mirror of https://github.com/CGAL/cgal
Initial revision
This commit is contained in:
Sylvain Pion
parent
6af98788f3
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6b6139555c
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#ifndef CGAL_ADDITIVELY_WEIGHTED_DELAUNAY_GRAPH_FTC2_H
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#define CGAL_ADDITIVELY_WEIGHTED_DELAUNAY_GRAPH_FTC2_H
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#include "../../CGAL/functions_on_signs.h"
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#include <CGAL/determinant.h>
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#include <CGAL/enum.h>
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CGAL_BEGIN_NAMESPACE
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#define awdg_sltcC2 sign_of_left_tritangent_circle
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#define awdg_sdltcC2 sign_of_distance_to_left_tritangent_circle
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template < class RT >
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Sign
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sign_of_left_tritangent_circle(const RT &x1, const RT &y1, const RT &w1,
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const RT &x2, const RT &y2, const RT &w2,
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const RT &x3, const RT &y3, const RT &w3)
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{
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// we assume that the first circle is the one of smallest radius
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// the result ON_BOUNDARY means that the three circles have a common
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// tangent line; the result ON_BOUNDED_SIDE means that
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// the common tangent circle contains the three original ones and
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// the result ON_UNBOUNDED_SIDE means that the three original
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// circles are on the unbounded side of the original one.
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RT x2s = x2 - x1;
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RT y2s = y2 - y1;
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RT w2s = w2 - w1;
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RT p2s = (CGAL_NTS square(x2s)) + (CGAL_NTS square(y2s))
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- (CGAL_NTS square(w2s));
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RT x3s = x3 - x1;
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RT y3s = y3 - y1;
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RT w3s = w3 - w1;
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RT p3s = (CGAL_NTS square(x3s)) + (CGAL_NTS square(y3s))
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- (CGAL_NTS square(w3s));
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RT dxp = det2x2_by_formula(x2s, p2s, x3s, p3s);
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RT dyp = det2x2_by_formula(y2s, p2s, y3s, p3s);
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RT drp = det2x2_by_formula(w2s, p2s, w3s, p3s);
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RT dxr = det2x2_by_formula(x2s, w2s, x3s, w3s);
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RT dyr = det2x2_by_formula(y2s, w2s, y3s, w3s);
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RT dxy = det2x2_by_formula(x2s, y2s, x3s, y3s);
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RT A = dxp * dxr + dyp * dyr;
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RT B = dxy;
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RT C = (CGAL_NTS square(dxp)) +
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(CGAL_NTS square(dyp)) - (CGAL_NTS square(drp));
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return opposite(sign_a_plus_b_x_sqrt_c(A, B, C));
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}
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template < class RT >
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Sign
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sign_of_distance_to_left_tritangent_circle(const RT &x1, const RT &y1,
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const RT &w1,
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const RT &x2, const RT &y2,
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const RT &w2,
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const RT &x3, const RT &y3,
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const RT &w3,
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const RT &x4, const RT &y4,
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const RT &w4)
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{
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// we assume that the first circle is the one of smallest radius
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// the result is the opposite of the sign of the distance of the
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// fourth one from the common tangent circle of the first three
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RT x2s = x2 - x1;
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RT y2s = y2 - y1;
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RT w2s = w2 - w1;
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RT p2s = (CGAL_NTS square(x2s)) + (CGAL_NTS square(y2s))
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- (CGAL_NTS square(w2s));
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RT x3s = x3 - x1;
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RT y3s = y3 - y1;
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RT w3s = w3 - w1;
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RT p3s = (CGAL_NTS square(x3s)) + (CGAL_NTS square(y3s))
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- (CGAL_NTS square(w3s));
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RT x4s = x4 - x1;
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RT y4s = y4 - y1;
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RT w4s = w4 - w1;
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RT p4s = (CGAL_NTS square(x4s)) + (CGAL_NTS square(y4s))
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- (CGAL_NTS square(w4s));
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RT dxp = det2x2_by_formula(x2s, p2s, x3s, p3s);
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RT dyp = det2x2_by_formula(y2s, p2s, y3s, p3s);
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RT drp = det2x2_by_formula(w2s, p2s, w3s, p3s);
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RT dxrp = det3x3_by_formula(x2s, w2s, p2s,
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x3s, w3s, p3s,
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x4s, w4s, p4s);
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RT dyrp = det3x3_by_formula(y2s, w2s, p2s,
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y3s, w3s, p3s,
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y4s, w4s, p4s);
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RT dxyp = det3x3_by_formula(x2s, y2s, p2s,
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x3s, y3s, p3s,
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x4s, y4s, p4s);
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RT A = dxrp * dxp + dyrp * dyp;
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RT B = dxyp;
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RT C = (CGAL_NTS square(dxp)) + (CGAL_NTS square(dyp))
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- (CGAL_NTS square(drp));
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return opposite(sign_a_plus_b_x_sqrt_c(A, B, C));
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}
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template < class RT >inline
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Bounded_side
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awdg_testC2(const RT &x1, const RT &y1, const RT &w1,
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const RT &x2, const RT &y2, const RT &w2,
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const RT &x3, const RT &y3, const RT &w3,
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const RT &x4, const RT &y4, const RT &w4)
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{
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// this test returns if the fourth weighted point is on the
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// unbounded side of the circle, ccw oriented and which is on the
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// unbounded side, corresponding to the first three weighted points
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// the result ON_BOUNDARY merans that the fourth circle touches the
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// common tangent circle of the first three;
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// the result ON_BOUNDED_SIDE means that the fourth circle
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// intersects the bounded side of the tritangent circle
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// the result ON_UNBOUNDED_SIDE means that the fourth circle does
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// not intersect the bounded side of the tritangent circle
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if ( CGAL_NTS compare(w2, w1) != LARGER &&
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CGAL_NTS compare(w2, w3) != LARGER &&
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CGAL_NTS compare(w2, w4) != LARGER) {
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// we have to perform the test {2, 1, 4, 3}
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return Bounded_side(awdg_sdltcC2(x2, y2, w2,
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x1, y1, w1,
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x4, y4, w4,
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x3, y3, w3));
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} else if ( CGAL_NTS compare(w3, w1) != LARGER &&
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CGAL_NTS compare(w3, w2) != LARGER &&
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CGAL_NTS compare(w3, w4) != LARGER) {
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// we have to perform the test {3, 4, 2, 1}
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// and reply negatively
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return Bounded_side(opposite(awdg_sdltcC2(x3, y3, w3,
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x4, y4, w4,
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x2, y2, w2,
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x1, y1, w1)));
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} else if ( CGAL_NTS compare(w4, w1) != LARGER &&
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CGAL_NTS compare(w4, w2) != LARGER &&
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CGAL_NTS compare(w4, w3) != LARGER) {
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// we have to perform the test {4, 3, 1, 2}
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// and reply negatively
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return Bounded_side(opposite(awdg_sdltcC2(x4, y4, w4,
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x3, y3, w3,
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x1, y1, w1,
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x2, y2, w2)));
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}
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return Bounded_side(awdg_sdltcC2(x1, y1, w1,
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x2, y2, w2,
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x3, y3, w3,
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x4, y4, w4));
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}
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template < class RT >
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Bounded_side
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awdg_testC2(const RT &x1, const RT &y1, const RT &w1,
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const RT &x2, const RT &y2, const RT &w2,
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const RT &x3, const RT &y3, const RT &w3)
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{
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// this test returns the left tritangent circle, ccw oriented
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// contains the weighted points on its unbounded side
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// the result ON_BOUNDARY means that the three circles have a common
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// tangent line; the result ON_BOUNDED_SIDE means that
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// the common tangent circle contains the three original ones and
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// the result ON_UNBOUNDED_SIDE means that the three original
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// circles are on the unbounded side of the cotangent circle.
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if ( CGAL_NTS compare(w2, w1) != LARGER &&
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CGAL_NTS compare(w2, w3) != LARGER) {
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// we have to perform the test {2, 3, 1}
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return Bounded_side(awdg_sltcC2(x2, y2, w2,
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x3, y3, w3,
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x1, y1, w1));
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} else if ( CGAL_NTS compare(w3, w1) != LARGER &&
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CGAL_NTS compare(w3, w2) != LARGER ) {
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// we have to perform the test {3, 1, 2}
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// and reply negatively
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return Bounded_side(awdg_sltcC2(x3, y3, w3,
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x1, y1, w1,
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x2, y2, w2));
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}
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return Bounded_side(awdg_sltcC2(x1, y1, w1,
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x2, y2, w2,
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x3, y3, w3));
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}
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CGAL_END_NAMESPACE
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#endif // CGAL_ADDITIVELY_WEIGHTED_DELAUNAY_GRAPH_FTC2_H
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@ -0,0 +1,205 @@
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#ifndef CGAL_ADDITIVELY_WEIGHTED_DELAUNAY_GRAPH_FTC2_H
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#define CGAL_ADDITIVELY_WEIGHTED_DELAUNAY_GRAPH_FTC2_H
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#include "../../CGAL/functions_on_signs.h"
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#include <CGAL/determinant.h>
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#include <CGAL/enum.h>
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CGAL_BEGIN_NAMESPACE
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#define awdg_sltcC2 sign_of_left_tritangent_circle
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#define awdg_sdltcC2 sign_of_distance_to_left_tritangent_circle
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template < class RT >
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Sign
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sign_of_left_tritangent_circle(const RT &x1, const RT &y1, const RT &w1,
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const RT &x2, const RT &y2, const RT &w2,
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const RT &x3, const RT &y3, const RT &w3)
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{
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// we assume that the first circle is the one of smallest radius
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// the result ON_BOUNDARY means that the three circles have a common
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// tangent line; the result ON_BOUNDED_SIDE means that
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// the common tangent circle contains the three original ones and
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// the result ON_UNBOUNDED_SIDE means that the three original
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// circles are on the unbounded side of the original one.
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RT x2s = x2 - x1;
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RT y2s = y2 - y1;
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RT w2s = w2 - w1;
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RT p2s = (CGAL_NTS square(x2s)) + (CGAL_NTS square(y2s))
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- (CGAL_NTS square(w2s));
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RT x3s = x3 - x1;
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RT y3s = y3 - y1;
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RT w3s = w3 - w1;
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RT p3s = (CGAL_NTS square(x3s)) + (CGAL_NTS square(y3s))
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- (CGAL_NTS square(w3s));
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RT dxp = det2x2_by_formula(x2s, p2s, x3s, p3s);
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RT dyp = det2x2_by_formula(y2s, p2s, y3s, p3s);
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RT drp = det2x2_by_formula(w2s, p2s, w3s, p3s);
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RT dxr = det2x2_by_formula(x2s, w2s, x3s, w3s);
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RT dyr = det2x2_by_formula(y2s, w2s, y3s, w3s);
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RT dxy = det2x2_by_formula(x2s, y2s, x3s, y3s);
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RT A = dxp * dxr + dyp * dyr;
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RT B = dxy;
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RT C = (CGAL_NTS square(dxp)) +
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(CGAL_NTS square(dyp)) - (CGAL_NTS square(drp));
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return opposite(sign_a_plus_b_x_sqrt_c(A, B, C));
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}
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template < class RT >
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Sign
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sign_of_distance_to_left_tritangent_circle(const RT &x1, const RT &y1,
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const RT &w1,
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const RT &x2, const RT &y2,
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const RT &w2,
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const RT &x3, const RT &y3,
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const RT &w3,
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const RT &x4, const RT &y4,
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const RT &w4)
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{
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// we assume that the first circle is the one of smallest radius
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// the result is the opposite of the sign of the distance of the
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// fourth one from the common tangent circle of the first three
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RT x2s = x2 - x1;
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RT y2s = y2 - y1;
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RT w2s = w2 - w1;
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RT p2s = (CGAL_NTS square(x2s)) + (CGAL_NTS square(y2s))
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- (CGAL_NTS square(w2s));
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RT x3s = x3 - x1;
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RT y3s = y3 - y1;
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RT w3s = w3 - w1;
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RT p3s = (CGAL_NTS square(x3s)) + (CGAL_NTS square(y3s))
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- (CGAL_NTS square(w3s));
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RT x4s = x4 - x1;
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RT y4s = y4 - y1;
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RT w4s = w4 - w1;
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RT p4s = (CGAL_NTS square(x4s)) + (CGAL_NTS square(y4s))
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- (CGAL_NTS square(w4s));
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RT dxp = det2x2_by_formula(x2s, p2s, x3s, p3s);
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RT dyp = det2x2_by_formula(y2s, p2s, y3s, p3s);
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RT drp = det2x2_by_formula(w2s, p2s, w3s, p3s);
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RT dxrp = det3x3_by_formula(x2s, w2s, p2s,
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x3s, w3s, p3s,
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x4s, w4s, p4s);
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RT dyrp = det3x3_by_formula(y2s, w2s, p2s,
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y3s, w3s, p3s,
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y4s, w4s, p4s);
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RT dxyp = det3x3_by_formula(x2s, y2s, p2s,
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x3s, y3s, p3s,
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x4s, y4s, p4s);
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RT A = dxrp * dxp + dyrp * dyp;
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RT B = dxyp;
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RT C = (CGAL_NTS square(dxp)) + (CGAL_NTS square(dyp))
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- (CGAL_NTS square(drp));
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return opposite(sign_a_plus_b_x_sqrt_c(A, B, C));
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}
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template < class RT >inline
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Bounded_side
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awdg_testC2(const RT &x1, const RT &y1, const RT &w1,
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const RT &x2, const RT &y2, const RT &w2,
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const RT &x3, const RT &y3, const RT &w3,
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const RT &x4, const RT &y4, const RT &w4)
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{
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// this test returns if the fourth weighted point is on the
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// unbounded side of the circle, ccw oriented and which is on the
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// unbounded side, corresponding to the first three weighted points
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// the result ON_BOUNDARY merans that the fourth circle touches the
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// common tangent circle of the first three;
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// the result ON_BOUNDED_SIDE means that the fourth circle
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// intersects the bounded side of the tritangent circle
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// the result ON_UNBOUNDED_SIDE means that the fourth circle does
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// not intersect the bounded side of the tritangent circle
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if ( CGAL_NTS compare(w2, w1) != LARGER &&
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CGAL_NTS compare(w2, w3) != LARGER &&
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CGAL_NTS compare(w2, w4) != LARGER) {
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// we have to perform the test {2, 1, 4, 3}
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return Bounded_side(awdg_sdltcC2(x2, y2, w2,
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x1, y1, w1,
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x4, y4, w4,
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x3, y3, w3));
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} else if ( CGAL_NTS compare(w3, w1) != LARGER &&
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CGAL_NTS compare(w3, w2) != LARGER &&
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CGAL_NTS compare(w3, w4) != LARGER) {
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// we have to perform the test {3, 4, 2, 1}
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// and reply negatively
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return Bounded_side(opposite(awdg_sdltcC2(x3, y3, w3,
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x4, y4, w4,
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x2, y2, w2,
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x1, y1, w1)));
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} else if ( CGAL_NTS compare(w4, w1) != LARGER &&
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CGAL_NTS compare(w4, w2) != LARGER &&
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CGAL_NTS compare(w4, w3) != LARGER) {
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// we have to perform the test {4, 3, 1, 2}
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// and reply negatively
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return Bounded_side(opposite(awdg_sdltcC2(x4, y4, w4,
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x3, y3, w3,
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x1, y1, w1,
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x2, y2, w2)));
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}
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return Bounded_side(awdg_sdltcC2(x1, y1, w1,
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x2, y2, w2,
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x3, y3, w3,
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x4, y4, w4));
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}
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template < class RT >
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Bounded_side
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awdg_testC2(const RT &x1, const RT &y1, const RT &w1,
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const RT &x2, const RT &y2, const RT &w2,
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const RT &x3, const RT &y3, const RT &w3)
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{
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// this test returns the left tritangent circle, ccw oriented
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// contains the weighted points on its unbounded side
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// the result ON_BOUNDARY means that the three circles have a common
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// tangent line; the result ON_BOUNDED_SIDE means that
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// the common tangent circle contains the three original ones and
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// the result ON_UNBOUNDED_SIDE means that the three original
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// circles are on the unbounded side of the cotangent circle.
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|
||||
if ( CGAL_NTS compare(w2, w1) != LARGER &&
|
||||
CGAL_NTS compare(w2, w3) != LARGER) {
|
||||
// we have to perform the test {2, 3, 1}
|
||||
return Bounded_side(awdg_sltcC2(x2, y2, w2,
|
||||
x3, y3, w3,
|
||||
x1, y1, w1));
|
||||
} else if ( CGAL_NTS compare(w3, w1) != LARGER &&
|
||||
CGAL_NTS compare(w3, w2) != LARGER ) {
|
||||
// we have to perform the test {3, 1, 2}
|
||||
// and reply negatively
|
||||
return Bounded_side(awdg_sltcC2(x3, y3, w3,
|
||||
x1, y1, w1,
|
||||
x2, y2, w2));
|
||||
}
|
||||
|
||||
return Bounded_side(awdg_sltcC2(x1, y1, w1,
|
||||
x2, y2, w2,
|
||||
x3, y3, w3));
|
||||
}
|
||||
|
||||
|
||||
CGAL_END_NAMESPACE
|
||||
|
||||
#endif // CGAL_ADDITIVELY_WEIGHTED_DELAUNAY_GRAPH_FTC2_H
|
||||
Loading…
Reference in New Issue