CGAL库高效几何问题解决方案详解

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CGAL（Computational Geometry Algorithms Library）是一个致力于为工业界和学术界用户提供高效计算几何领域解决方案的C++软件库。它的目标是将该领域内开发的关键算法标准化，并以易于使用的接口提供给开发者。CGAL特别关注于三维几何问题，如点、线、面的处理，以及更复杂的几何结构如多边形和多面体。在给出的部分代码片段中，可以看到一个警告提示，可能是在使用某种特定的数据结构或函数时需要注意的问题。这段代码涉及到CGAL的高级数据结构，如`CGAL__Hlv`（可能是一个混合类型容器，用于存储不同类型的顶点、半边和多面体面基）。这里的`lasthidesrb_tree`函数似乎在对一个复合类型的`CGAL_Vertex_max_base<CGAL_Point_3<CGAL_Cartesian<double>>>`、`CGAL_Halfedge_max_base`和`CGAL_Polyhedron_facet_base_3<CGAL_Cartesian<double>>`进行操作，它接受两个这样的复合类型指针作为参数，并返回一个可能包含这些复合类型元素的配对。 `select1st`函数则用来从这个配对中选择第一个元素，可能是为了获取特定的`CGAL__Hlv`对象。函数签名表明它接受一个指向常量配对的指针，然后根据某种比较规则`less<constCGAL__Hlv<...>>`来决定选择哪个元素。这可能涉及到对这些复合类型对象的有序性或者优先级进行操作。这部分代码展示了如何在CGAL库中处理和操作复杂几何数据结构，特别是对于多面体的精细管理，包括其顶点、边和面的组织形式。理解这些细节对于在实际项目中有效利用CGAL库以解决三维几何问题至关重要。开发者需要熟悉CGAL的数据模型、接口和方法，以便正确地构造和操作这些数据结构，同时处理可能出现的警告和错误情况。

• All names in the kernel traits have the dimension as a sufﬁx. This is necessary because in some cases

(e.g., the Orientation 2 object) the absence of the sufﬁx would cause a name conﬂict with an existing type

or class (e.g., the enumeration type Orientation).

• The names of generalized predicates are determined by their results. Furthermore, names are as much

as possible consistent with the current kernel and the STL. So, for example, we have objects like Has

on bounded side 2, Is degenerate 2, and Is horizontal 2. According to the current kernel we also have

Left turn 2. For reasons of consistency with STL, all “less-than”-objects start with Less , e.g., Less xy 2.

Further examples are Less distance to point 2 and Less distance to line 2. However, we have Equal

2, whereas the corresponding STL functor is called equal to. Here, we give our dimension rule higher

priority.

• The names of construction objects (category 2 above) follow the pattern Construct type d, where type d

is the type constructed, e.g., Construct point 2 and Construct line 2. The operator() of these functor

classes is overloaded. This reduces the number of names to remember drastically, while replacing one of

the constructions gets more complicated, but is still possible.

• Functors in category 3 above can be further subdivided into two classes:

– constructive procedures that construct objects whose types are known a priori

– procedures that construct objects whose types are not known a priori

The names of functors in the ﬁrst class also start with Construct whenever a geometric object is con-

structed, otherwise they start with Compute . Here, real numbers are not considered to be 1-dimensional

geometric objects. For example, on the one hand we have Construct perpendicular vector 2, Construct

midpoint 3, Construct circumcenter d, Construct bisector 2, and Construct point on 3, while on the

other hand there are Compute area 2 and Compute squared length 3.

For the second class, the names of the objects describe the (generic) action, e.g. Intersect 2.

• The equality operator (operator==()) is replaced by function objects with names of the form Equal k,

where k is the dimension number (i.e., 2, 3, or d). For replacing arithmetic operators, we might also

provide Add 2, Subtract 2, Multiply 2, and Divide 2. (As mentioned above, the action determines the

name, not the result.) We think that these objects are not really needed. They are likely to be part of

primitive operations that have a corresponding function object in the traits.

In addition, for each functor the kernel traits class has a member function that returns an instance of this functor.

The name of this function should be the (uncapitalized) name of the functor followed by the sufﬁx object.For

example, the function that retuns an instance of the Less xy 2 functor is called less xy 2 object.

File names

• File names should be chosen in the “spirit” of the naming rules given above.

• If a single geometric object, data structure, or algorithm is provided in a single ﬁle, its name (and its

capitalization) should be used for the ﬁle name. For example, the ﬁle Triangulation 2.h contains the data

structure Triangulation 2.

• If a ﬁle does not contain a single class, its name should not begin with a capital letter.

• No two ﬁles should have the same names even when capitalization is ignored. This is to prevent over-

writing of ﬁles on operating systems where ﬁle names are not case sensitive. A package that contains ﬁle

names that are the same as ﬁles already in the release will be rejected by the submission script.

• The names of ﬁles should not contain any characters not allowed by all the platforms the library supports.

In particular, it should not contain the characters ‘:’, ‘*’, or ‘ ’.

2.2 Programming conventions

The ﬁrst list of items are meant as rules, i.e., you should follow them.

• Give typedefs for all template arguments of a class that may be accessed later from outside the class.

The template parameter is a concept and should follow the concept naming scheme outlines in the previous

section. As a general rule, the typedef should identify the template parameter with a type of the same name

that follows the naming convention of types. For example

template < class GeometricTraits_2 >

class Something {

public:

typedef GeometricTraits_2 Geometric_traits_2;

};

For one-word template arguments, the template parameter name should be followed by an underscore.

(Note that using a preceding underscore is not allowed according to the C

standard; all such names are

reserved.)

template < class Arg_ >

class Something {

public:

typedef Arg_ Arg;

};

• Use const when a call by reference argument is not modiﬁed, e.g. int f( const A& a).

• Use const to indicate that a member function does not modify the object to which it is applied, e.g., class

A { int f( void) const; };. This should also be done when it is only conceptually const. This means that the

member function f() is const as seen from the outside, but internally it may modify some data members

that are declared mutable. An example is the caching of results from expensive computations. For more

information about conceptually const functions and mutable data members see [Mey97].

• Prefer C

-style to C-style casts, e.g., use static cast<double>( i) instead of (double)i.

• Protect header ﬁles against multiple inclusion, e.g. the ﬁle This is an example.h should begin/end with

#ifndef CGAL_THIS_IS_AN_EXAMPLE_H

#define CGAL_THIS_IS_AN_EXAMPLE_H

...

#endif // CGAL_THIS_IS_AN_EXAMPLE_H

The following items can be seen as recommendations in contrast to the rules of previous paragraph.

• Use #define sparingly.

• Do not rename the base types of C

using typedef.

• When using an overloaded call, always give the exact match. Use explicit casting if necessary.

• Do not call global functions unqualiﬁed, that is, always specify explicitly the namespace where the func-

tion is deﬁned.

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