CGAL开发手册：提升三维项目开发效率与稳定性

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CGAL（Computational Geometry Algorithms Library）是一个由国际顶级计算机科学家共同开发的开源几何算法库，主要用于处理各种复杂的几何问题，包括线条、表面、多边形和多面体等在三维空间中的计算。这个库广泛应用于三维图形渲染系统、计算机辅助设计（CAD）、计算机视觉以及游戏开发等领域，因为它提供了高度优化的几何操作和数据结构，能够提高开发效率和软件的稳定性。手册中的这段代码示例涉及到CGAL库中一个特定的类和函数，它涉及到了一种名为Hierarchical Linear Vertex (Hlv)的数据结构，这是一种在处理三维多面体时常用的高效组织方式。具体来说，`CGAL_Vertex_max_base<CGAL_Point_3<CGAL_Cartesian<double>>>` 表示一个基于点（Point）的顶点基类，`CGAL_Halfedge_max_base` 和 `CGAL_Polyhedron_facet_base_3<CGAL_Cartesian<double>>` 分别表示半边和多面体面基类，这些都在三维笛卡尔坐标系（Cartesian<double>）下工作。 `lasthidesrb_tree` 函数似乎是实现了一个后序遍历（Last In, First Out，LIFO）的红黑树，用于存储这些几何结构的元素。输入参数包括两个Hlv类型的指针，它们分别代表一个已隐藏的树（hidden srb tree）和一个可选的常量Hlv对象。`select1st` 函数可能用于从这两个Hlv指针中选择第一个，而`less` 函数则提供了一个比较操作，用于定义排序规则。通过这段代码，开发者可以访问和操作复杂的几何对象，如通过Hlv数据结构来高效地搜索、插入和删除多面体的顶点、半边和面。这在处理大规模或动态变化的几何场景时尤为重要，因为它减少了不必要的计算和内存消耗，从而提高了整个程序的性能和响应速度。总结来说，CGAL手册中的这部分内容展示了如何在三维几何处理中利用高级数据结构和算法进行高效的操作，这对于任何需要处理复杂几何形状的软件项目来说都是一份宝贵的资源。理解并掌握这些概念和技术，能够显著提升开发人员的工作效率，并确保软件的质量和稳定性。

• 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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