGAL_NTS sign(h1b) *
CGAL_NTS sign(h2b) *
CGAL_NTS sign(den);

14
Cartesian_kernel/include/CGAL/predicates/kernel_ftC3.h
View File

@ -417,14 +417,14 @@ side_of_bounded_sphereC3(const FT &px, const FT &py, const FT &pz,
FT tsy = ty-sy;
FT tsz = tz-sz;
FT num_x = ps2 * det2x2_by_formula(qsy,qsz,rsy,rsz)
- qs2 * det2x2_by_formula(psy,psz,rsy,rsz);
FT num_y = ps2 * det2x2_by_formula(qsx,qsz,rsx,rsz)
- qs2 * det2x2_by_formula(psx,psz,rsx,rsz);
FT num_z = ps2 * det2x2_by_formula(qsx,qsy,rsx,rsy)
- qs2 * det2x2_by_formula(psx,psy,rsx,rsy);
FT num_x = ps2 * determinant(qsy,qsz,rsy,rsz)
- qs2 * determinant(psy,psz,rsy,rsz);
FT num_y = ps2 * determinant(qsx,qsz,rsx,rsz)
- qs2 * determinant(psx,psz,rsx,rsz);
FT num_z = ps2 * determinant(qsx,qsy,rsx,rsy)
- qs2 * determinant(psx,psy,rsx,rsy);
FT den2 = 2 * det3x3_by_formula(psx,psy,psz,
FT den2 = 2 * determinant(psx,psy,psz,
qsx,qsy,qsz,
rsx,rsy,rsz);

2
Cartesian_kernel/package_info/Cartesian_kernel/changes.txt
View File

@ -21,7 +21,7 @@
- Remove <FT> qualification for functions part of the NT interface
(sign, compare...), for efficiency.
- Add <FT> qualification for functions which are not part of the
NT interface (det3x3_by_formula...) to support GMP++ like types.
NT interface (determinant...) to support GMP++ like types.
1 August 2005 Sylvain Pion
- Cartesian_converter : specialize when same_type<K1, K2>.

2
Distance_2/include/CGAL/squared_distance_utils.h
View File

@ -110,7 +110,7 @@ wcross_tag(const typename K::Point_2 &p,
const K&,
const Homogeneous_tag&)
{
return det3x3_by_formula(
return determinant(
p.hx(), q.hx(), r.hx(),
p.hy(), q.hy(), r.hy(),
p.hw(), q.hw(), r.hw());

2
Filtered_kernel/include/CGAL/Static_filters/Coplanar_orientation_3.h
View File

@ -143,7 +143,7 @@ private:
double prx = rx-px;
double pry = ry-py;
double det = det2x2_by_formula(pqx, pqy,
double det = determinant(pqx, pqy,
prx, pry);
// Then semi-static filter.

4
Filtered_kernel/include/CGAL/Static_filters/Coplanar_side_of_bounded_circle_3.h
View File

@ -42,7 +42,7 @@ class SF_Side_of_bounded_circle_3
F sq = t1*t1+t1*t1+t1*t1; // squares
F n1 = t1*t1 - t1*t1; // normal vector
F sq_n1 = n1*n1 + n1*n1 + n1*n1;
F det = det4x4_by_formula(t1, t1, t1, sq,
F det = determinant(t1, t1, t1, sq,
t1, t1, t1, sq,
t1, t1, t1, sq,
n1, n1, n1, sq_n1); // Full det
@ -99,7 +99,7 @@ public:
double v2 = CGAL_NTS square(vx) + CGAL_NTS square(vy) +
CGAL_NTS square(vz);
double det = det4x4_by_formula(ptx,pty,ptz,pt2,
double det = determinant(ptx,pty,ptz,pt2,
rtx,rty,rtz,rt2,
qtx,qty,qtz,qt2,
vx,vy,vz,v2);

4
Filtered_kernel/include/CGAL/Static_filters/Orientation_2.h
View File

@ -76,7 +76,7 @@ public:
double prx = rx - px;
double pry = ry - py;
double det = det2x2_by_formula(pqx, pqy,
double det = determinant(pqx, pqy,
prx, pry);
// Then semi-static filter.
@ -111,7 +111,7 @@ public:
{
typedef Static_filter_error F;
F t1 = F(1, F::ulp()/2); // First translation
F det = det2x2_by_formula(t1, t1,
F det = determinant(t1, t1,
t1, t1); // Full det
double err = det.error();
err += err * 2 * F::ulp(); // Correction due to "epsilon * maxx * maxy".

4
Filtered_kernel/include/CGAL/Static_filters/Orientation_3.h
View File

@ -97,7 +97,7 @@ public:
if (maxz < fabs(prz)) maxz = fabs(prz);
if (maxz < fabs(psz)) maxz = fabs(psz);
double eps = 5.1107127829973299e-15 * maxx * maxy * maxz;
double det = det3x3_by_formula(pqx, pqy, pqz,
double det = determinant(pqx, pqy, pqz,
prx, pry, prz,
psx, psy, psz);
@ -131,7 +131,7 @@ public:
{
typedef Static_filter_error F;
F t1 = F(1, F::ulp()/2); // First translation
F det = det3x3_by_formula(t1, t1, t1,
F det = determinant(t1, t1, t1,
t1, t1, t1,
t1, t1, t1); // Full det
double err = det.error();

4
Filtered_kernel/include/CGAL/Static_filters/Side_of_oriented_circle_2.h
View File

@ -64,7 +64,7 @@ public:
double rqx = rx-qx;
double rqy = ry-qy;
double det = det2x2_by_formula(qpx*tpy - qpy*tpx, tpx*tqx + tpy*tqy,
double det = determinant(qpx*tpy - qpy*tpx, tpx*tqx + tpy*tqy,
qpx*rpy - qpy*rpx, rpx*rqx + rpy*rqy);
// We compute the semi-static bound.
@ -106,7 +106,7 @@ public:
F t1 = F(1, F::ulp()/2); // First translation
F a = t1*t1 - t1*t1;
F b = t1*t1 + t1*t1;
F det = det2x2_by_formula(a, b, a, b);
F det = determinant(a, b, a, b);
double err = det.error();
err += err * 3 * F::ulp(); // Correction due to "eps * maxx * maxy...".

4
Filtered_kernel/include/CGAL/Static_filters/Side_of_oriented_sphere_3.h
View File

@ -104,7 +104,7 @@ public:
double eps = 1.2466136531027298e-13 * maxx * maxy * maxz
* (maxz * maxz);
double det = det4x4_by_formula(ptx,pty,ptz,pt2,
double det = determinant(ptx,pty,ptz,pt2,
rtx,rty,rtz,rt2,
qtx,qty,qtz,qt2,
stx,sty,stz,st2);
@ -131,7 +131,7 @@ public:
typedef CGAL::Static_filter_error F;
F t1 = F(1,F::ulp()/2); // First translation
F sq = t1*t1+t1*t1+t1*t1; // squares
F det = det4x4_by_formula(t1, t1, t1, sq,
F det = determinant(t1, t1, t1, sq,
t1, t1, t1, sq,
t1, t1, t1, sq,
t1, t1, t1, sq); // Full det

28
Homogeneous_kernel/include/CGAL/Homogeneous/Aff_transformationH3.h
View File

@ -441,58 +441,58 @@ Aff_transformation_repH3<R>::inverse() const
typedef typename R::RT RT;
const RT RT0(0);
return Aff_transformation_3(
det3x3_by_formula( t11, t12, t13,
determinant( t11, t12, t13,
t21, t22, t23, // i 00
RT0, RT0, t33 ),
- det3x3_by_formula( t01, t02, t03,
- determinant( t01, t02, t03,
t21, t22, t23, // i 01
RT0, RT0, t33 ),
det3x3_by_formula( t01, t02, t03,
determinant( t01, t02, t03,
t11, t12, t13, // i 02
RT0, RT0, t33 ),
- det3x3_by_formula( t01, t02, t03,
- determinant( t01, t02, t03,
t11, t12, t13, // i 03
t21, t22, t23 ),
- det3x3_by_formula( t10, t12, t13,
- determinant( t10, t12, t13,
t20, t22, t23, // i 10
RT0, RT0, t33 ),
det3x3_by_formula( t00, t02, t03,
determinant( t00, t02, t03,
t20, t22, t23, // i 11
RT0, RT0, t33 ),
- det3x3_by_formula( t00, t02, t03,
- determinant( t00, t02, t03,
t10, t12, t13, // i 12
RT0, RT0, t33 ),
det3x3_by_formula( t00, t02, t03,
determinant( t00, t02, t03,
t10, t12, t13, // i 13
t20, t22, t23 ),
det3x3_by_formula( t10, t11, t13,
determinant( t10, t11, t13,
t20, t21, t23, // i 20
RT0, RT0, t33 ),
- det3x3_by_formula( t00, t01, t03,
- determinant( t00, t01, t03,
t20, t21, t23, // i 21
RT0, RT0, t33 ),
det3x3_by_formula( t00, t01, t03,
determinant( t00, t01, t03,
t10, t11, t13, // i 22
RT0, RT0, t33 ),
- det3x3_by_formula( t00, t01, t03,
- determinant( t00, t01, t03,
t10, t11, t13, // i 23
t20, t21, t23 ),
det3x3_by_formula( t00, t01, t02,
determinant( t00, t01, t02,
t10, t11, t12, // i 33
t20, t21, t22 )
) ;
@ -523,7 +523,7 @@ bool
Aff_transformation_repH3<R>::is_even() const
{
return (CGAL_NTS sign<RT>( t33 *
det3x3_by_formula(t00, t01, t02,
determinant(t00, t01, t02,
t10, t11, t12,
t20, t21, t22 ) ) == POSITIVE );
}

2
Homogeneous_kernel/include/CGAL/Homogeneous/PlaneH3.h
View File

@ -495,7 +495,7 @@ PlaneH3<R>::transform_to_2d() const
RT t32 = -( e1phx*e2phz - e1phz*e2phx );
RT t33 = ( e1phx*e2phy - e1phy*e2phx );
RT scale = det3x3_by_formula( orthohx, orthohy, orthohz,
RT scale = determinant( orthohx, orthohy, orthohz,
e1phx, e1phy, e1phz,
e2phx, e2phy, e2phz );

8
Homogeneous_kernel/include/CGAL/Homogeneous/basic_constructionsH3.h
View File

@ -60,16 +60,16 @@ gp_linear_intersection(const PlaneH3<R> &f,
{
typedef typename R::RT RT;
return typename R::Point_3(
det3x3_by_formula<RT>(-f.d(), f.b(), f.c(),
determinant<RT>(-f.d(), f.b(), f.c(),
-g.d(), g.b(), g.c(),
-h.d(), h.b(), h.c()),
det3x3_by_formula<RT>( f.a(),-f.d(), f.c(),
determinant<RT>( f.a(),-f.d(), f.c(),
g.a(),-g.d(), g.c(),
h.a(),-h.d(), h.c()),
det3x3_by_formula<RT>( f.a(), f.b(),-f.d(),
determinant<RT>( f.a(), f.b(),-f.d(),
g.a(), g.b(),-g.d(),
h.a(), h.b(),-h.d()),
det3x3_by_formula<RT>( f.a(), f.b(), f.c(),
determinant<RT>( f.a(), f.b(), f.c(),
g.a(), g.b(), g.c(),
h.a(), h.b(), h.c()));
}

22
Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
View File

@ -178,16 +178,16 @@ namespace HomogeneousKernelFunctors {
const RT & vpy = vp.hy();
const RT & vpz = vp.hz();
RT alpha = det3x3_by_formula( vpx, v2x, v3x,
RT alpha = determinant( vpx, v2x, v3x,
vpy, v2y, v3y,
vpz, v2z, v3z );
RT beta = det3x3_by_formula( v1x, vpx, v3x,
RT beta = determinant( v1x, vpx, v3x,
v1y, vpy, v3y,
v1z, vpz, v3z );
RT gamma = det3x3_by_formula( v1x, v2x, vpx,
RT gamma = determinant( v1x, v2x, vpx,
v1y, v2y, vpy,
v1z, v2z, vpz );
RT det = det3x3_by_formula( v1x, v2x, v3x,
RT det = determinant( v1x, v2x, v3x,
v1y, v2y, v3y,
v1z, v2z, v3z );
@ -1277,7 +1277,7 @@ namespace HomogeneousKernelFunctors {
result_type
operator()(const Vector_2& v, const Vector_2& w) const
{
return det2x2_by_formula(v.hx(), v.hy(),
return determinant(v.hx(), v.hy(),
w.hx(), w.hy()) / FT(v.hw() * w.hw());
}
};
@ -1294,7 +1294,7 @@ namespace HomogeneousKernelFunctors {
result_type
operator()(const Vector_3& v, const Vector_3& w, const Vector_3& t) const
{
return det3x3_by_formula(v.hx(), v.hy(), v.hz(),
return determinant(v.hx(), v.hy(), v.hz(),
w.hx(), w.hy(), w.hz(),
t.hx(), t.hy(), t.hz())
/ FT(v.hw() * w.hw() * t.hw());
@ -2385,19 +2385,19 @@ namespace HomogeneousKernelFunctors {
shz *= shw;
shw *= shw;
RT chx = det4x4_by_formula(phy, phz, pssq, phw,
RT chx = determinant(phy, phz, pssq, phw,
qhy, qhz, qssq, qhw,
rhy, rhz, rssq, rhw,
shy, shz, sssq, shw );
RT chy = det4x4_by_formula(phx, phz, pssq, phw,
RT chy = determinant(phx, phz, pssq, phw,
qhx, qhz, qssq, qhw,
rhx, rhz, rssq, rhw,
shx, shz, sssq, shw );
RT chz = det4x4_by_formula(phx, phy, pssq, phw,
RT chz = determinant(phx, phy, pssq, phw,
qhx, qhy, qssq, qhw,
rhx, rhy, rssq, rhw,
shx, shy, sssq, shw );
RT chw = det4x4_by_formula(phx, phy, phz, phw,
RT chw = determinant(phx, phy, phz, phw,
qhx, qhy, qhz, qhw,
rhx, rhy, rhz, rhw,
shx, shy, shz, shw );
@ -4657,7 +4657,7 @@ namespace HomogeneousKernelFunctors {
const RT & thw = t.hw();
const RT thw2 = thw*thw;
const RT det = det5x5_by_formula<RT>(
const RT det = determinant<RT>(
phx*phw, phy*phw, phz*phw, phx*phx + phy*phy + phz*phz, phw2,
qhx*qhw, qhy*qhw, qhz*qhw, qhx*qhx + qhy*qhy + qhz*qhz, qhw2,
rhx*rhw, rhy*rhw, rhz*rhw, rhx*rhx + rhy*rhy + rhz*rhz, rhw2,

24
Interpolation/include/CGAL/constructions/constructions_for_voronoi_intersection_cartesian_2_3.h
View File

@ -34,7 +34,7 @@ plane_centered_circumcenter_translateC3(const RT &ax, const RT &ay,
const RT &rz,
RT &x, RT &y, RT &z)
{
RT den = RT(2) * det3x3_by_formula(nx,qx,rx,
RT den = RT(2) * determinant(nx,qx,rx,
ny,qy,ry,
nz,qz,rz);
// The 3 points aren't collinear.
@ -48,15 +48,15 @@ plane_centered_circumcenter_translateC3(const RT &ax, const RT &ay,
RT na = nx*ax + ny*ay + nz*az;
na *= RT(2.0);
x = det3x3_by_formula(ny,nz,na,
x = determinant(ny,nz,na,
qy,qz,q2,
ry,rz,r2)/ den ;
y = - det3x3_by_formula(nx,nz,na,
y = - determinant(nx,nz,na,
qx,qz,q2,
rx,rz,r2)/ den ;
z = det3x3_by_formula(nx,ny,na,
z = determinant(nx,ny,na,
qx,qy,q2,
rx,ry,r2)/ den ;
}
@ -106,18 +106,18 @@ bisector_plane_intersection_translateC3(const RT &ax, const RT &ay,
// the line is defined by p1 and p2 with
//=> p1: z1 =0, p2: z2=1
// precondition: (nx!=0 || ny!=0) && (qx!=0 && qy!=0) && den!=0
// where RT den = RT(2.0) * det2x2_by_formula(qx,qy,nx, ny);
// where RT den = RT(2.0) * determinant(qx,qy,nx, ny);
RT q2 = CGAL_NTS square(qx) + CGAL_NTS square(qy)
+ CGAL_NTS square(qz);
RT na = nx*ax + ny*ay + nz*az;
na *= RT(2.0);
x1 = det2x2_by_formula(ny, na, qy, q2);
y1 = - det2x2_by_formula(nx, na, qx, q2);
x1 = determinant(ny, na, qy, q2);
y1 = - determinant(nx, na, qx, q2);
x2 = x1 + RT(2.0) * det2x2_by_formula(qy,qz,ny, nz);
y2 = y1 - RT(2.0) * det2x2_by_formula(qx,qz,nx, nz);
x2 = x1 + RT(2.0) * determinant(qy,qz,ny, nz);
y2 = y1 - RT(2.0) * determinant(qx,qz,nx, nz);
x1 /= den;
x2 /= den;
@ -199,7 +199,7 @@ bisector_plane_intersectionC3(const RT &ax, const RT &ay, const RT &az,
// 2) the projection of n and (p-q) onto the plane is not
// identical
// computation for (z=0) with adequate permutations
RT den = RT(2.0) * det2x2_by_formula(qx-px,qy-py,nx, ny);
RT den = RT(2.0) * determinant(qx-px,qy-py,nx, ny);
if ((nx!=0 || ny!=0) && (qx!=px || qy!=py) && den!=RT(0))
//den==0 <=> projections of (qx,qy) and (nx,ny) are identical
//intersection with z=0/z=1
@ -207,14 +207,14 @@ bisector_plane_intersectionC3(const RT &ax, const RT &ay, const RT &az,
qx,qy,qz,den,
x1,y1,z1,x2,y2,z2);
else{
den = RT(2.0) * det2x2_by_formula(qy-py,qz-pz,ny,nz);
den = RT(2.0) * determinant(qy-py,qz-pz,ny,nz);
if ((ny!=0 || nz!=0) && (qy!=py || qz!=pz) && den!=RT(0))
//intersection with x=0/x=1 => permutations
bisector_plane_intersection_permuteC3(ay,az,ax,ny,nz,nx,py,pz,px,
qy,qz,qx,den,
y1,z1,x1,y2,z2,x2);
else{
den = RT(2.0) * det2x2_by_formula(qz-pz,qx-px,nz,nx);
den = RT(2.0) * determinant(qz-pz,qx-px,nz,nx);
CGAL_assertion((nx!=0 || nz!=0) && (qx!=px || qz!=pz) && den!=RT(0));
//intersection with y=0/y=1 => permutations
bisector_plane_intersection_permuteC3(az,ax,ay,nz,nx,ny,pz,px,py,

2
Kernel_23/include/CGAL/Kernel/Wutils.h
View File

@ -156,7 +156,7 @@ struct wcross_tag_2<Homogeneous_tag>
const Point_2 &q,
const Point_2 &r) const
{
return det3x3_by_formula(p.hx(), q.hx(), r.hx(),
return determinant(p.hx(), q.hx(), r.hx(),
p.hy(), q.hy(), r.hy(),
p.hw(), q.hw(), r.hw());
}

10
Kernel_23/include/CGAL/determinant.h
View File

@ -30,7 +30,7 @@ CGAL_BEGIN_NAMESPACE
template <class RT>
inline
RT
det2x2_by_formula(
determinant(
const RT& a00, const RT& a01,
const RT& a10, const RT& a11)
{
@ -42,7 +42,7 @@ det2x2_by_formula(
template <class RT>
CGAL_KERNEL_MEDIUM_INLINE
RT
det3x3_by_formula(
determinant(
const RT& a00, const RT& a01, const RT& a02,
const RT& a10, const RT& a11, const RT& a12,
const RT& a20, const RT& a21, const RT& a22)
@ -59,7 +59,7 @@ det3x3_by_formula(
template <class RT>
CGAL_KERNEL_LARGE_INLINE
RT
det4x4_by_formula(
determinant(
const RT& a00, const RT& a01, const RT& a02, const RT& a03,
const RT& a10, const RT& a11, const RT& a12, const RT& a13,
const RT& a20, const RT& a21, const RT& a22, const RT& a23,
@ -85,7 +85,7 @@ det4x4_by_formula(
template <class RT>
CGAL_KERNEL_LARGE_INLINE
RT
det5x5_by_formula(
determinant(
const RT& a00, const RT& a01, const RT& a02, const RT& a03, const RT& a04,
const RT& a10, const RT& a11, const RT& a12, const RT& a13, const RT& a14,
const RT& a20, const RT& a21, const RT& a22, const RT& a23, const RT& a24,
@ -127,7 +127,7 @@ det5x5_by_formula(
template <class RT>
RT
det6x6_by_formula(
determinant(
const RT& a00, const RT& a01, const RT& a02, const RT& a03, const RT& a04,
const RT& a05,
const RT& a10, const RT& a11, const RT& a12, const RT& a13, const RT& a14,

8
Kernel_23/include/CGAL/predicates/sign_of_determinant.h
View File

@ -45,7 +45,7 @@ sign_of_determinant( const RT& a00, const RT& a01, const RT& a02,
const RT& a10, const RT& a11, const RT& a12,
const RT& a20, const RT& a21, const RT& a22)
{
return CGAL_NTS sign(det3x3_by_formula(a00, a01, a02,
return CGAL_NTS sign(determinant(a00, a01, a02,
a10, a11, a12,
a20, a21, a22));
}
@ -59,7 +59,7 @@ sign_of_determinant(
const RT& a20, const RT& a21, const RT& a22, const RT& a23,
const RT& a30, const RT& a31, const RT& a32, const RT& a33)
{
return CGAL_NTS sign(det4x4_by_formula(a00, a01, a02, a03,
return CGAL_NTS sign(determinant(a00, a01, a02, a03,
a10, a11, a12, a13,
a20, a21, a22, a23,
a30, a31, a32, a33));
@ -75,7 +75,7 @@ sign_of_determinant(
const RT& a30, const RT& a31, const RT& a32, const RT& a33, const RT& a34,
const RT& a40, const RT& a41, const RT& a42, const RT& a43, const RT& a44)
{
return CGAL_NTS sign(det5x5_by_formula(a00, a01, a02, a03, a04,
return CGAL_NTS sign(determinant(a00, a01, a02, a03, a04,
a10, a11, a12, a13, a14,
a20, a21, a22, a23, a24,
a30, a31, a32, a33, a34,
@ -99,7 +99,7 @@ sign_of_determinant(
const RT& a50, const RT& a51, const RT& a52, const RT& a53, const RT& a54,
const RT& a55)
{
return CGAL_NTS sign(det6x6_by_formula(a00, a01, a02, a03, a04, a05,
return CGAL_NTS sign(determinant(a00, a01, a02, a03, a04, a05,
a10, a11, a12, a13, a14, a15,
a20, a21, a22, a23, a24, a25,
a30, a31, a32, a33, a34, a35,

2
Kernel_23/package_info/Kernel_23/changes.txt
View File

@ -2086,7 +2086,7 @@ Version 1.106 (09 February 2004) [rursu]
- authors for determinant.h updated
1.2.8 -> 1.2.9
- det4x4_by_formula improved as suggested by Sylvain and Olivier
- determinant improved as suggested by Sylvain and Olivier
1.2.7 -> 1.2.8
- #define CGAL_KERNEL_INLINE inline added again

28
Kernel_23/test/Kernel_23/include/CGAL/_test_fct_determinant.h
View File

@ -33,54 +33,54 @@ _test_fct_determinant(const NT&)
NT one = NT(1);
NT two = NT(2);
// detDxD_by_formula
// determinant()
assert( CGAL::det2x2_by_formula<NT>( zero, one, \
assert( CGAL::determinant<NT>( zero, one, \
one, zero) == - one );
assert( CGAL::det2x2_by_formula<NT>( one, one, \
assert( CGAL::determinant<NT>( one, one, \
zero, -one) == - one );
assert( CGAL::det3x3_by_formula<NT>( one, zero, one, \
assert( CGAL::determinant<NT>( one, zero, one, \
zero, one, one, \
-one, -one, zero ) == \
one * CGAL::det2x2_by_formula<NT>( one, one, \
one * CGAL::determinant<NT>( one, one, \
-one, zero ) \
- one * CGAL::det2x2_by_formula<NT>( zero, one, \
- one * CGAL::determinant<NT>( zero, one, \
one, one ) );
assert( CGAL::det4x4_by_formula<NT>( one, zero, one, -one, \
assert( CGAL::determinant<NT>( one, zero, one, -one, \
zero, one, one, -one, \
one, two, zero, one, \
-one, -one, zero, zero ) == \
one * CGAL::det3x3_by_formula<NT>( zero, one, -one, \
one * CGAL::determinant<NT>( zero, one, -one, \
one, one, -one, \
two, zero, one ) \
- one * CGAL::det3x3_by_formula<NT>( one, one, -one, \
- one * CGAL::determinant<NT>( one, one, -one, \
zero, one, -one, \
one, zero, one ) );
assert( CGAL::det5x5_by_formula<NT>( one, zero, one, -one, zero, \
assert( CGAL::determinant<NT>( one, zero, one, -one, zero, \
zero, one, one, -one, zero, \
one, two, zero, one, two, \
one, one, zero, -one, zero, \
-one, -one, zero, zero, one ) == \
two * CGAL::det4x4_by_formula<NT>( one, zero, one, -one, \
two * CGAL::determinant<NT>( one, zero, one, -one, \
zero, one, one, -one, \
one, one, zero, -one, \
-one, -one, zero, zero) \
+ one * CGAL::det4x4_by_formula<NT>( one, zero, one, -one, \
+ one * CGAL::determinant<NT>( one, zero, one, -one, \
zero, one, one, -one, \
one, two, zero, one, \
one, one, zero, -one) );
assert( CGAL::det6x6_by_formula<NT>( one, zero, zero, zero, zero, zero, \
assert( CGAL::determinant<NT>( one, zero, zero, zero, zero, zero, \
zero, one, zero, one, -one, zero, \
zero, zero, one, one, -one, zero, \
zero, one, two, zero, one, two, \
zero, one, one, zero, -one, zero, \
zero, -one, -one, zero, zero, one ) == \
CGAL::det5x5_by_formula<NT>( one, zero, one, -one, zero, \
CGAL::determinant<NT>( one, zero, one, -one, zero, \
zero, one, one, -one, zero, \
one, two, zero, one, two, \
one, one, zero, -one, zero, \

2
Kinetic_data_structures/hidden/example/Kinetic_data_structures/update_Delaunay_triangulation_2.cpp
View File

@ -145,7 +145,7 @@ CNT incircle(CNT ax, CNT ay, CNT bx, CNT by,
CNT rpy = cy - ay;
CNT tpx = dx - ax;
CNT tpy = dy - ay;
CNT det=CGAL::det2x2_by_formula(qpx*tpy - qpy*tpx, tpx*(dx - bx)
CNT det=CGAL::determinant(qpx*tpy - qpy*tpx, tpx*(dx - bx)
+ tpy*(dy - by),
qpx*rpy - qpy*rpx, rpx*(cx - bx)
+ rpy*(cy - by));

4
Kinetic_data_structures/hidden/include/CGAL/Updatable_Delaunay_triangulation_table_2.h
View File

@ -1015,7 +1015,7 @@ public:
CNT rpy = cy;
CNT tpx = dx;
CNT tpy = dy;
CNT det=CGAL::det2x2_by_formula(qpx*tpy - qpy*tpx,
CNT det=CGAL::determinant(qpx*tpy - qpy*tpx,
tpx*(dx - bx) + tpy*(dy - by),
qpx*rpy - qpy*rpx,
rpx*(cx - bx) + rpy*(cy - by));
@ -1032,7 +1032,7 @@ public:
CNT rpy = cy - ay;
CNT tpx = dx - ax;
CNT tpy = dy - ay;
CNT det=CGAL::det2x2_by_formula(qpx*tpy - qpy*tpx,
CNT det=CGAL::determinant(qpx*tpy - qpy*tpx,
tpx*(dx - bx) + tpy*(dy - by),
qpx*rpy - qpy*rpx,
rpx*(cx - bx) + rpy*(cy - by));

20
Kinetic_data_structures/include/CGAL/Kinetic/internal/Kernel/cartesian_predicates_3.h
View File

@ -64,7 +64,7 @@ struct Cartesian_side_of_oriented_sphere_3
FT dsy = (d.y()) - (e.y());
FT dsz = (d.z()) - (e.z());
FT dst = dsx*dsx + dsy*dsy + dsz*dsz;
FT ret= CGAL::det4x4_by_formula(dpx, dpy, dpz, dpt,
FT ret= CGAL::determinant(dpx, dpy, dpz, dpt,
dqx, dqy, dqz, dqt,
drx, dry, drz, drt,
dsx, dsy, dsz, dst);
@ -127,7 +127,7 @@ struct Cartesian_power_test_3
FT dst = dsx*dsx + dsy*dsy
+ dsz*dsz - (d.weight()) + (e.weight());
return ::CGAL::det4x4_by_formula(dpx, dpy, dpz, dpt,
return ::CGAL::determinant(dpx, dpy, dpz, dpt,
dqx, dqy, dqz, dqt,
drx, dry, drz, drt,
dsx, dsy, dsz, dst);
@ -192,7 +192,7 @@ struct Cartesian_lifted_power_test_3
FT dsz = (d.point().z()) - (e.point().z());
FT dst = (d.lifted()) - (e.lifted());
return CGAL::det4x4_by_formula(dpx, dpy, dpz, dpt,
return CGAL::determinant(dpx, dpy, dpz, dpt,
dqx, dqy, dqz, dqt,
drx, dry, drz, drt,
dsx, dsy, dsz, dst);
@ -244,7 +244,7 @@ struct Cartesian_linear_lifted_power_test_3
FT dsz = (d.point().z()) - (e.point().z());
FT dst = (d.lifted()) - (e.lifted());
safe_ret = CGAL::det4x4_by_formula(dpx, dpy, dpz, dpt,
safe_ret = CGAL::determinant(dpx, dpy, dpz, dpt,
dqx, dqy, dqz, dqt,
drx, dry, drz, drt,
dsx, dsy, dsz, dst);
@ -354,7 +354,7 @@ typename Pt::Coordinate co3(const Pt &a, const Pt &b, const Pt &c, const Pt &d)
RT a20= qz-pz;
RT a21= rz-pz;
RT a22= sz-pz;
RT ret= CGAL::det3x3_by_formula(a00, a01, a02,
RT ret= CGAL::determinant(a00, a01, a02,
a10, a11, a12,
a20, a21, a22);
/*CGAL_LOG_MAPLE(std::endl << std::endl);
@ -554,7 +554,7 @@ typename CC::result_type co3(const Pt &a, const Pt &b, const Pt &c, const Pt &d,
RT a20= qz-pz;
RT a21= rz-pz;
RT a22= sz-pz;
RT ret= CGAL::det3x3_by_formula(a00, a01, a02,
RT ret= CGAL::determinant(a00, a01, a02,
a10, a11, a12,
a20, a21, a22);
CGAL::Kinetic::log()->stream(CGAL::KDS::Log::MAPLE) << std::endl << std::endl;
@ -600,7 +600,7 @@ typename CC::result_type pt3(const Pt &a, const Pt &b, const Pt &c, const Pt &d,
FT dst = dsx*dsx + dsy*dsy
+ dsz*dsz - cc(d.weight()) + cc(e.weight());
return CGAL::det4x4_by_formula(dpx, dpy, dpz, dpt,
return CGAL::determinant(dpx, dpy, dpz, dpt,
dqx, dqy, dqz, dqt,
drx, dry, drz, drt,
dsx, dsy, dsz, dst);
@ -633,7 +633,7 @@ typename CC::result_type pt3(const Cartesian_moving_point_3<C> &a,
FT dsy = cc(d.y()) - cc(e.y());
FT dsz = cc(d.z()) - cc(e.z());
FT dst = dsx*dsx + dsy*dsy + dsz*dsz;
FT ret= CGAL::det4x4_by_formula(dpx, dpy, dpz, dpt,
FT ret= CGAL::determinant(dpx, dpy, dpz, dpt,
dqx, dqy, dqz, dqt,
drx, dry, drz, drt,
dsx, dsy, dsz, dst);
@ -728,7 +728,7 @@ typename CC::result_type pt3(Cartesian_moving_lifted_point_3<CGAL::Polynomial::L
ret= m0123;
}
if (flip) ret=-ret;
/*FT ret = CGAL::det4x4_by_formula(dpx, dpy, dpz, dpt,
/*FT ret = CGAL::determinant(dpx, dpy, dpz, dpt,
dqx, dqy, dqz, dqt,
drx, dry, drz, drt,
dsx, dsy, dsz, dst);*/
@ -788,7 +788,7 @@ typename CC::result_type pt3(Cartesian_moving_lifted_point_3<C> a,
FT dsz = cc(d.point().z()) - cc(e.point().z());
FT dst = cc(d.lifted()) - cc(e.lifted());
FT ret = CGAL::det4x4_by_formula(dpx, dpy, dpz, dpt,
FT ret = CGAL::determinant(dpx, dpy, dpz, dpt,
dqx, dqy, dqz, dqt,
drx, dry, drz, drt,
dsx, dsy, dsz, dst);

2
Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Are_parallel_C2.h
View File

@ -61,7 +61,7 @@ private:
x4 = s2.target().x(),
y4 = s2.target().y();
FT det = det2x2_by_formula(x2 - x1, x4 - x3,
FT det = determinant(x2 - x1, x4 - x3,
y2 - y1, y4 - y3);
return ( CGAL::sign(det) == CGAL::ZERO );

8
Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_2/Arrangement_type_C2.h
View File

@ -79,7 +79,7 @@ private:
const RT& x3, const RT& y3,
const RT& x4, const RT& y4) const
{
RT delta = -det2x2_by_formula(x2 - x1, x4 - x3, y2 - y1, y4 - y3);
RT delta = -determinant(x2 - x1, x4 - x3, y2 - y1, y4 - y3);
Sign s = CGAL::sign( delta );
if ( s != CGAL::ZERO ) {
@ -94,8 +94,8 @@ private:
const RT& x3, const RT& y3, const RT& x4, const RT& y4,
const RT& D) const
{
RT Dt = -det2x2_by_formula(x3 - x1, x4 - x3, y3 - y1, y4 - y3);
RT Ds = det2x2_by_formula(x2 - x1, x3 - x1, y2 - y1, y3 - y1);
RT Dt = -determinant(x3 - x1, x4 - x3, y3 - y1, y4 - y3);
RT Ds = determinant(x2 - x1, x3 - x1, y2 - y1, y3 - y1);
Sign s_D = CGAL::sign( D );
Sign s_Dt = CGAL::sign( Dt );
@ -164,7 +164,7 @@ private:
parallel_C2(const RT& x1, const RT& y1, const RT& x2, const RT& y2,
const RT& x3, const RT& y3, const RT& x4, const RT& y4) const
{
RT D1 = det2x2_by_formula(x2 - x1, x3 - x1, y2 - y1, y3 - y1);
RT D1 = determinant(x2 - x1, x3 - x1, y2 - y1, y3 - y1);
if ( CGAL::sign( D1 ) != CGAL::ZERO ) {
return Enum::DISJOINT;

4
Segment_Delaunay_graph_2/include/CGAL/Segment_Delaunay_graph_site_2.h
View File

@ -284,8 +284,8 @@ protected:
RT x3 = p3.x(), y3 = p3.y();
RT x4 = p4.x(), y4 = p4.y();
RT D = det2x2_by_formula(x2 - x1, x4 - x3, y2 - y1, y4 - y3);
RT Dt = det2x2_by_formula(x3 - x1, x4 - x3, y3 - y1, y4 - y3);
RT D = determinant(x2 - x1, x4 - x3, y2 - y1, y4 - y3);
RT Dt = determinant(x3 - x1, x4 - x3, y3 - y1, y4 - y3);
RT t = Dt / D;

20
Surface_mesh_simplification/include/CGAL/Cartesian/MatrixC33.h
View File

@ -145,7 +145,7 @@ public:
RT determinant() const
{
return det3x3_by_formula(r0().x(),r0().y(),r0().z()
return determinant(r0().x(),r0().y(),r0().z()
,r1().x(),r1().y(),r1().z()
,r2().x(),r2().y(),r2().z()
);
@ -189,17 +189,17 @@ MatrixC33<R> cofactors_matrix ( MatrixC33<R> const& m )
{
typedef typename R::RT RT ;
RT c00 = det2x2_by_formula(m.r1().y(),m.r1().z(),m.r2().y(),m.r2().z());
RT c01 = -det2x2_by_formula(m.r1().x(),m.r1().z(),m.r2().x(),m.r2().z());
RT c02 = det2x2_by_formula(m.r1().x(),m.r1().y(),m.r2().x(),m.r2().y());
RT c00 = determinant(m.r1().y(),m.r1().z(),m.r2().y(),m.r2().z());
RT c01 = -determinant(m.r1().x(),m.r1().z(),m.r2().x(),m.r2().z());
RT c02 = determinant(m.r1().x(),m.r1().y(),m.r2().x(),m.r2().y());
RT c10 = -det2x2_by_formula(m.r0().y(),m.r0().z(),m.r2().y(),m.r2().z());
RT c11 = det2x2_by_formula(m.r0().x(),m.r0().z(),m.r2().x(),m.r2().z());
RT c12 = -det2x2_by_formula(m.r0().x(),m.r0().y(),m.r2().x(),m.r2().y());
RT c10 = -determinant(m.r0().y(),m.r0().z(),m.r2().y(),m.r2().z());
RT c11 = determinant(m.r0().x(),m.r0().z(),m.r2().x(),m.r2().z());
RT c12 = -determinant(m.r0().x(),m.r0().y(),m.r2().x(),m.r2().y());
RT c20 = det2x2_by_formula(m.r0().y(),m.r0().z(),m.r1().y(),m.r1().z());
RT c21 = -det2x2_by_formula(m.r0().x(),m.r0().z(),m.r1().x(),m.r1().z());
RT c22 = det2x2_by_formula(m.r0().x(),m.r0().y(),m.r1().x(),m.r1().y());
RT c20 = determinant(m.r0().y(),m.r0().z(),m.r1().y(),m.r1().z());
RT c21 = -determinant(m.r0().x(),m.r0().z(),m.r1().x(),m.r1().z());
RT c22 = determinant(m.r0().x(),m.r0().y(),m.r1().x(),m.r1().y());
return MatrixC33<R>(c00,c01,c02
,c10,c11,c12

6
Triangulation_2/include/CGAL/constructions_on_weighted_points_cartesian_2.h
View File

@ -39,7 +39,7 @@ weighted_circumcenter_translateC2(const RT &dqx, const RT &dqy, const RT &dqw,
RT r2 = CGAL_NTS square(drx) + CGAL_NTS square(dry) - drw;
RT q2 = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) - dqw;
RT den = RT(2) * det2x2_by_formula(dqx, dqy, drx, dry);
RT den = RT(2) * determinant(dqx, dqy, drx, dry);
// The 3 points aren't collinear.
// Hopefully, this is already checked at the upper level.
@ -47,8 +47,8 @@ weighted_circumcenter_translateC2(const RT &dqx, const RT &dqy, const RT &dqw,
// One possible optimization here is to precompute 1/den, to avoid one
// division. However, we loose precision, and it's maybe not worth it (?).
dcx = det2x2_by_formula (dry, dqy, r2, q2) / den;
dcy = - det2x2_by_formula (drx, dqx, r2, q2) / den;
dcx = determinant (dry, dqy, r2, q2) / den;
dcy = - determinant (drx, dqx, r2, q2) / den;
}
//template < class RT >

2
Triangulation_2/test/Triangulation_2/include/CGAL/_test_traits.h
View File

@ -222,7 +222,7 @@ public:
RT RT0(0);
RT RT1(1);
RT det = CGAL::det4x4_by_formula(px, py, px*px + py*py, RT1,
RT det = CGAL::determinant(px, py, px*px + py*py, RT1,
qx, qy, qx*qx + qy*qy, RT1,
rx, ry, rx*rx + ry*ry, RT1,
tx, ty, tx*tx + ty*ty, RT1);

36
Triangulation_3/include/CGAL/constructions/constructions_on_weighted_points_cartesian_3.h
View File

@ -50,16 +50,16 @@ determinants_for_weighted_circumcenterC3(
FT sp2 = CGAL_NTS square(spx) + CGAL_NTS square(spy) +
CGAL_NTS square(spz) - sw + pw;
num_x = det3x3_by_formula(qpy,qpz,qp2,
num_x = determinant(qpy,qpz,qp2,
rpy,rpz,rp2,
spy,spz,sp2);
num_y = det3x3_by_formula(qpx,qpz,qp2,
num_y = determinant(qpx,qpz,qp2,
rpx,rpz,rp2,
spx,spz,sp2);
num_z = det3x3_by_formula(qpx,qpy,qp2,
num_z = determinant(qpx,qpy,qp2,
rpx,rpy,rp2,
spx,spy,sp2);
den = det3x3_by_formula(qpx,qpy,qpz,
den = determinant(qpx,qpy,qpz,
rpx,rpy,rpz,
spx,spy,spz);
}
@ -182,26 +182,26 @@ determinants_for_weighted_circumcenterC3(
// The following determinants can be developped and simplified.
//
// FT num_x = det3x3_by_formula(qpy,qpz,qp2,
// FT num_x = determinant(qpy,qpz,qp2,
// rpy,rpz,rp2,
// sy,sz,FT(0));
// FT num_y = det3x3_by_formula(qpx,qpz,qp2,
// FT num_y = determinant(qpx,qpz,qp2,
// rpx,rpz,rp2,
// sx,sz,FT(0));
// FT num_z = det3x3_by_formula(qpx,qpy,qp2,
// FT num_z = determinant(qpx,qpy,qp2,
// rpx,rpy,rp2,
// sx,sy,FT(0));
num_x = qp2 * det2x2_by_formula(rpy,rpz,sy,sz)
- rp2 * det2x2_by_formula(qpy,qpz,sy,sz);
num_x = qp2 * determinant(rpy,rpz,sy,sz)
- rp2 * determinant(qpy,qpz,sy,sz);
num_y = qp2 * det2x2_by_formula(rpx,rpz,sx,sz)
- rp2 * det2x2_by_formula(qpx,qpz,sx,sz);
num_y = qp2 * determinant(rpx,rpz,sx,sz)
- rp2 * determinant(qpx,qpz,sx,sz);
num_z = qp2 * det2x2_by_formula(rpx,rpy,sx,sy)
- rp2 * det2x2_by_formula(qpx,qpy,sx,sy);
num_z = qp2 * determinant(rpx,rpy,sx,sy)
- rp2 * determinant(qpx,qpy,sx,sy);
den = det3x3_by_formula(qpx,qpy,qpz,
den = determinant(qpx,qpy,qpz,
rpx,rpy,rpz,
sx,sy,sz);
}
@ -383,9 +383,9 @@ radical_axisC3(const RT &px, const RT &py, const RT &pz, const We &pw,
//il manque des tests...
a= RT(1)*det2x2_by_formula(dqy, dqz, dry, drz);
b= - RT(1)*det2x2_by_formula(dqx, dqz, drx, drz);
c= RT(1)*det2x2_by_formula(dqx, dqy, drx, dry);
a= RT(1)*determinant(dqy, dqz, dry, drz);
b= - RT(1)*determinant(dqx, dqz, drx, drz);
c= RT(1)*determinant(dqx, dqy, drx, dry);
}
// function used in critical_squared_radiusC3
@ -423,7 +423,7 @@ power_to_orthogonal_sphereC3(
FT dst = CGAL_NTS square(dsx) + CGAL_NTS square(dsy) +
CGAL_NTS square(dsz) - sw + tw;
return det4x4_by_formula(dpx, dpy, dpz, dpt,
return determinant(dpx, dpy, dpz, dpt,
dqx, dqy, dqz, dqt,
drx, dry, drz, drt,
dsx, dsy, dsz, dst);

20
Triangulation_3/include/CGAL/predicates/predicates_on_weighted_points_cartesian_3.h
View File

@ -72,11 +72,11 @@ in_smallest_orthogonal_sphereC3(
FT qpw = qq - qw + pw ;
FT rpw = rr - rw + pw ;
FT den = det2x2_by_formula(qq,qr,
FT den = determinant(qq,qr,
qr,rr);
FT detq = det2x2_by_formula(qpw,qr,
FT detq = determinant(qpw,qr,
rpw,rr);
FT detr = det2x2_by_formula(qq,qpw,
FT detr = determinant(qq,qpw,
qr,rpw);
// Smallest smallest orthogonal sphere center
@ -159,16 +159,16 @@ does_simplex_intersect_weighted_dual_supportC3(
FT rpw = rr - rw + pw ;
FT spw = ss - sw + pw ;
FT den = det3x3_by_formula(qq,qr,qs,
FT den = determinant(qq,qr,qs,
qr,rr,rs,
qs,rs,ss);
FT detq = det3x3_by_formula(qpw,qr,qs,
FT detq = determinant(qpw,qr,qs,
rpw,rr,rs,
spw,rs,ss);
FT detr = det3x3_by_formula(qq,qpw,qs,
FT detr = determinant(qq,qpw,qs,
qr,rpw,rs,
qs,spw,ss);
FT dets = det3x3_by_formula(qq,qr,qpw,
FT dets = determinant(qq,qr,qpw,
qr,rr,rpw,
qs,rs,spw);
CGAL_kernel_assertion( ! CGAL_NTS is_zero(den) );
@ -222,11 +222,11 @@ does_simplex_intersect_weighted_dual_supportC3(
FT qpw = qq - qw + pw ;
FT rpw = rr - rw + pw ;
FT den = det2x2_by_formula(qq,qr,
FT den = determinant(qq,qr,
qr,rr);
FT detq = det2x2_by_formula(qpw,qr,
FT detq = determinant(qpw,qr,
rpw,rr);
FT detr = det2x2_by_formula(qq,qpw,
FT detr = determinant(qq,qpw,
qr,rpw);
CGAL_kernel_assertion( ! CGAL_NTS is_zero(den) );