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// Copyright (c) 2000 // Utrecht University (The Netherlands), // ETH Zurich (Switzerland), // INRIA Sophia-Antipolis (France), // Max-Planck-Institute Saarbruecken (Germany), // and Tel-Aviv University (Israel). All rights reserved. // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Cartesian_kernel/include/CGAL/constructions/kernel_ftC2.h $ // $Id: include/CGAL/constructions/kernel_ftC2.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Sven Schoenherr, Herve Bronnimann, Sylvain Pion #ifndef CGAL_CONSTRUCTIONS_KERNEL_FTC2_H #define CGAL_CONSTRUCTIONS_KERNEL_FTC2_H #include #include #include namespace CGAL { template < class FT > CGAL_KERNEL_INLINE void midpointC2( const FT &px, const FT &py, const FT &qx, const FT &qy, FT &x, FT &y ) { x = (px+qx) / 2; y = (py+qy) / 2; } template < class FT > CGAL_KERNEL_LARGE_INLINE void circumcenter_translateC2(const FT &dqx, const FT &dqy, const FT &drx, const FT &dry, FT &dcx, FT &dcy) { // Given 3 points P, Q, R, this function takes as input: // qx-px, qy-py, rx-px, ry-py. And returns cx-px, cy-py, // where (cx, cy) are the coordinates of the circumcenter C. // 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 * determinant(dqx, dqy, drx, dry); // The 3 points aren't collinear. // Hopefully, this is already checked at the upper level. CGAL_kernel_assertion ( ! CGAL_NTS is_zero(den) ); // One possible optimization here is to precompute 1/den, to avoid one // division. However, we lose precision, and it's maybe not worth it (?). dcx = determinant (dry, dqy, r2, q2) / den; dcy = - determinant (drx, dqx, r2, q2) / den; } template < class FT > CGAL_KERNEL_MEDIUM_INLINE void circumcenterC2( const FT &px, const FT &py, const FT &qx, const FT &qy, const FT &rx, const FT &ry, FT &x, FT &y ) { circumcenter_translateC2(qx-px, qy-py, rx-px, ry-py, x, y); x += px; y += py; } template < class FT > void barycenterC2(const FT &p1x, const FT &p1y, const FT &w1, const FT &p2x, const FT &p2y, FT &x, FT &y) { FT w2 = 1 - w1; x = w1 * p1x + w2 * p2x; y = w1 * p1y + w2 * p2y; } template < class FT > void barycenterC2(const FT &p1x, const FT &p1y, const FT &w1, const FT &p2x, const FT &p2y, const FT &w2, FT &x, FT &y) { FT sum = w1 + w2; CGAL_kernel_assertion(sum != 0); x = (w1 * p1x + w2 * p2x) / sum; y = (w1 * p1y + w2 * p2y) / sum; } template < class FT > void barycenterC2(const FT &p1x, const FT &p1y, const FT &w1, const FT &p2x, const FT &p2y, const FT &w2, const FT &p3x, const FT &p3y, FT &x, FT &y) { FT w3 = 1 - w1 - w2; x = w1 * p1x + w2 * p2x + w3 * p3x; y = w1 * p1y + w2 * p2y + w3 * p3y; } template < class FT > void barycenterC2(const FT &p1x, const FT &p1y, const FT &w1, const FT &p2x, const FT &p2y, const FT &w2, const FT &p3x, const FT &p3y, const FT &w3, FT &x, FT &y) { FT sum = w1 + w2 + w3; CGAL_kernel_assertion(sum != 0); x = (w1 * p1x + w2 * p2x + w3 * p3x) / sum; y = (w1 * p1y + w2 * p2y + w3 * p3y) / sum; } template < class FT > void barycenterC2(const FT &p1x, const FT &p1y, const FT &w1, const FT &p2x, const FT &p2y, const FT &w2, const FT &p3x, const FT &p3y, const FT &w3, const FT &p4x, const FT &p4y, FT &x, FT &y) { FT w4 = 1 - w1 - w2 - w3; x = w1 * p1x + w2 * p2x + w3 * p3x + w4 * p4x; y = w1 * p1y + w2 * p2y + w3 * p3y + w4 * p4y; } template < class FT > void barycenterC2(const FT &p1x, const FT &p1y, const FT &w1, const FT &p2x, const FT &p2y, const FT &w2, const FT &p3x, const FT &p3y, const FT &w3, const FT &p4x, const FT &p4y, const FT &w4, FT &x, FT &y) { FT sum = w1 + w2 + w3 + w4; CGAL_kernel_assertion(sum != 0); x = (w1 * p1x + w2 * p2x + w3 * p3x + w4 * p4x) / sum; y = (w1 * p1y + w2 * p2y + w3 * p3y + w4 * p4y) / sum; } template < class FT > CGAL_KERNEL_MEDIUM_INLINE void centroidC2( const FT &px, const FT &py, const FT &qx, const FT &qy, const FT &rx, const FT &ry, FT &x, FT &y) { x = (px + qx + rx) / 3; y = (py + qy + ry) / 3; } template < class FT > CGAL_KERNEL_MEDIUM_INLINE void centroidC2( const FT &px, const FT &py, const FT &qx, const FT &qy, const FT &rx, const FT &ry, const FT &sx, const FT &sy, FT &x, FT &y) { x = (px + qx + rx + sx) / 4; y = (py + qy + ry + sy) / 4; } template < class FT > inline void line_from_pointsC2(const FT &px, const FT &py, const FT &qx, const FT &qy, FT &a, FT &b, FT &c) { // The horizontal and vertical line get a special treatment // in order to make the intersection code robust for doubles if(py == qy){ a = 0 ; if(qx > px){ b = 1; c = -py; } else if(qx == px){ b = 0; c = 0; }else{ b = -1; c = py; } } else if(qx == px){ b = 0; if(qy > py){ a = -1; c = px; } else if (qy == py){ a = 0; c = 0; } else { a = 1; c = -px; } } else { a = py - qy; b = qx - px; c = -px*a - py*b; } } template < class FT > inline void line_from_point_directionC2(const FT &px, const FT &py, const FT &dx, const FT &dy, FT &a, FT &b, FT &c) { a = - dy; b = dx; c = px*dy - py*dx; } template < class FT > CGAL_KERNEL_INLINE void bisector_of_pointsC2(const FT &px, const FT &py, const FT &qx, const FT &qy, FT &a, FT &b, FT& c ) { a = 2 * (px - qx); b = 2 * (py - qy); c = CGAL_NTS square(qx) + CGAL_NTS square(qy) - CGAL_NTS square(px) - CGAL_NTS square(py); } template < class FT > CGAL_KERNEL_INLINE void bisector_of_linesC2(const FT &pa, const FT &pb, const FT &pc, const FT &qa, const FT &qb, const FT &qc, FT &a, FT &b, FT &c) { // We normalize the equations of the 2 lines, and we then add them. FT n1 = CGAL_NTS approximate_sqrt( FT(CGAL_NTS square(pa) + CGAL_NTS square(pb)) ); FT n2 = CGAL_NTS approximate_sqrt( FT(CGAL_NTS square(qa) + CGAL_NTS square(qb)) ); a = n2 * pa + n1 * qa; b = n2 * pb + n1 * qb; c = n2 * pc + n1 * qc; // Care must be taken for the case when this produces a degenerate line. if (a == 0 && b == 0) { a = n2 * pa - n1 * qa; b = n2 * pb - n1 * qb; c = n2 * pc - n1 * qc; } } template < class FT > inline FT line_y_at_xC2(const FT &a, const FT &b, const FT &c, const FT &x) { return (-a*x-c) / b; } // Silence a warning for MSVC 2017 // > include\cgal\constructions\kernel_ftc2.h(287) : // > warning C4723: potential divide by 0 #if defined(BOOST_MSVC) #pragma warning(push) #pragma warning(disable:4723) #endif template < class FT > inline void line_get_pointC2(const FT &a, const FT &b, const FT &c, const FT &i, FT &x, FT &y) { if (CGAL_NTS is_zero(b)) { x = -c/a; y = 1 - i * a; } else { x = 1 + i * b; y = -(a+c)/b - i * a; } } #if defined(BOOST_MSVC) #pragma warning(pop) #endif template < class FT > inline void perpendicular_through_pointC2(const FT &la, const FT &lb, const FT &px, const FT &py, FT &a, FT &b, FT &c) { a = -lb; b = la; c = lb * px - la * py; } template < class FT > CGAL_KERNEL_MEDIUM_INLINE void line_project_pointC2(const FT &la, const FT &lb, const FT &lc, const FT &px, const FT &py, FT &x, FT &y) { if (certainly(is_zero(la))) // horizontal line { x = px; y = -lc/lb; } else if (certainly(is_zero(lb))) // vertical line { x = -lc/la; y = py; } else { FT a2 = CGAL_NTS square(la); FT b2 = CGAL_NTS square(lb); FT d = a2 + b2; x = (b2*px - la*lb*py - la*lc) / d; y = (-la*lb*px + a2*py - lb*lc) / d; } } template < class FT > CGAL_KERNEL_MEDIUM_INLINE FT squared_radiusC2(const FT &px, const FT &py, const FT &qx, const FT &qy, const FT &rx, const FT &ry, FT &x, FT &y ) { circumcenter_translateC2(qx-px, qy-py, rx-px, ry-py, x, y); FT r2 = CGAL_NTS square(x) + CGAL_NTS square(y); x += px; y += py; return r2; } template < class FT > CGAL_KERNEL_MEDIUM_INLINE FT squared_radiusC2(const FT &px, const FT &py, const FT &qx, const FT &qy, const FT &rx, const FT &ry) { FT x, y; circumcenter_translateC2(qx-px, qy-py, rx-px, ry-py, x, y); return CGAL_NTS square(x) + CGAL_NTS square(y); } template < class FT > inline FT squared_distanceC2( const FT &px, const FT &py, const FT &qx, const FT &qy) { return CGAL_NTS square(px-qx) + CGAL_NTS square(py-qy); } template < class FT > inline FT squared_radiusC2(const FT &px, const FT &py, const FT &qx, const FT &qy) { return squared_distanceC2(px, py,qx, qy) / 4; } template < class FT > CGAL_KERNEL_INLINE FT scaled_distance_to_lineC2( const FT &la, const FT &lb, const FT &lc, const FT &px, const FT &py) { // for comparisons, use distance_to_directionsC2 instead // since lc is irrelevant return la*px + lb*py + lc; } template < class FT > CGAL_KERNEL_INLINE FT scaled_distance_to_directionC2( const FT &la, const FT &lb, const FT &px, const FT &py) { // scalar product with direction return la*px + lb*py; } template < class FT > CGAL_KERNEL_MEDIUM_INLINE FT scaled_distance_to_lineC2( const FT &px, const FT &py, const FT &qx, const FT &qy, const FT &rx, const FT &ry) { return determinant(px-rx, py-ry, qx-rx, qy-ry); } template < class RT > void weighted_circumcenter_translateC2(const RT &dqx, const RT &dqy, const RT &dqw, const RT &drx, const RT &dry, const RT &drw, RT &dcx, RT &dcy) { // Given 3 points P, Q, R, this function takes as input: // qx-px, qy-py,qw-pw, rx-px, ry-py, rw-pw. And returns cx-px, cy-py, // where (cx, cy) are the coordinates of the circumcenter C. // What we do is intersect the radical axis 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) * determinant(dqx, dqy, drx, dry); // The 3 points aren't collinear. // Hopefully, this is already checked at the upper level. CGAL_assertion ( den != RT(0) ); // One possible optimization here is to precompute 1/den, to avoid one // division. However, we lose precision, and it's maybe not worth it (?). dcx = determinant (dry, dqy, r2, q2) / den; dcy = - determinant (drx, dqx, r2, q2) / den; } //template < class RT > template < class RT, class We> void weighted_circumcenterC2( const RT &px, const RT &py, const We &pw, const RT &qx, const RT &qy, const We &qw, const RT &rx, const RT &ry, const We &rw, RT &x, RT &y ) { RT dqw = RT(qw-pw); RT drw = RT(rw-pw); weighted_circumcenter_translateC2(qx-px, qy-py, dqw,rx-px, ry-py,drw,x, y); x += px; y += py; } template< class FT > FT power_productC2(const FT &px, const FT &py, const FT &pw, const FT &qx, const FT &qy, const FT &qw) { // computes the power product of two weighted points FT qpx = qx - px; FT qpy = qy - py; FT qp2 = CGAL_NTS square(qpx) + CGAL_NTS square(qpy); return qp2 - pw - qw; } template < class RT , class We> void radical_axisC2(const RT &px, const RT &py, const We &pw, const RT &qx, const RT &qy, const We &qw, RT &a, RT &b, RT& c ) { a = RT(2)*(px - qx); b = RT(2)*(py - qy); c = - CGAL_NTS square(px) - CGAL_NTS square(py) + CGAL_NTS square(qx) + CGAL_NTS square(qy) + RT(pw) - RT(qw); } template< class FT > CGAL_KERNEL_MEDIUM_INLINE FT squared_radius_orthogonal_circleC2(const FT &px, const FT &py, const FT &pw, const FT &qx, const FT &qy, const FT &qw, const FT &rx, const FT &ry, const FT &rw) { FT FT4(4); FT dpx = px - rx; FT dpy = py - ry; FT dqx = qx - rx; FT dqy = qy - ry; 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 = determinant(dpx, dpy, dqx, dqy); FT det1 = determinant(dpp, dpy, dqq, dqy); FT det2 = determinant(dpx, dpp, dqx, dqq); return (CGAL_NTS square(det1) + CGAL_NTS square(det2)) / (FT4 * CGAL_NTS square(det0)) - rw; } template< class FT > CGAL_KERNEL_MEDIUM_INLINE FT squared_radius_smallest_orthogonal_circleC2(const FT &px, const FT &py, const FT &pw, const FT &qx, const FT &qy, const FT &qw) { FT FT4(4); FT dpz = CGAL_NTS square(px - qx) + CGAL_NTS square(py - qy); return (CGAL_NTS square(dpz - pw + qw) / (FT4 * dpz) - qw); } } //namespace CGAL #endif // CGAL_CONSTRUCTIONS_KERNEL_FTC2_H