mirror of https://github.com/CGAL/cgal
508 lines
16 KiB
C++
508 lines
16 KiB
C++
// ======================================================================
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//
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// Copyright (c) 2000 The CGAL Consortium
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//
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// This software and related documentation is part of an INTERNAL release
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// of the Computational Geometry Algorithms Library (CGAL). It is not
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// intended for general use.
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//
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// ----------------------------------------------------------------------
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//
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// release :
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// release_date :
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//
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// file : include/CGAL/predicates/kernel_ftC3.h
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// revision : $Revision$
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// revision_date : $Date$
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// author(s) : Herve Bronnimann, Sylvain Pion
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// coordinator : INRIA Sophia-Antipolis (Mariette.Yvinec@sophia.inria.fr)
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//
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// ======================================================================
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#ifndef CGAL_PREDICATES_KERNEL_FTC3_H
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#define CGAL_PREDICATES_KERNEL_FTC3_H
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#include <CGAL/predicates/sign_of_determinant.h>
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#include <CGAL/predicates/kernel_ftC2.h>
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#include <CGAL/constructions/kernel_ftC3.h>
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CGAL_BEGIN_NAMESPACE
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template < class FT >
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/*CGAL_NO_FILTER*/
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CGAL_KERNEL_MEDIUM_INLINE
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Comparison_result
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compare_lexicographically_xyzC3(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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{
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Comparison_result c = CGAL_NTS compare(px, qx);
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if (c != EQUAL) return c;
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c = CGAL_NTS compare(py, qy);
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if (c != EQUAL) return c;
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return CGAL_NTS compare(pz, qz);
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}
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template < class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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bool
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strict_dominanceC3(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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{
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return CGAL_NTS compare(px, qx) == LARGER &&
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CGAL_NTS compare(py, qy) == LARGER &&
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CGAL_NTS compare(pz, qz) == LARGER;
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}
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template < class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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bool
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dominanceC3(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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{
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return CGAL_NTS compare(px, qx) != SMALLER &&
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CGAL_NTS compare(py, qy) != SMALLER &&
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CGAL_NTS compare(pz, qz) != SMALLER;
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}
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template < class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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bool
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collinearC3(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 &rx, const FT &ry, const FT &rz)
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{
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FT dpx = px-rx;
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FT dqx = qx-rx;
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FT dpy = py-ry;
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FT dqy = qy-ry;
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if (sign_of_determinant2x2(dpx, dqx, dpy, dqy) != ZERO)
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return false;
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FT dpz = pz-rz;
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FT dqz = qz-rz;
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return sign_of_determinant2x2(dpx, dqx, dpz, dqz) == ZERO
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&& sign_of_determinant2x2(dpy, dqy, dpz, dqz) == ZERO;
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}
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template < class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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Orientation
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orientationC3(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 &rx, const FT &ry, const FT &rz,
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const FT &sx, const FT &sy, const FT &sz)
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{
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return Orientation(sign_of_determinant3x3<FT>(qx-px,rx-px,sx-px,
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qy-py,ry-py,sy-py,
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qz-pz,rz-pz,sz-pz));
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}
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template < class FT >
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inline
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Angle
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angleC3(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 &rx, const FT &ry, const FT &rz)
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{
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return (Angle) CGAL_NTS sign<FT>((px-qx)*(rx-qx)+
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(py-qy)*(ry-qy)+
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(pz-qz)*(rz-qz));
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}
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template < class FT >
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/*CGAL_NO_FILTER*/
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CGAL_KERNEL_MEDIUM_INLINE
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Orientation
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coplanar_orientationC3(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 &rx, const FT &ry, const FT &rz,
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const FT &sx, const FT &sy, const FT &sz)
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{
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Orientation oxy_pqr = orientationC2(px,py,qx,qy,rx,ry);
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if (oxy_pqr != COLLINEAR)
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return Orientation( oxy_pqr * orientationC2(px,py,qx,qy,sx,sy));
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Orientation oyz_pqr = orientationC2(py,pz,qy,qz,ry,rz);
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if (oyz_pqr != COLLINEAR)
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return Orientation( oyz_pqr * orientationC2(py,pz,qy,qz,sy,sz));
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Orientation oxz_pqr = orientationC2(px,pz,qx,qz,rx,rz);
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CGAL_kernel_assertion(oxz_pqr != COLLINEAR);
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return Orientation( oxz_pqr * orientationC2(px,pz,qx,qz,sx,sz));
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}
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template < class FT >
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/*CGAL_NO_FILTER*/
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CGAL_KERNEL_MEDIUM_INLINE
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Orientation
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coplanar_orientationC3(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 &rx, const FT &ry, const FT &rz)
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{
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Orientation oxy_pqr = orientationC2(px,py,qx,qy,rx,ry);
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if (oxy_pqr != COLLINEAR)
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return oxy_pqr;
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Orientation oyz_pqr = orientationC2(py,pz,qy,qz,ry,rz);
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if (oyz_pqr != COLLINEAR)
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return oyz_pqr;
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return orientationC2(px,pz,qx,qz,rx,rz);
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}
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template < class FT >
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CGAL_KERNEL_LARGE_INLINE
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Bounded_side
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coplanar_side_of_bounded_circleC3(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 &rx, const FT &ry, const FT &rz,
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const FT &tx, const FT &ty, const FT &tz)
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{
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// The approach is to compute side_of_bounded_sphere(p,q,r,t+v,t),
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// with v = pq ^ pr.
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// Note : since the circle defines the orientation of the plane, it can not
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// be considered oriented.
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FT ptx = px - tx;
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FT pty = py - ty;
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FT ptz = pz - tz;
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FT pt2 = CGAL_NTS square(ptx) + CGAL_NTS square(pty) + CGAL_NTS square(ptz);
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FT qtx = qx - tx;
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FT qty = qy - ty;
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FT qtz = qz - tz;
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FT qt2 = CGAL_NTS square(qtx) + CGAL_NTS square(qty) + CGAL_NTS square(qtz);
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FT rtx = rx - tx;
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FT rty = ry - ty;
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FT rtz = rz - tz;
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FT rt2 = CGAL_NTS square(rtx) + CGAL_NTS square(rty) + CGAL_NTS square(rtz);
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FT pqx = qx - px;
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FT pqy = qy - py;
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FT pqz = qz - pz;
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FT prx = rx - px;
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FT pry = ry - py;
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FT prz = rz - pz;
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FT vx = pqy*prz - pqz*pry;
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FT vy = pqz*prx - pqx*prz;
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FT vz = pqx*pry - pqy*prx;
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FT v2 = CGAL_NTS square(vx) + CGAL_NTS square(vy) + CGAL_NTS square(vz);
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return Bounded_side(sign_of_determinant4x4(ptx,pty,ptz,pt2,
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rtx,rty,rtz,rt2,
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qtx,qty,qtz,qt2,
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vx,vy,vz,v2));
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}
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template < class FT >
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/*CGAL_NO_FILTER*/
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CGAL_KERNEL_MEDIUM_INLINE
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bool
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collinear_are_ordered_along_lineC3(
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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 &rx, const FT &ry, const FT &rz)
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{
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if (px < qx) return !(rx < qx);
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if (qx < px) return !(qx < rx);
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if (py < qy) return !(ry < qy);
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if (qy < py) return !(qy < ry);
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if (pz < qz) return !(rz < qz);
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if (qz < pz) return !(qz < rz);
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return true; // p==q
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}
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template < class FT >
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/*CGAL_NO_FILTER*/
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CGAL_KERNEL_MEDIUM_INLINE
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bool
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collinear_are_strictly_ordered_along_lineC3(
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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 &rx, const FT &ry, const FT &rz)
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{
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if (px < qx) return (qx < rx);
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if (qx < px) return (rx < qx);
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if (py < qy) return (qy < ry);
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if (qy < py) return (ry < qy);
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if (pz < qz) return (qz < rz);
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if (qz < pz) return (rz < qz);
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return false; // p==q
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}
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template < class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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bool
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equal_directionC3(const FT &dx1, const FT &dy1, const FT &dz1,
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const FT &dx2, const FT &dy2, const FT &dz2)
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{
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return sign_of_determinant2x2(dx1, dy1, dx2, dy2) == ZERO
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&& sign_of_determinant2x2(dx1, dz1, dx2, dz2) == ZERO
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&& sign_of_determinant2x2(dy1, dz1, dy2, dz2) == ZERO
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&& CGAL_NTS sign(dx1) == CGAL_NTS sign(dx2)
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&& CGAL_NTS sign(dy1) == CGAL_NTS sign(dy2)
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&& CGAL_NTS sign(dz1) == CGAL_NTS sign(dz2);
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}
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template < class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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bool
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equal_planeC3(const FT &ha, const FT &hb, const FT &hc, const FT &hd,
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const FT &pa, const FT &pb, const FT &pc, const FT &pd)
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{
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if (!equal_directionC3(ha, hb, hc, pa, pb, pc))
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return false; // Not parallel.
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CGAL::Sign s1a = CGAL_NTS sign(ha);
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if (s1a != ZERO)
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return s1a == CGAL_NTS sign(pa)
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&& sign_of_determinant2x2(pa, pd, ha, hd) == ZERO;
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CGAL::Sign s1b = CGAL_NTS sign(hb);
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if (s1b != ZERO)
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return s1b == CGAL_NTS sign(pb)
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&& sign_of_determinant2x2(pb, pd, hb, hd) == ZERO;
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return CGAL_NTS sign(pc) == CGAL_NTS sign(hc)
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&& sign_of_determinant2x2(pc, pd, hc, hd) == ZERO;
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}
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template <class FT >
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CGAL_KERNEL_LARGE_INLINE
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Oriented_side
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side_of_oriented_planeC3(const FT &a, const FT &b, const FT &c, const FT &d,
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const FT &px, const FT &py, const FT &pz)
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{
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return Oriented_side(CGAL_NTS sign<FT>(a*px + b*py + c*pz +d));
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}
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template <class FT >
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CGAL_KERNEL_LARGE_INLINE
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Oriented_side
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side_of_oriented_sphereC3(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 &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 &tx, const FT &ty, const FT &tz)
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{
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FT ptx = px - tx;
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FT pty = py - ty;
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FT ptz = pz - tz;
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FT pt2 = CGAL_NTS square(ptx) + CGAL_NTS square(pty) + CGAL_NTS square(ptz);
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FT qtx = qx - tx;
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FT qty = qy - ty;
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FT qtz = qz - tz;
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FT qt2 = CGAL_NTS square(qtx) + CGAL_NTS square(qty) + CGAL_NTS square(qtz);
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FT rtx = rx - tx;
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FT rty = ry - ty;
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FT rtz = rz - tz;
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FT rt2 = CGAL_NTS square(rtx) + CGAL_NTS square(rty) + CGAL_NTS square(rtz);
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FT stx = sx - tx;
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FT sty = sy - ty;
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FT stz = sz - tz;
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FT st2 = CGAL_NTS square(stx) + CGAL_NTS square(sty) + CGAL_NTS square(stz);
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return Oriented_side(sign_of_determinant4x4(ptx,pty,ptz,pt2,
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rtx,rty,rtz,rt2,
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qtx,qty,qtz,qt2,
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stx,sty,stz,st2));
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}
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template <class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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Bounded_side
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side_of_bounded_sphereC3(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 &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 &tx, const FT &ty, const FT &tz)
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{
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Oriented_side s = side_of_oriented_sphereC3(px, py, pz,
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qx, qy, qz,
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rx, ry, rz,
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sx, sy, sz,
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tx, ty, tz);
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Orientation o = orientationC3(px, py, pz,
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qx, qy, qz,
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rx, ry, rz,
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sx, sy, sz);
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return Bounded_side(s * o);
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}
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template <class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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Bounded_side
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side_of_bounded_sphereC3(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 &tx, const FT &ty, const FT &tz)
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{
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// Returns whether T lies inside or outside the sphere which diameter is PQ.
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return Bounded_side( CGAL_NTS sign<FT>((tx-px)*(qx-tx)
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+ (ty-py)*(qy-ty)
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+ (tz-pz)*(qz-tz)) );
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}
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template < class FT >
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CGAL_KERNEL_INLINE
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Comparison_result
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cmp_dist_to_pointC3(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 &rx, const FT &ry, const FT &rz)
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{
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return CGAL_NTS compare(squared_distanceC3(px,py,pz,qx,qy,qz),
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squared_distanceC3(px,py,pz,rx,ry,rz));
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}
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// Because of the way the filtered predicates generator script works,
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// cmp_dist_to_pointC3() must be defined _before_ ths following one.
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template <class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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Bounded_side
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side_of_bounded_sphereC3(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 &sx, const FT &sy, const FT &sz,
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const FT &tx, const FT &ty, const FT &tz)
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{
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// Returns whether T lies inside or outside the sphere which equatorial
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// circle is PQR.
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// This code is inspired by the one of circumcenterC3(3 points).
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FT psx = px-sx;
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FT psy = py-sy;
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FT psz = pz-sz;
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FT ps2 = CGAL_NTS square(psx) + CGAL_NTS square(psy) + CGAL_NTS square(psz);
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FT qsx = qx-sx;
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FT qsy = qy-sy;
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FT qsz = qz-sz;
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FT qs2 = CGAL_NTS square(qsx) + CGAL_NTS square(qsy) + CGAL_NTS square(qsz);
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FT rsx = psy*qsz-psz*qsy;
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FT rsy = psz*qsx-psx*qsz;
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FT rsz = psx*qsy-psy*qsx;
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FT tsx = tx-sx;
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FT tsy = ty-sy;
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FT tsz = tz-sz;
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FT num_x = ps2 * det2x2_by_formula(qsy,qsz,rsy,rsz)
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- qs2 * det2x2_by_formula(psy,psz,rsy,rsz);
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FT num_y = ps2 * det2x2_by_formula(qsx,qsz,rsx,rsz)
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- qs2 * det2x2_by_formula(psx,psz,rsx,rsz);
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FT num_z = ps2 * det2x2_by_formula(qsx,qsy,rsx,rsy)
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- qs2 * det2x2_by_formula(psx,psy,rsx,rsy);
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FT den = det3x3_by_formula(psx,psy,psz,
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qsx,qsy,qsz,
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rsx,rsy,rsz);
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FT den2 = FT(2) * den;
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// The following could be simplified a bit.
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return Bounded_side(cmp_dist_to_pointC3<FT>(num_x, - num_y, num_z,
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psx*den2, psy*den2, psz*den2,
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tsx*den2, tsy*den2, tsz*den2) );
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}
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template < class FT >
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/*CGAL_NO_FILTER*/
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CGAL_KERNEL_MEDIUM_INLINE
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bool
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has_larger_dist_to_pointC3(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 &rx, const FT &ry, const FT &rz)
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{
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return cmp_dist_to_pointC3(px,py,pz,qx,qy,qz,rx,ry,rz) == LARGER;
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}
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template < class FT >
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/*CGAL_NO_FILTER*/
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CGAL_KERNEL_MEDIUM_INLINE
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bool
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has_smaller_dist_to_pointC3(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 &rx, const FT &ry, const FT &rz)
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{
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return cmp_dist_to_pointC3(px,py,pz,qx,qy,qz,rx,ry,rz) == SMALLER;
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}
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template < class FT >
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CGAL_KERNEL_MEDIUM_INLINE
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Comparison_result
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cmp_signed_dist_to_directionC3(
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const FT &pa, const FT &pb, const FT &pc,
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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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{
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return CGAL_NTS compare(scaled_distance_to_directionC3(pa,pb,pc,px,py,pz),
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scaled_distance_to_directionC3(pa,pb,pc,qx,qy,qz));
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}
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|
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template < class FT >
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/*CGAL_NO_FILTER*/
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CGAL_KERNEL_MEDIUM_INLINE
|
|
bool
|
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has_larger_signed_dist_to_directionC3(
|
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const FT &pa, const FT &pb, const FT &pc,
|
|
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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{
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|
return cmp_signed_dist_to_directionC3(pa,pb,pc,px,py,pz,qx,qy,qz) == LARGER;
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}
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|
|
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template < class FT >
|
|
/*CGAL_NO_FILTER*/
|
|
CGAL_KERNEL_MEDIUM_INLINE
|
|
bool
|
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has_smaller_signed_dist_to_directionC3(
|
|
const FT &pa, const FT &pb, const FT &pc,
|
|
const FT &px, const FT &py, const FT &pz,
|
|
const FT &qx, const FT &qy, const FT &qz)
|
|
{
|
|
return cmp_signed_dist_to_directionC3(pa,pb,pc,px,py,pz,qx,qy,qz) == SMALLER;
|
|
}
|
|
|
|
template < class FT >
|
|
CGAL_KERNEL_MEDIUM_INLINE
|
|
Comparison_result
|
|
cmp_signed_dist_to_planeC3(
|
|
const FT &ppx, const FT &ppy, const FT &ppz,
|
|
const FT &pqx, const FT &pqy, const FT &pqz,
|
|
const FT &prx, const FT &pry, const FT &prz,
|
|
const FT &px, const FT &py, const FT &pz,
|
|
const FT &qx, const FT &qy, const FT &qz)
|
|
{
|
|
return Comparison_result(sign_of_determinant3x3(
|
|
pqx-ppx, pqy-ppy, pqz-ppz,
|
|
prx-ppx, pry-ppy, prz-ppz,
|
|
qx-px, qy-py, qz-pz));
|
|
}
|
|
|
|
template < class FT >
|
|
/*CGAL_NO_FILTER*/
|
|
CGAL_KERNEL_MEDIUM_INLINE
|
|
bool
|
|
has_larger_signed_dist_to_planeC3(
|
|
const FT &ppx, const FT &ppy, const FT &ppz,
|
|
const FT &pqx, const FT &pqy, const FT &pqz,
|
|
const FT &prx, const FT &pry, const FT &prz,
|
|
const FT &px, const FT &py, const FT &pz,
|
|
const FT &qx, const FT &qy, const FT &qz)
|
|
{
|
|
return cmp_signed_dist_to_planeC3(ppx, ppy, ppz, pqx, pqy, pqz,
|
|
prx, pry, prz, px, py, pz, qx, qy, qz) == LARGER;
|
|
}
|
|
|
|
template < class FT >
|
|
/*CGAL_NO_FILTER*/
|
|
CGAL_KERNEL_MEDIUM_INLINE
|
|
bool
|
|
has_smaller_signed_dist_to_planeC3(
|
|
const FT &ppx, const FT &ppy, const FT &ppz,
|
|
const FT &pqx, const FT &pqy, const FT &pqz,
|
|
const FT &prx, const FT &pry, const FT &prz,
|
|
const FT &px, const FT &py, const FT &pz,
|
|
const FT &qx, const FT &qy, const FT &qz)
|
|
{
|
|
return cmp_signed_dist_to_planeC3(ppx, ppy, ppz, pqx, pqy, pqz,
|
|
prx, pry, prz, px, py, pz, qx, qy, qz) == SMALLER;
|
|
}
|
|
|
|
CGAL_END_NAMESPACE
|
|
|
|
#ifdef CGAL_ARITHMETIC_FILTER_H
|
|
#include <CGAL/Arithmetic_filter/predicates/kernel_ftC3.h>
|
|
#endif
|
|
|
|
#endif // CGAL_PREDICATES_KERNEL_FTC3_H
|