mirror of https://github.com/CGAL/cgal
remove color from doc and add eps for latex version
This commit is contained in:
Sébastien Loriot
parent
b843eefc3e
commit
30d99aaced
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@ -1335,6 +1335,7 @@ Circular_kernel_3/demo/Circular_kernel_3/images/d_solid_b.gif -text svneol=unset
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Circular_kernel_3/demo/Circular_kernel_3/images/d_wire_b.gif -text svneol=unset#image/gif
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Circular_kernel_3/doc_tex/Circular_kernel_3/def_circles_extreme_pt.eps -text
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Circular_kernel_3/doc_tex/Circular_kernel_3/def_circles_extreme_pt.pdf -text
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Circular_kernel_3/doc_tex/Circular_kernel_3/def_meridian.eps -text
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Circular_kernel_3/doc_tex/Circular_kernel_3/def_meridian.pdf -text
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Circular_kernel_3/doc_tex/Circular_kernel_3/segment_sphere_intersection.png -text
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Circular_kernel_3/doc_tex/Circular_kernel_3/segment_sphere_intersection_detail.png -text
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@ -40,7 +40,6 @@ fundamental functionalities like intersection, comparisons, inclusion,
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etc. More might be provided in the future, as long as only algebraic
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numbers of degree two are used.
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{\color{cyan} %TAG SKOS
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\paragraph{Functionalities relative to a sphere}~
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%\label{section-def-on-sphere}
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@ -70,9 +69,7 @@ $(\theta,z)$.
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% the comparison of $\phi$-coordinates is totally equivalent to the
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% comparison of $z$-coordinates, and that $z$-coordinates are already
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% used for the general objects in 3D.
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}%TAG SKOS
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{\color{magenta} %TAG SKOS
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\textbf{Definition of a meridian.}
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Given a sphere and its associated cylindrical coordinate system, a meridian of that
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sphere is a circular arc consisting of the points having the same theta-coordinate
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@ -84,7 +81,6 @@ direction of $M$ and the two poles. The sense of $M$ disambiguates the choice am
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pair of meridians thus defined.
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On Fig.~\ref{fig-def-meridian}, the normal vectors $n_0$ and $n_1$ define
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two meridians of $S$: the circular arcs $A_0$ and $A_1$ respectively.
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}%TAG SKOS
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\begin{ccTexOnly}
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\begin{figure}[ht!]
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@ -99,7 +95,6 @@ The $\theta$-coordinates of meridians $A_0$ and $A_1$ are $\theta_0$ and $\theta
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\end{figure}
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\end{ccTexOnly}
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{\color{cyan} %TAG SKOS
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\textbf{Types of circles on a sphere.}
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Given a sphere, a circle on that sphere is termed
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\textit{polar} if it goes through only one pole, \textit{bipolar} if
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@ -166,7 +161,6 @@ circular arc on a threaded circle is always $\theta$-monotone, and an
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arc on a polar or normal circle is $\theta$-monotone if it does not
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contain a $\theta$-extremal point, unless it is an endpoint. No such
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arc is defined on a bipolar circle.
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}%TAG SKOS
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\section{Software Design}
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@ -213,14 +207,12 @@ The second example illustrates the use of a functor.
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\ccIncludeExampleCode{Circular_kernel_3/functor_has_on_3.cpp}
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{\color{cyan} %TAG SKOS
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The third example illustrates the use of a functor on objects on the
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same sphere. The intersection points of two circles on
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the same sphere are computed and their cylindrical coordinates are
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then compared.
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\ccIncludeExampleCode{Circular_kernel_3/functor_compare_theta_3.cpp}
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} %TAG SKOS
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\section{Design and Implementation History}
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@ -231,13 +223,11 @@ choices of design.
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Julien Hazebrouck and Damien Leroy participated in a first
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prototype.
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{\color{cyan} %TAG SKOS
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The first version of the package was co-authored by Pedro Machado
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Manh\~{a}es de Castro and Monique Teillaud, and integrated in CGAL
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3.4. Fr\'ed\'eric Cazals and S\'ebastien Loriot extended the
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package by providing functionalities restricted on a given sphere
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\cite{cclt-dc3sk-08}.
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}%TAG SKOS
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Sylvain Pion is acknowledged for helpful discussions.
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||||
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|
||||
397.995 795.414 m
|
||||
397.995 688.677 l
|
||||
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|
||||
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|
||||
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|
||||
0.4 w
|
||||
397.995 688.677 m
|
||||
397.995 446.036 l
|
||||
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|
||||
Q
|
||||
q 0.4 w
|
||||
170.999 292.894 m
|
||||
302.961 381.919 l
|
||||
S
|
||||
Q
|
||||
q [4] 0 d
|
||||
0.4 w
|
||||
302.961 381.919 m
|
||||
397.996 446.032 l
|
||||
S
|
||||
Q
|
||||
q 1 w
|
||||
304.542 379.541 m
|
||||
304.542 380.922 303.422 382.041 302.042 382.041 c
|
||||
300.661 382.041 299.542 380.922 299.542 379.541 c
|
||||
299.542 378.16 300.661 377.041 302.042 377.041 c
|
||||
303.422 377.041 304.542 378.16 304.542 379.541 c
|
||||
h q f* Q S
|
||||
Q
|
||||
q 1 w
|
||||
292.075 722.378 m
|
||||
292.075 723.759 290.956 724.878 289.575 724.878 c
|
||||
288.194 724.878 287.075 723.759 287.075 722.378 c
|
||||
287.075 720.998 288.194 719.878 289.575 719.878 c
|
||||
290.956 719.878 292.075 720.998 292.075 722.378 c
|
||||
h q f* Q S
|
||||
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|
||||
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|
||||
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|
||||
|
||||
1 0 0 1 0 -782.005 cm
|
||||
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|
||||
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|
||||
ET
|
||||
Q
|
||||
q 1 0 0 1 439.443 718.082 cm 1 0 0 1 0 0 cm 0 g
|
||||
0 G
|
||||
|
||||
1 0 0 1 0 -782.005 cm
|
||||
BT
|
||||
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|
||||
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|
||||
Q
|
||||
q 1 0 0 1 452.786 463.493 cm 1 0 0 1 0 0 cm 0 g
|
||||
0 G
|
||||
|
||||
1 0 0 1 0 -775.062 cm
|
||||
BT
|
||||
/F17 24.7871 Tf 0 775.062 Td [(S)]TJ
|
||||
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|
||||
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|
||||
q 1 0 0 1 143.374 296.509 cm 1 0 0 1 0 0 cm 0 g
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|
||||
|
||||
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|
||||
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|
||||
/F17 24.7871 Tf 0 775.062 Td [(P)]TJ
|
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|
||||
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|
||||
q 1 0 0 1 207.405 493.73 cm 1 0 0 1 0 0 cm 0 g
|
||||
0 G
|
||||
|
||||
1 0 0 1 0 -770.281 cm
|
||||
BT
|
||||
/F17 24.7871 Tf 0 775.063 Td [(A)]TJ/F15 20.6625 Tf 18.194 -4.782 Td [(0)]TJ
|
||||
ET
|
||||
Q
|
||||
q 1 0 0 1 354.741 632.19 cm 1 0 0 1 0 0 cm 0 g
|
||||
0 G
|
||||
|
||||
1 0 0 1 0 -770.281 cm
|
||||
BT
|
||||
/F17 24.7871 Tf 0 775.063 Td [(A)]TJ/F15 20.6625 Tf 18.194 -4.782 Td [(1)]TJ
|
||||
ET
|
||||
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|
||||
q 0.4 w
|
||||
292.792 609.512 m
|
||||
292.792 553.285 l
|
||||
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|
||||
q 292.792 609.512 m
|
||||
289.459 599.512 l
|
||||
296.125 599.512 l
|
||||
h q f* Q S
|
||||
Q
|
||||
Q
|
||||
q 1 0 0 1 223.17 546.152 cm 1 0 0 1 0 0 cm 0 g
|
||||
0 G
|
||||
|
||||
1 0 0 1 0 -784.588 cm
|
||||
BT
|
||||
/F17 17.2154 Tf 0 784.588 Td [(x)]TJ
|
||||
ET
|
||||
Q
|
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q 1 0 0 1 333.639 505.775 cm 1 0 0 1 0 0 cm 0 g
|
||||
0 G
|
||||
|
||||
1 0 0 1 0 -781.24 cm
|
||||
BT
|
||||
/F17 17.2154 Tf 0 784.587 Td [(y)]TJ
|
||||
ET
|
||||
Q
|
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q 1 0 0 1 287.703 615.133 cm 1 0 0 1 0 0 cm 0 g
|
||||
0 G
|
||||
|
||||
1 0 0 1 0 -784.588 cm
|
||||
BT
|
||||
/F17 17.2154 Tf 0 784.588 Td [(z)]TJ
|
||||
ET
|
||||
Q
|
||||
q 1 w
|
||||
295.292 553.17 m
|
||||
295.292 554.551 294.173 555.67 292.792 555.67 c
|
||||
291.411 555.67 290.292 554.551 290.292 553.17 c
|
||||
290.292 551.789 291.411 550.67 292.792 550.67 c
|
||||
294.173 550.67 295.292 551.789 295.292 553.17 c
|
||||
h q f* Q S
|
||||
Q
|
||||
q 1 0 0 1 283.558 555.187 cm 1 0 0 1 0 0 cm 0 g
|
||||
0 G
|
||||
|
||||
1 0 0 1 0 -784.588 cm
|
||||
BT
|
||||
/F17 17.2154 Tf 0 784.588 Td [(c)]TJ
|
||||
ET
|
||||
Q
|
||||
q 0.4 w
|
||||
292.793 553.172 m
|
||||
330.802 517.98 l
|
||||
S
|
||||
q 330.802 517.98 m
|
||||
325.729 527.22 l
|
||||
321.199 522.328 l
|
||||
h q f* Q S
|
||||
Q
|
||||
Q
|
||||
q 0.4 w
|
||||
292.791 553.168 m
|
||||
237.638 550.475 l
|
||||
S
|
||||
q 237.638 550.475 m
|
||||
247.789 547.633 l
|
||||
247.464 554.292 l
|
||||
h q f* Q S
|
||||
Q
|
||||
Q
|
||||
q [1 3] 0 d
|
||||
0.4 w
|
||||
170.997 470.585 m
|
||||
397.994 623.725 l
|
||||
S
|
||||
Q
|
||||
q 0.4 w
|
||||
302.697 559.232 m
|
||||
317.263 557.975 324.637 554.241 319.167 550.893 c
|
||||
313.697 547.545 297.455 545.85 282.888 547.107 c
|
||||
273.492 547.918 266.682 549.817 265.012 552.092 c
|
||||
S
|
||||
q 302.697 559.232 m
|
||||
309.47 556.305 l
|
||||
309.871 560.955 l
|
||||
h q f* Q S
|
||||
Q
|
||||
Q
|
||||
q 1 0 0 1 252.44 532.604 cm 1 0 0 1 0 0 cm 0 g
|
||||
0 G
|
||||
|
||||
1 0 0 1 0 -777.463 cm
|
||||
BT
|
||||
/F17 17.2154 Tf 0 780.045 Td [(\022)]TJ/F16 11.9552 Tf 7.855 -2.582 Td [(0)]TJ
|
||||
ET
|
||||
Q
|
||||
q 1 0 0 1 321.375 553.994 cm 1 0 0 1 0 0 cm 0 g
|
||||
0 G
|
||||
|
||||
1 0 0 1 0 -777.463 cm
|
||||
BT
|
||||
/F17 17.2154 Tf 0 780.045 Td [(\022)]TJ/F16 11.9552 Tf 7.855 -2.582 Td [(1)]TJ
|
||||
ET
|
||||
Q
|
||||
q 0.4 w
|
||||
279.331 544.351 m
|
||||
269.624 545.876 262.14 548.279 259.301 550.781 c
|
||||
S
|
||||
q 279.331 544.351 m
|
||||
272.779 547.743 l
|
||||
272.054 543.133 l
|
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h q f* Q S
|
||||
Q
|
||||
Q
|
||||
q 0.4 w
|
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117.544 367.958 m
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170.998 404.019 l
|
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|
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q 117.544 367.958 m
|
||||
127.698 370.787 l
|
||||
123.97 376.314 l
|
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h q f* Q S
|
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Q
|
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Q
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q 0.4 w
|
||||
397.996 722.854 m
|
||||
451.449 758.915 l
|
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|
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q 451.449 758.915 m
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||||
441.295 756.086 l
|
||||
445.023 750.559 l
|
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|
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showpage
|
||||
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end
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%%EOF
|
||||
|
|
@ -130,7 +130,6 @@ and $z$-coordinates.}
|
|||
|
||||
\end{ccRefFunctionObjectConcept}
|
||||
|
||||
{\color{cyan} %TAG SKOS
|
||||
\begin{ccRefFunctionObjectConcept}{SphericalKernel::CompareTheta_3}
|
||||
|
||||
\ccCreationVariable{fo}
|
||||
|
|
@ -143,13 +142,11 @@ An object \ccVar\ of this type must provide:
|
|||
\ccMemberFunction{Comparison_result operator()
|
||||
(const SphericalKernel::Circular_arc_point_3 &p,
|
||||
const SphericalKernel::Circular_arc_point_3 &q );}
|
||||
{Compares the $\theta$-coordinates of $p$ and $q$ in the cylindrical coordinate system relative to {\color{magenta} the context sphere used by the function \ccc{SphericalKernel::compare_theta_3_object}.}%TAG SKOS
|
||||
\ccPrecond{\ccc{p} and \ccc{q} lie on {\color{magenta} the context sphere used by the function \ccc{SphericalKernel::compare_theta_3_object}}, but do not coincide with its poles.}
|
||||
{Compares the $\theta$-coordinates of $p$ and $q$ in the cylindrical coordinate system relative to the context sphere used by the function \ccc{SphericalKernel::compare_theta_3_object}.
|
||||
\ccPrecond{\ccc{p} and \ccc{q} lie on the context sphere used by the function \ccc{SphericalKernel::compare_theta_3_object}, but do not coincide with its poles.}
|
||||
}
|
||||
|
||||
|
||||
{\color{magenta} %TAG SKOS
|
||||
|
||||
\ccMemberFunction{Comparison_result operator()
|
||||
(const SphericalKernel::Circular_arc_point_3 &p,
|
||||
const SphericalKernel::Vector_3 &m );}
|
||||
|
|
@ -167,7 +164,6 @@ An object \ccVar\ of this type must provide:
|
|||
in the cylindrical coordinate system relative to the context sphere used by the function \ccc{SphericalKernel::compare_theta_3_object}.
|
||||
$m1 \neq (0,0,0)$, $m2 \neq (0,0,0)$ and the $z$-coordinate of $m1$ and $m2$ is $0$.}
|
||||
|
||||
} %TAG SKOS
|
||||
|
||||
|
||||
\ccSeeAlso
|
||||
|
|
@ -197,8 +193,8 @@ An object \ccVar\ of this type must provide:
|
|||
(const SphericalKernel::Circular_arc_point_3 &p,
|
||||
const SphericalKernel::Circular_arc_point_3 &q );}
|
||||
{Compares $p$ and $q$ according to the lexicographic ordering on $\theta$- and $z$-coordinates
|
||||
in the cylindrical coordinate system relative to {\color{magenta} the context sphere used by the function \ccc{SphericalKernel::compare_theta_z_3_object}.}%TAG SKOS
|
||||
\ccPrecond{\ccc{p} and \ccc{q} lie on {\color{magenta} the context sphere used by the function \ccc{SphericalKernel::compare_theta_z_3_object}}, but do not coincide with its poles.}
|
||||
in the cylindrical coordinate system relative to the context sphere used by the function \ccc{SphericalKernel::compare_theta_z_3_object}.
|
||||
\ccPrecond{\ccc{p} and \ccc{q} lie on the context sphere used by the function \ccc{SphericalKernel::compare_theta_z_3_object}, but do not coincide with its poles.}
|
||||
}
|
||||
|
||||
\ccSeeAlso
|
||||
|
|
@ -224,7 +220,6 @@ An object \ccVar\ of this type must provide:
|
|||
% {Constructs a functor \ccVar\ to compare the position of objects lying on \ccc{sphere} along a given meridian.}
|
||||
|
||||
|
||||
{\color{magenta} %TAG SKOS
|
||||
\ccMemberFunction{Comparison_result operator()
|
||||
( const SphericalKernel::Circular_arc_3& a0,
|
||||
const SphericalKernel::Circular_arc_3& a1,
|
||||
|
|
@ -232,18 +227,18 @@ An object \ccVar\ of this type must provide:
|
|||
{
|
||||
compares the $z$-coordinates of the two intersections points of $a0$ and $a1$ with the meridian defined by $m$ (see section \ref{section-SK-objects}).
|
||||
\ccPrecond{
|
||||
\ccc{a0} and \ccc{a1} lie on {\color{magenta} the context sphere used by the function \ccc{SphericalKernel::compare_z_at_theta_3_object}.} %TAG SKOS
|
||||
\ccc{a0} and \ccc{a1} lie on the context sphere used by the function \ccc{SphericalKernel::compare_z_at_theta_3_object}.
|
||||
$m \neq (0,0,0)$ and the $z$-coordinate of $m$ is $0$.
|
||||
Arcs $a0$ and $a1$ are $\theta$-monotone and both intersected by the meridian defined by $m$ (see section \ref{section-SK-objects}).}}
|
||||
} %TAG SKOS
|
||||
|
||||
|
||||
|
||||
\ccMemberFunction{Comparison_result operator()
|
||||
( const SphericalKernel::Circular_arc_point_3& p,
|
||||
const SphericalKernel::Circular_arc_3& a);}
|
||||
{given a meridian anchored at the poles of {\color{magenta} the context sphere used by the function \ccc{SphericalKernel::compare_z_at_theta_3_object}}, and passing through point $p$,
|
||||
{given a meridian anchored at the poles of the context sphere used by the function \ccc{SphericalKernel::compare_z_at_theta_3_object}, and passing through point $p$,
|
||||
compares the $z$-coordinate of point $p$ and that of the intersection of the meridian with $a$.
|
||||
\ccPrecond{\ccc{a} and \ccc{p} lie on {\color{magenta} the context sphere used by the function \ccc{SphericalKernel::compare_z_at_theta_3_object}},
|
||||
\ccPrecond{\ccc{a} and \ccc{p} lie on the context sphere used by the function \ccc{SphericalKernel::compare_z_at_theta_3_object},
|
||||
arc $a$ is $\theta$-monotone and the meridian passing through $p$ intersects arc $a$.}}
|
||||
|
||||
\ccSeeAlso
|
||||
|
|
@ -267,10 +262,10 @@ An object \ccVar\ of this type must provide:
|
|||
const SphericalKernel::Circular_arc_3& a1,
|
||||
const SphericalKernel::Circular_arc_point_3 &p);}
|
||||
{Compares the $z$-coordinates of the intersection points of both arcs
|
||||
with a meridian anchored at the poles of {\color{magenta} the context sphere used by the function \ccc{SphericalKernel::compare_z_to_right_3_object}}, at a $\theta$-coordinate
|
||||
with a meridian anchored at the poles of the context sphere used by the function \ccc{SphericalKernel::compare_z_to_right_3_object}, at a $\theta$-coordinate
|
||||
infinitesimally greater that the $\theta$-coordinate of point $p$.
|
||||
\ccPrecond{
|
||||
\ccc{a0} and \ccc{a1} lie on {\color{magenta} the context sphere used by the function \ccc{SphericalKernel::compare_z_to_right_3_object}},
|
||||
\ccc{a0} and \ccc{a1} lie on the context sphere used by the function \ccc{SphericalKernel::compare_z_to_right_3_object},
|
||||
\ccc{a0} and \ccc{a1} are $\theta$-monotone, $p$ lies on \ccc{a0} and \ccc{a1} and is not a $\theta$-extremal
|
||||
point of the supporting circle of \ccc{a0} or \ccc{a1}.}}
|
||||
|
||||
|
|
@ -281,6 +276,6 @@ point of the supporting circle of \ccc{a0} or \ccc{a1}.}}
|
|||
\ccRefIdfierPage{SphericalKernel::CompareZAtTheta_3}
|
||||
|
||||
\end{ccRefFunctionObjectConcept}
|
||||
} %TAG SKOS
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -20,7 +20,6 @@ A model \ccVar\ of this type must provide:
|
|||
|
||||
\end{ccRefFunctionObjectConcept}
|
||||
|
||||
{\color{cyan} %TAG SKOS
|
||||
\begin{ccRefFunctionObjectConcept}{SphericalKernel::MakeThetaMonotone_3}
|
||||
|
||||
\ccCreationVariable{fo}
|
||||
|
|
@ -37,13 +36,13 @@ A model \ccVar\ of this concept must provide:
|
|||
(const SphericalKernel::Circular_arc_3 &a,OutputIterator res);}
|
||||
{
|
||||
Copies in the output iterator the results of the split of arc $a$ at the $\theta$-extremal
|
||||
point(s) of its supporting circle relatively to {\color{magenta} the context sphere used by the function \ccc{SphericalKernel::make_theta_monotone_3_object}} % TAG SKOS.
|
||||
point(s) of its supporting circle relatively to the context sphere used by the function \ccc{SphericalKernel::make_theta_monotone_3_object}
|
||||
(Refer to section~\ref{section-SK-objects} for the definition of these points.)
|
||||
The output iterator may contain no arc (if the supporting circle is a bipolar circle),
|
||||
one arc (if $a$ is already $\theta$-monotone), two arcs (if only one $\theta$-extremal point is on $a$), or
|
||||
three arcs (if two $\theta$-extremal points are on $a$).
|
||||
\ccPrecond{\ccc{a} lies on {\color{magenta} the context sphere used by the function \ccc{SphericalKernel::make_theta_monotone_3_object}},
|
||||
and the supporting circle of \ccc{a} is not bipolar. } % TAG SKOS
|
||||
\ccPrecond{\ccc{a} lies on the context sphere used by the function \ccc{SphericalKernel::make_theta_monotone_3_object},
|
||||
and the supporting circle of \ccc{a} is not bipolar. }
|
||||
}
|
||||
|
||||
|
||||
|
|
@ -52,7 +51,7 @@ and the supporting circle of \ccc{a} is not bipolar. } % TAG SKOS
|
|||
OutputIterator operator()
|
||||
(const SphericalKernel::Circle_3 &c,OutputIterator res);}
|
||||
{Copies in the output iterator the results of the split of circle $c$ at its $\theta$-extremal
|
||||
point(s) relatively to {\color{magenta} the context sphere used by the function \ccc{SphericalKernel::make_theta_monotone_3_object}.} % TAG SKOS
|
||||
point(s) relatively to the context sphere used by the function \ccc{SphericalKernel::make_theta_monotone_3_object}.
|
||||
(Refer to section~\ref{section-SK-objects} for the definition of these points.)
|
||||
The output iterator may contain no arc (if the circle is bipolar),
|
||||
one arc (if the circle is polar or threaded), or two arcs (if the circle is normal).
|
||||
|
|
@ -69,8 +68,8 @@ $(a>0) || (a==0) \&\& (b>0) || (a==0)\&\&(b==0)\&\&(c>0)$.
|
|||
For a threaded circle, the arc returned the one built using the full circle.
|
||||
|
||||
For a polar circle, the arc returned is the full circle, the source and target correspond to the pole the circle goes through.
|
||||
\ccPrecond{\ccc{c} lies on {\color{magenta} the context sphere used by the function \ccc{SphericalKernel::make_theta_monotone_3_object}},
|
||||
and \ccc{c} is not bipolar.} % TAG SKOS
|
||||
\ccPrecond{\ccc{c} lies on the context sphere used by the function \ccc{SphericalKernel::make_theta_monotone_3_object},
|
||||
and \ccc{c} is not bipolar.}
|
||||
}
|
||||
|
||||
\ccSeeAlso
|
||||
|
|
@ -78,7 +77,7 @@ and \ccc{c} is not bipolar.} % TAG SKOS
|
|||
\ccRefIdfierPage{SphericalKernel::IsThetaMonotone_3}
|
||||
|
||||
\end{ccRefFunctionObjectConcept}
|
||||
}%TAG SKOS
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -179,7 +179,6 @@ An object \ccVar\ of this type must provide:
|
|||
\end{ccRefFunctionObjectConcept}
|
||||
|
||||
|
||||
{\color{cyan}%TAG SKOS
|
||||
\begin{ccRefFunctionObjectConcept}{SphericalKernel::IsThetaMonotone_3}
|
||||
|
||||
\ccCreationVariable{fo}
|
||||
|
|
@ -192,11 +191,11 @@ An object \ccVar\ of this type must provide:
|
|||
\ccMemberFunction{bool operator()
|
||||
(const SphericalKernel::Circular_arc_3 &a);}
|
||||
{Tests whether the arc $a$ is $\theta$-monotone, i.e. the intersection of
|
||||
any meridian anchored at the poles of {\color{magenta} the context sphere used by the function \ccc{SphericalKernel::is_theta_monotone_3_object}} % TAG SKOS
|
||||
any meridian anchored at the poles of the context sphere used by the function \ccc{SphericalKernel::is_theta_monotone_3_object}
|
||||
and the arc $a$ is reduced to at most one point in general, and two points if a pole of that sphere is
|
||||
an endpoint of \ccc{a}. Note that a bipolar circle has no such arcs.
|
||||
\ccPrecond{\ccc{a} lies on {\color{magenta} the context sphere used by the function \ccc{SphericalKernel::is_theta_monotone_3_object}},
|
||||
and the supporting circle of \ccc{a} is not bipolar.} % TAG SKOS
|
||||
\ccPrecond{\ccc{a} lies on the context sphere used by the function \ccc{SphericalKernel::is_theta_monotone_3_object},
|
||||
and the supporting circle of \ccc{a} is not bipolar.}
|
||||
}
|
||||
|
||||
|
||||
|
|
@ -206,4 +205,3 @@ and the supporting circle of \ccc{a} is not bipolar.} % TAG SKOS
|
|||
|
||||
|
||||
\end{ccRefFunctionObjectConcept}
|
||||
}%TAG SKOS
|
||||
|
|
@ -65,8 +65,6 @@ constructions and other functionalities.
|
|||
\ccGlue
|
||||
\ccNestedType{Compare_xyz_3}{Model of \ccc{SphericalKernel::CompareXYZ_3}.}
|
||||
\ccGlue
|
||||
{%TAG SKOS
|
||||
\color{cyan}
|
||||
\ccNestedType{Compare_theta_3}{Model of \ccc{SphericalKernel::CompareTheta_3}.}
|
||||
\ccGlue
|
||||
\ccNestedType{Compare_theta_z_3}{Model of \ccc{SphericalKernel::CompareThetaZ_3}.}
|
||||
|
|
@ -74,7 +72,7 @@ constructions and other functionalities.
|
|||
\ccNestedType{Compare_z_at_theta_3}{Model of \ccc{SphericalKernel::CompareZAtTheta_3}.}
|
||||
\ccGlue
|
||||
\ccNestedType{Compare_z_to_right_3}{Model of \ccc{SphericalKernel::CompareZToRight_3}.}
|
||||
}%TAG SKOS
|
||||
|
||||
|
||||
\ccNestedType{Equal_3}{Model of \ccc{SphericalKernel::Equal_3}.}
|
||||
|
||||
|
|
@ -90,10 +88,7 @@ constructions and other functionalities.
|
|||
\ccGlue
|
||||
\ccNestedType{Has_on_unbounded_side_3}{Model of \ccc{SphericalKernel::HasOnUnboundedSide_3}.}
|
||||
|
||||
{%TAG SKOS
|
||||
\color{cyan}
|
||||
\ccNestedType{Is_theta_monotone_3}{Model of \ccc{SphericalKernel::IsThetaMonotone_3}.}
|
||||
}%TAG SKOS
|
||||
|
||||
\ccHeading{Constructions}
|
||||
|
||||
|
|
@ -125,10 +120,7 @@ constructions and other functionalities.
|
|||
|
||||
\ccNestedType{Split_3}{Model of \ccc{SphericalKernel::Split_3}.}
|
||||
|
||||
{%TAG SKOS
|
||||
\color{cyan}
|
||||
\ccNestedType{Make_theta_monotone_3}{Model of \ccc{SphericalKernel::MakeThetaMonotone_3}.}
|
||||
}%TAG SKOS
|
||||
|
||||
\ccHeading{Computations}
|
||||
|
||||
|
|
@ -159,8 +151,6 @@ must exist:
|
|||
\ccCreationVariable{sk}
|
||||
\ccMethod{Construct_circular_arc_3 construct_circular_arc_3_object() const;}{}
|
||||
|
||||
{%TAG SKOS
|
||||
\color{magenta}
|
||||
For operations on a given sphere, a \textit{context} sphere must be provided to the following functions:
|
||||
|
||||
\ccMethod{Compare_theta_3 compare_theta_3_object(const Sphere_3& sphere) const;}{}
|
||||
|
|
@ -169,7 +159,6 @@ For operations on a given sphere, a \textit{context} sphere must be provided to
|
|||
\ccMethod{Compare_z_to_right_3 compare_z_to_right_3_object(const Sphere_3& sphere) const;}{}
|
||||
\ccMethod{Make_theta_monotone_3 make_theta_monotone_3_object(const Sphere_3& sphere) const;}{}
|
||||
\ccMethod{Is_theta_monotone_3 is_theta_monotone_3_object(const Sphere_3& sphere) const;}{}
|
||||
}%TAG SKOS
|
||||
|
||||
|
||||
\ccSeeAlso
|
||||
|
|
|
|||
|
|
@ -1,5 +1,3 @@
|
|||
{%TAG SKOS
|
||||
\color{cyan}
|
||||
\begin{ccRefFunction}{is_theta_monotone}
|
||||
|
||||
\ccInclude{CGAL/global_functions_spherical_kernel_3.h}
|
||||
|
|
@ -27,8 +25,6 @@ Note that a bipolar circle has no such arcs.
|
|||
}
|
||||
|
||||
|
||||
{\color{magenta} %TAG SKOS
|
||||
|
||||
\ccFunction{Comparison_result
|
||||
compare_theta(const SphericalKernel::Circular_arc_point_3 &p,
|
||||
const SphericalKernel::Vector_3 &m, const SphericalKernel::Sphere_3& sphere );}
|
||||
|
|
@ -40,8 +36,6 @@ in the cylindrical coordinate system relative to \ccc{sphere} .
|
|||
\ccFunction{Comparison_result
|
||||
compare_theta(const SphericalKernel::Vector_3 &m,const SphericalKernel::Circular_arc_point_3 &p);}{Same as previous, with opposite result.}
|
||||
|
||||
} %TAG SKOS
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
@ -85,7 +79,7 @@ in the cylindrical coordinate system relative to \ccc{sphere}.
|
|||
\ccRefIdfierPage{CGAL::compare_theta} \\
|
||||
|
||||
\end{ccRefFunction}
|
||||
}%TAG SKOS
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
@ -142,8 +136,6 @@ in the cylindrical coordinate system relative to \ccc{sphere}.
|
|||
|
||||
\end{ccRefFunction}
|
||||
|
||||
{%TAG SKOS
|
||||
\color{cyan}
|
||||
\begin{ccRefFunction}{theta_extremal_point}
|
||||
|
||||
\ccInclude{CGAL/global_functions_spherical_kernel_3.h}
|
||||
|
|
@ -158,7 +150,6 @@ relative to \ccc{sphere}, and that has the smallest (resp. largest)
|
|||
}
|
||||
|
||||
\end{ccRefFunction}
|
||||
}%TAG SKOS
|
||||
|
||||
|
||||
|
||||
|
|
@ -233,8 +224,6 @@ relative to \ccc{sphere}, and that has the smallest (resp. largest)
|
|||
\end{ccRefFunction}
|
||||
|
||||
|
||||
{%TAG SKOS
|
||||
\color{cyan}
|
||||
\begin{ccRefFunction}{theta_extremal_points}
|
||||
|
||||
\ccInclude{CGAL/global_functions_spherical_kernel_3.h}
|
||||
|
|
@ -271,9 +260,6 @@ relative to \ccc{sphere}, and that has the smallest (resp. largest)
|
|||
|
||||
\end{ccRefFunction}
|
||||
|
||||
}%TAG SKOS
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -32,13 +32,11 @@
|
|||
\ccRefConceptPage{SphericalKernel::CompareZ_3}\\
|
||||
\ccRefConceptPage{SphericalKernel::CompareXY_3}\\
|
||||
\ccRefConceptPage{SphericalKernel::CompareXYZ_3}\\
|
||||
{%TAG SKOS
|
||||
\color{cyan}
|
||||
\ccRefConceptPage{SphericalKernel::CompareTheta_3}\\
|
||||
\ccRefConceptPage{SphericalKernel::CompareThetaZ_3}\\
|
||||
\ccRefConceptPage{SphericalKernel::CompareZAtTheta_3}\\
|
||||
\ccRefConceptPage{SphericalKernel::CompareZToRight_3}
|
||||
}%TAG SKOS
|
||||
|
||||
|
||||
\ccRefConceptPage{SphericalKernel::Equal_3}
|
||||
|
||||
|
|
@ -48,10 +46,8 @@
|
|||
|
||||
\ccRefConceptPage{SphericalKernel::DoIntersect_3}
|
||||
|
||||
{%TAG SKOS
|
||||
\color{cyan}
|
||||
\ccRefConceptPage{SphericalKernel::IsThetaMonotone_3}
|
||||
}%TAG SKOS
|
||||
|
||||
|
||||
\ccRefConceptPage{SphericalKernel::BoundedSide_3}\\
|
||||
\ccRefConceptPage{SphericalKernel::HasOnBoundedSide_3}\\
|
||||
|
|
@ -61,10 +57,7 @@
|
|||
|
||||
\ccRefConceptPage{SphericalKernel::Split_3}
|
||||
|
||||
{%TAG SKOS
|
||||
\color{cyan}
|
||||
\ccRefConceptPage{SphericalKernel::MakeThetaMonotone_3}
|
||||
}%TAG SKOS
|
||||
|
||||
\ccRefConceptPage{SphericalKernel::ComputeCircularX_3}\\
|
||||
\ccRefConceptPage{SphericalKernel::ComputeCircularY_3}\\
|
||||
|
|
@ -92,11 +85,9 @@
|
|||
\ccRefIdfierPage{CGAL::Line_arc_3<SphericalKernel>}\\
|
||||
\ccRefIdfierPage{CGAL::Circular_arc_3<SphericalKernel>}\\
|
||||
|
||||
{%TAG SKOS
|
||||
\color{cyan}
|
||||
\subsubsection*{Constants and Enumerations}
|
||||
\ccRefIdfierPage{CGAL::Circle_type}
|
||||
}%TAG SKOS
|
||||
|
||||
|
||||
\section{Geometric Global Functions}
|
||||
|
||||
|
|
@ -105,36 +96,21 @@
|
|||
\ccRefIdfierPage{CGAL::compare_z}\\
|
||||
\ccRefIdfierPage{CGAL::compare_xy}\\
|
||||
\ccRefIdfierPage{CGAL::compare_xyz}\\
|
||||
{%TAG SKOS
|
||||
\color{cyan}
|
||||
\ccRefIdfierPage{CGAL::compare_theta}\\
|
||||
\ccRefIdfierPage{CGAL::compare_theta_z}
|
||||
}%TAG SKOS
|
||||
|
||||
{%TAG SKOS
|
||||
\color{cyan}
|
||||
\ccRefIdfierPage{CGAL::is_theta_monotone}
|
||||
}%TAG SKOS
|
||||
|
||||
{%TAG SKOS
|
||||
\color{cyan}
|
||||
\ccRefIdfierPage{CGAL::classify}
|
||||
}%TAG SKOS
|
||||
|
||||
\ccRefIdfierPage{CGAL::x_extremal_point}\\
|
||||
\ccRefIdfierPage{CGAL::y_extremal_point}\\
|
||||
\ccRefIdfierPage{CGAL::z_extremal_point}\\
|
||||
{%TAG SKOS
|
||||
\color{cyan}
|
||||
\ccRefIdfierPage{CGAL::theta_extremal_point}\\
|
||||
}%TAG SKOS
|
||||
\ccRefIdfierPage{CGAL::x_extremal_points}\\
|
||||
\ccRefIdfierPage{CGAL::y_extremal_points}\\
|
||||
\ccRefIdfierPage{CGAL::z_extremal_points}\\
|
||||
{%TAG SKOS
|
||||
\color{cyan}
|
||||
\ccRefIdfierPage{CGAL::theta_extremal_points}
|
||||
}%TAG SKOS
|
||||
|
||||
\ccRefIdfierPage[Kernel::do_intersect]{CGAL::do_intersect}\\
|
||||
\ccRefIdfierPage[Kernel::intersection]{CGAL::intersection}
|
||||
|
|
|
|||
|
|
@ -18,9 +18,7 @@
|
|||
\input{Circular_kernel_3_ref/CircularArc_3}
|
||||
\input{Circular_kernel_3_ref/Circular_arc_3}
|
||||
|
||||
{\color{cyan} %TAG SKOS
|
||||
\input{Circular_kernel_3_ref/Circle_on_sphere_type_3}
|
||||
}%TAG SKOS
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% geometric functors
|
||||
|
|
|
|||
Loading…
Reference in New Issue