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// Copyright (c) 2003,2006 INRIA Sophia-Antipolis (France). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Constructions_ftC2.h $ // $Id: include/CGAL/Apollonius_graph_2/Constructions_ftC2.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Menelaos Karavelas #ifndef CGAL_APOLLONIUS_GRAPH_2_CONSTRUCTIONS_FTC2_H #define CGAL_APOLLONIUS_GRAPH_2_CONSTRUCTIONS_FTC2_H 1 #include #include #include namespace CGAL { namespace ApolloniusGraph_2 { template < class FT > inline void invert_C2(const FT &x, const FT &y, const FT &wt, FT &new_x, FT &new_y, FT &new_wt) { FT p = CGAL::square(x) + CGAL::square(y) - CGAL::square(wt); CGAL_assertion( CGAL::is_positive(p) ); new_x = x / p; new_y = -y / p; new_wt = wt / p; } template < class FT > void w_plane_tangent_line_2(const FT &x1, const FT &y1, const FT &w1, const FT &x2, const FT &y2, const FT &w2, const FT &x3, const FT &y3, const FT &w3, FT & a, FT & b, FT & c) { // we assume that the weight w1 is the smallest among w1, w2, w3. FT u2, v2; FT u3, v3; FT r2, r3; invert_C2(x2-x1, y2-y1, w2-w1, u2, v2, r2); invert_C2(x3-x1, y3-y1, w3-w1, u3, v3, r3); FT Du = u2 - u3; FT Dv = v2 - v3; FT Dr = r2 - 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; FT sqrtD = CGAL::sqrt(D1 - CGAL::square(Dr)); a = (Du * Dr - Dv * sqrtD) * D1inv; b = (Dv * Dr + Du * sqrtD) * D1inv; c = (Du * Dur + Dv * Dvr - Duv * sqrtD) * D1inv; } template < class FT > inline void z_plane_circumcircle_2(const FT &x1, const FT &y1, const FT &w1, const FT &x2, const FT &y2, const FT &w2, const FT &x3, const FT &y3, const FT &w3, FT &cx, FT &cy, FT &cwt) { // we assume that the weight w1 is the smallest among w1, w2, w3. FT a, b, c; w_plane_tangent_line_2(x1, y1, w1, x2, y2, w2, x3, y3, w3, a, b, c); cx = -a / (FT(2) * c) + x1; cy = b / (FT(2) * c) + y1; // this the only part that is computed at vain when only the center // is needed. #if 0 FT cwt2 = (CGAL::square(a) + CGAL::square(b)) / (FT(4) * CGAL::square(c)); #endif // cwt = CGAL::sqrt(cwt2) - FT(w1); cwt = FT(1) / (FT(2) * c) - FT(w1); } template < class FT > void ad_circumcircleC2(const FT &x1, const FT &y1, const FT &w1, const FT &x2, const FT &y2, const FT &w2, const FT &x3, const FT &y3, const FT &w3, FT &cx, FT &cy, FT &cwt) { if (CGAL::compare(w2, w1) != LARGER && CGAL::compare(w2, w3) != LARGER) { z_plane_circumcircle_2(x2, y2, w2, x3, y3, w3, x1, y1, w1, cx, cy, cwt); return; } else if (CGAL::compare(w3, w1) != LARGER && CGAL::compare(w3, w2) != LARGER) { z_plane_circumcircle_2(x3, y3, w3, x1, y1, w1, x2, y2, w2, cx, cy, cwt); return; } z_plane_circumcircle_2(x1, y1, w1, x2, y2, w2, x3, y3, w3, cx, cy, cwt); } template < class FT > inline void ad_circumcenterC2(const FT &x1, const FT &y1, const FT &w1, const FT &x2, const FT &y2, const FT &w2, const FT &x3, const FT &y3, const FT &w3, FT &cx, FT &cy) { FT cwt; ad_circumcircleC2(x1, y1, w1, x2, y2, w2, x3, y3, w3, cx, cy, cwt); } template < class FT > void ad_left_bitangent_lineC2(const FT &x1, const FT &y1, const FT &w1, const FT &x2, const FT &y2, const FT &w2, FT & a, FT & b, FT & c) { FT dx = x1 - x2; FT dy = y1 - y2; FT dw = w1 - w2; 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; FT D = D1 - CGAL::square(dw); FT sqrtD = CGAL::sqrt(D); a = -(dx * dw - dy * sqrtD) * invD1; b = -(dy * dw + dx * sqrtD) * invD1; c = -(dx * dxw + dy * dyw - dxy * sqrtD) * invD1; } } //namespace ApolloniusGraph_2 } //namespace CGAL #endif // CGAL_APOLLONIUS_GRAPH_2_CONSTRUCTIONS_FTC2_H