Geometry Structure and Algorithm.#

Geometry Structure#

struct Radian#

Can easily get the degree of the radian conversion.

Public Functions

explicit Radian(float radian = 0)#

Construct a new Radian object.

Parameters:: radian – Radian.

bool operator==(const Radian &rhs) const#

Check if two Radian are equal.

Parameters:: rhs – Other Radian.
Returns:: true if two Radian are equal.

Radian operator-() const#

Get negative Radian.

Returns:: Radian negative Radian.

float degree() const#

Get the degree of the radian conversion.

Returns:: NO_DISCARD float degree.

Radian &from_degree(float degree)#

Set the radian of the degree conversion.

Parameters:: degree – Degree.
Returns:: Radian& reference to this object.

Public Members

float radian#: Radian data.

struct Vector2f#

浮点型向量

表示从原点(0,0)出发的一个具有大小和方向的浮点型向量.

Public Types

using Elem = float#: Element type.

using Point = Point2f #: 向量对应的同类型浮点型点

Public Functions

Vector2f() = default#: Default constructor,no initialization.

Vector2f(const Elem &x, const Elem &y)#: Constructor to set two values.

explicit Vector2f(const Point &rhs)#: Constructor to set a Point.

Vector2f operator-() const#: 向量的取反

Vector2f operator+(const Vector2f &rhs) const#: 向量的加法

Vector2f operator-(const Vector2f &rhs) const#: 向量的减法

Vector2f operator*(const Elem &rhs) const#: 向量的放大

Vector2f operator/(const Elem &rhs) const#: 向量的缩小

Elem operator*(const Vector2f &rhs) const#: 向量积

Radian azimuth() const#

向量的方位角

Returns:: 向量从x轴正方向向y轴正方向旋转的弧度(±π).

float length() const#: 向量的模

struct Vector2i#

整型向量

表示从原点(0,0)出发的一个具有大小和方向的整型向量.

Public Types

using Elem = int32_t#: Element type.

using Point = Point2i #: 向量对应的同类型整型点

Public Functions

Vector2i() = default#: Default constructor,no initialization.

Vector2i(const Elem &x, const Elem &y)#: Constructor to set two values.

explicit Vector2i(const Point2i &rhs)#: Constructor to set a Point.

Vector2i operator-() const#: 向量的取反

Vector2i operator+(const Vector2i &rhs) const#: 向量的加法

Vector2i operator-(const Vector2i &rhs) const#: 向量的减法

Vector2i operator*(const Elem &rhs) const#: 向量的放大

Vector2i operator/(const Elem &rhs) const#: 向量的缩小

Elem operator*(const Vector2i &rhs) const#: 向量积

Radian azimuth() const#

向量的方位角

Returns:: 向量从x轴正方向向y轴正方向旋转的弧度(±π).

float length() const#: 向量的模

struct Point2f#

浮点型点

Public Types

using Elem = float#: Element type.

using Vector = Vector2f #: 点对应的同类型向量.

using Line = Line2f #: 点对应的同类型直线.

Public Functions

Point2f() = default#: Default constructor,no initialization.

Point2f(const Elem &x, const Elem &y)#: Constructor to set two values.

explicit Point2f(const Vector &rhs)#: Constructor to set a Vector.

bool operator==(const Vector &rhs) const#: 与同类型向量进行数值上的比较.

Point2f operator+(const Vector &rhs) const#: 点的平移

Point2f operator-(const Vector &rhs) const#: 点的平移

Point2f operator*(const Elem &rhs) const#: 点坐标放大

Point2f operator/(const Elem &rhs) const#: 点坐标缩小

Elem operator*(const Point2f &rhs) const#: 点积

struct Point2i#

整型点

Public Types

using Elem = int32_t#: Element type.

using Vector = Vector2i #: 点对应的同类型向量.

using Line = Line2i #: 点对应的同类型直线.

Public Functions

Point2i() = default#: Default constructor,no initialization.

Point2i(const Elem &x, const Elem &y)#: Constructor to set two values.

explicit Point2i(const Vector &rhs)#: Constructor to set a Vector.

bool operator==(const Vector &rhs) const#: 与同类型向量进行数值上的比较.

Point2i operator+(const Vector &rhs) const#: 点的平移

Point2i operator-(const Vector &rhs) const#: 点的平移

Point2i operator*(const Elem &rhs) const#: 点坐标放大

Point2i operator/(const Elem &rhs) const#: 点坐标缩小

Elem operator*(const Point2i &rhs) const#: 点积

struct Segment2f : public std::pair<Point2f, Point2f>#

浮点型线段

Public Types

using Point = Point2f #: 线段对应的同类型点.

using Vector = Vector2f #: 线段对应的同类型方向向量.

using Line = Line2f #: 线段对应的同类型直线.

using Elem = Point2f::Elem #: Element type.

Public Functions

Segment2f(const Point &lhs, const Point &rhs)#: Constructor to set two Points.

Segment2f(const Point &lhs, const Vector &direction, const float &dis)#: Constructor to set Point,direction Vector and distance.

float length() const#: 线段长度

Line in_line() const#: 线段所在直线

Radian azimuth() const#: 线段的方位角

struct Segment2i : public std::pair<Point2i, Point2i>#

整型线段

Public Types

using Point = Point2i #: 线段对应的同类型点.

using Vector = Vector2i #: 线段对应的同类型方向向量.

using Line = Line2i #: 线段对应的同类型直线.

using Elem = Point2i::Elem #: Element type.

Public Functions

Segment2i(const Point &lhs, const Point &rhs)#: Constructor to set two Points.

Segment2i(const Point &lhs, const Vector &direction, const float &dis)#: Constructor to set Point,direction Vector and distance.

float length() const#: 线段长度

Line in_line() const#: 线段所在直线

Radian azimuth() const#: 线段的方位角

struct Line2f#

浮点型直线

Public Types

using Point = Point2f #: 直线对应的同类型点.

using Segment = Segment2f #: 直线对应的同类型线段.

using Vector = Vector2f #: 直线对应的同类型方向向量.

using Elem = Point2f::Elem #: Element type.

Public Functions

Line2f(const Elem &a, const Elem &b, const Elem &c)#: Constructor to set ax+by+c=0.

Line2f(const Point &lhs, const Point &rhs)#: Constructor to set two Points.

Line2f(const Point &lhs, const Vector &rhs)#: Constructor to set Point and direction Vector.

explicit Line2f(const Segment &rhs)#: Constructor to set a Segment.

Point passing_point() const#

直线的经过点.

优先返回y轴交点,其次返回x轴交点.

Returns:: NO_DISCARD Point

Vector direction() const#: 直线的方向向量.

Radian azimuth() const#: 直线的方位角.

struct Line2i#

整型直线

Public Types

using Point = Point2i #: 直线对应的同类型点.

using Segment = Segment2i #: 直线对应的同类型线段.

using Vector = Vector2i #: 直线对应的同类型方向向量.

using Elem = Point2f::Elem #: Element type.

Public Functions

Line2i(const Elem &a, const Elem &b, const Elem &c)#: Constructor to set ax+by+c=0.

Line2i(const Point &lhs, const Point &rhs)#: Constructor to set two Points.

Line2i(const Point &lhs, const Vector &rhs)#: Constructor to set Point and direction Vector.

explicit Line2i(const Segment &rhs)#: Constructor to set a Segment.

Point passing_point() const#

直线的经过点.

优先返回y轴交点,其次返回x轴交点.

Returns:: NO_DISCARD Point

Vector direction() const#: 直线的方向向量.

Radian azimuth() const#: 直线的方位角.

struct Ray2f#

浮点型射线

Public Types

using Point = Point2f #: 射线对应的同类型射线.

using Vector = Vector2f #: 射线对应的同类型方向向量.

using Line = Line2f #: 射线对应的同类直线.

Public Functions

Ray2f(const Point &lhs, const Vector &rhs)#: Constructor to set Point and direction Vector.

Ray2f(const Point &lhs, const Point &rhs)#: Constructor to set two Points.

Radian azimuth() const#: 射线的方位角.

Line in_line() const#: 射线所在直线.

Public Members

Point start#: 射线起始点.

Vector direction#: 射线对应的方向向量.

struct Ray2i#

整型射线

Public Types

using Point = Point2i #: 射线对应的同类型射线.

using Vector = Vector2i #: 射线对应的同类型方向向量.

using Line = Line2i #: 射线对应的同类直线.

Public Functions

Ray2i(const Point &lhs, const Vector &rhs)#: Constructor to set Point and direction Vector.

Ray2i(const Point &lhs, const Point &rhs)#: Constructor to set two Points.

Radian azimuth() const#: 射线的方位角.

Line in_line() const#: 射线所在直线.

Public Members

Point start#: 射线起始点.

Vector direction#: 射线对应的方向向量.

struct LineString2f : public std::vector<Point2f>#

浮点型线

一条线被认为是一些点的集合(std::vector),且按一定顺序连接相邻两点形成折线段.

Note

线可以是自交的,但这对于某些算法会产生错误的影响.可以通过 is_simple() 检测是否自交等问题.

Public Types

using Point = Point2f #: 线对应的同类型点

using Rect = Rect2f #: 线对应的同类型矩形 envelope()

Public Functions

LineString2f() = default#: Default constructor,creating an empty LineString.

LineString2f(const Point &lhs, const Point &rhs)#: Constructor to set two Points.

LineString2f(const std::initializer_list<Point> &rhs)#: Constructor taking std::initializer_list,filling the LineString.

float length() const#: 折线段长度和

struct LineString2i : public std::vector<Point2i>#

整型线

一条线被认为是一些点的集合(std::vector),且按一定顺序形成折线段.

Note

线可以是自交的,但这对于某些算法会产生错误的影响.可以通过 is_simple() 检测是否自交等问题.

Public Types

using Point = Point2i #: 线对应的同类型点

using Rect = Rect2i #: 线对应的同类型矩形 envelope()

Public Functions

LineString2i() = default#: Default constructor,creating an empty LineString.

LineString2i(const Point &lhs, const Point &rhs)#: Constructor to set two Points.

LineString2i(const std::initializer_list<Point> &rhs)#: Constructor taking std::initializer_list,filling the LineString.

float length() const#: 折线段长度和

struct Ring2f : public std::vector<Point2f>#

浮点型环

环是一条不应自交的闭合线,即不带孔的多边形. 应遵循从x轴正方向向y轴正方向描述环上的点,开包(第一点与最后一点不同).

Public Types

using Point = Point2f #: 环对应的同类型点

using LineString = LineString2f #: 环对应的同类型线 convert()

using Rect = Rect2f #: 环对应的同类型矩形 envelope()

using Ring = Ring2f #: 用于统一与polygon的部分算法接口 convex_hull()

Public Functions

Ring2f() = default#: Default constructor,creating an empty Ring.

Ring2f(const std::initializer_list<Point> &rhs)#: Constructor taking std::initializer_list,filling the Ring.

float area() const#: 环面积

float perimeter() const#: 环周长

struct Ring2i : public std::vector<Point2i>#

整型环

环是一条不应自交的闭合线,即不带孔的多边形. 应遵循从x轴正方向向y轴正方向描述环上的点,开包(第一点与最后一点不同).

Public Types

using Point = Point2i #: 环对应的同类型点

using LineString = LineString2i #: 环对应的同类型线 convert()

using Rect = Rect2i #: 环对应的同类型矩形 envelope()

using Ring = Ring2i #: 用于统一与polygon的部分算法接口 convex_hull()

Public Functions

Ring2i() = default#: Default constructor,creating an empty Ring.

Ring2i(const std::initializer_list<Point> &rhs)#: Constructor taking std::initializer_list,filling the Ring.

float area() const#: 环面积

float perimeter() const#: 环周长

struct Size2f#

Specify rect or image size.

Public Types

using Elem = float#: Element type.

Public Functions

Size2f(Elem w, Elem h)#

Construct a new Size 2f object.

Parameters:

w – Width (cols).
h – Height (rows).

Public Members

Elem h = 0.0#: Width (cols) and height (rows).

struct Size2i#

Specify rect or image size.

Public Types

using Elem = uint32_t#: Element type.

Public Functions

Size2i(Elem w, Elem h)#

Construct a new Size2i object.

Parameters:

w – Width (cols).
h – Height (rows).

Public Members

Elem h = 0#: Width and height.

struct Rect2f#

浮点型矩形

有一个角为直角的平行四边形,与坐标轴平行.

Public Types

using Point = Point2f #: 矩形对应的同类型点

using Elem = Size2f::Elem #: Element type.

using LineString = LineString2f #: 矩形边对应类型的线段

using Ring = Ring2f #: 矩形对应的同类型环 convert()

Public Functions

Rect2f() = default#: Default constructor,no initialization.

Rect2f(const Point &min_corner, const Elem &w, const Elem &h)#: 矩形的最小顶点和矩形宽高描述矩形.

Rect2f(const Point &lhs, const Point &rhs)#: 任意对角两点描述矩形.

Point xmin_ymin() const#: x最小,y最小顶点,同 min_corner.

Point xmax_ymin() const#: x最大,y最小顶点.

Point xmax_ymax() const#: x最大,y最大顶点.

Point xmin_ymax() const#: x最小,y最大顶点.

Elem area() const#: 矩形面积

Elem perimeter() const#: 矩形周长

Public Members

Point min_corner#: 矩形的最小顶点.

Size size#: 矩形的宽高.

struct Rect2i#

整型矩形

有一个角为直角的平行四边形,与坐标轴平行.

Public Types

using Point = Point2i #: 矩形对应的同类型点

using Elem = Size2i::Elem #: Element type.

using LineString = LineString2i #: 矩形边对应类型的线段

using Ring = Ring2i #: 矩形对应的同类型环 convert()

Public Functions

Rect2i() = default#: Default constructor,no initialization.

Rect2i(const Point &min_corner, const Elem &w, const Elem &h)#: 矩形的最小顶点和矩形宽高描述矩形.

Rect2i(const Point &lhs, const Point &rhs)#: 任意对角两点描述矩形.

Point xmin_ymin() const#: x最小,y最小顶点,同 min_corner.

Point xmax_ymin() const#: x最大,y最小顶点.

Point xmax_ymax() const#: x最大,y最大顶点.

Point xmin_ymax() const#: x最小,y最大顶点.

Elem area() const#: 矩形面积

Elem perimeter() const#: 矩形周长

Public Members

Point min_corner#: 矩形的最小顶点.

Size size#: 矩形的宽高.

struct Polygon2f#

浮点型多边形

多边形由一个外环和零个或多个内环组成,内环方向与外环相反,形成带孔或不带孔的多边形. 应遵循从x轴正方向向y轴正方向描述外环上的点,开包(第一点与最后一点不同).

Public Types

using Ring = Ring2f #: 外环对应的同类型环

using RingList = std::vector<Ring>#: 内环对应的同类型环集合

using Rect = Rect2f #: 多边形对应的同类型矩形 envelope()

Public Functions

Polygon2f() = default#: Default constructor,creating an empty Polygon.

Polygon2f(const std::initializer_list<Ring> &rhs)#: Constructor taking std::initializer_list,filling the Polygon.

float area() const#: 多边形面积

Warning

如果内环描述不正确,如与外环相同方向,则计算面积时会重复计算内环面积. 可以通过 correct() 来修正几何图形,以得到正确的期望结果. 内环相互相切或与外环相切时仍可以得到正确的多边形面积.

float perimeter() const#: 多边形周长

Warning

如果内环互相相切,或与外环相切,则计算周长时会重复计算相切边长.

Public Members

Ring outer#: 外环,从x轴正方向向y轴正方向描述各点,开包.

RingList inners#: 零个或多个内环,方向与外环相反.

struct Polygon2i#

整型多边形

Public Types

using Ring = Ring2i #: 外环对应的同类型环

using RingList = std::vector<Ring>#: 内环对应的同类型环集合

using Rect = Rect2i #: 多边形对应的同类型矩形 envelope()

Public Functions

Polygon2i() = default#: Default constructor,creating an empty Polygon.

Polygon2i(const std::initializer_list<Ring> &rhs)#: Constructor taking std::initializer_list,filling the Polygon.

float area() const#: 多边形面积

Warning

如果内环描述不正确,如与外环相同方向,则计算面积时会重复计算内环面积. 可以通过 correct() 来修正几何图形,以得到正确的期望结果. 内环相互相切或与外环相切时仍可以得到正确的多边形面积.

float perimeter() const#: 多边形周长

Warning

如果内环互相相切,或与外环相切,则计算周长时会重复计算相切边长.

Public Members

Ring outer#: 外环,从x轴正方向向y轴正方向描述各点,开包.

RingList inners#: 零个或多个内环,方向与外环相反.

struct RotateRect2f#

浮点型旋转矩形

有一个角为直角的平行四边形,不一定与坐标轴平行.

Public Types

using Point = Point2f #: 旋转矩形对应的同类型点

using LineString = LineString2f #: 旋转矩形边对应类型的线段

using Ring = Ring2f #: 旋转矩形对应的同类型环 convert()

using Rect = Rect2f #: 旋转矩形对应的同类型矩形 envelope()

Public Functions

RotateRect2f() = default#: Default constructor,no initialization.

RotateRect2f(const Point &min_corner, const float &w, const float &h, const Radian &radian = Radian())#: y最小点,宽,高和方位角描述旋转矩形.

RotateRect2f(const Point &lhs, const Point &rhs)#: 任意对角两点描述平行矩形.

RotateRect2f(const std::initializer_list<Point> &rhs)#: 任意从x轴正方向向y轴正方向描述旋转矩形.

Point ymin() const#: y最小点,同 min_corner.

Point xmax() const#: x最大点.

Point ymax() const#: y最大点.

Point xmin() const#: x最小点.

float area() const#: 旋转矩形面积

float perimeter() const#: 旋转矩形周长

Public Members

Point min_corner#: y最小点.

Radian radian#: 旋转矩形y最小点以及从x轴正方向向y轴正方向临近点组成边,与x轴正方向组成的弧度.

struct RotateRect2i#

整型旋转矩形

有一个角为直角的平行四边形,不一定与坐标轴平行.

Public Types

using Point = Point2i #: 旋转矩形对应的同类型点

using LineString = LineString2i #: 旋转矩形边对应类型的线段

using Ring = Ring2i #: 旋转矩形对应的同类型环 convert()

using Rect = Rect2i #: 旋转矩形对应的同类型矩形 envelope()

Public Functions

RotateRect2i() = default#: Default constructor,no initialization.

RotateRect2i(const Point &min_corner, const float &w, const float &h, const Radian &radian = Radian())#: y最小点,宽,高和方位角描述旋转矩形.

RotateRect2i(const Point &lhs, const Point &rhs)#: 任意对角两点描述平行矩形.

RotateRect2i(const std::initializer_list<Point> &rhs)#: 任意从x轴正方向向y轴正方向描述旋转矩形.

Point ymin() const#: y最小点,同 min_corner.

Point xmax() const#: x最大点.

Point ymax() const#: y最大点.

Point xmin() const#: x最小点.

float area() const#: 旋转矩形面积

float perimeter() const#: 旋转矩形周长

Public Members

Point min_corner#: y最小点.

Radian radian#: 旋转矩形y最小点以及从x轴正方向向y轴正方向临近点组成边,与x轴正方向组成的弧度.

struct Arc2f#

浮点型弧

Public Types

using Point = Point2f #: 弧对应的同类型点

Public Functions

Arc2f() = default#: Default constructor,no initialization.

Arc2f(const Point &start, const Point &end, const Point &center, const float &radius)#: 从x轴正方向向y轴正方向描述弧起点,终点,对应圆心和对应半径.

Arc2f(const Point &start, const Point &end, const Point &center)#: 从x轴正方向向y轴正方向描述弧起点,终点和对应圆心.

Public Members

Point center#: 弧对应圆的圆心

float radius = 0#: 弧对应圆的半径

struct Arc2i#

整型弧

Public Types

using Point = Point2i #: 弧对应的同类型点

Public Functions

Arc2i() = default#: Default constructor,no initialization.

Arc2i(const Point &start, const Point &end, const Point &center, const float &radius)#: 从x轴正方向向y轴正方向描述弧起点,终点,对应圆心和对应半径.

Arc2i(const Point &start, const Point &end, const Point &center)#: 从x轴正方向向y轴正方向描述弧起点,终点和对应圆心.

Public Members

Point center#: 弧对应圆的圆心

float radius = 0#: 弧对应圆的半径

struct Circle2f#

浮点型圆

Public Types

using Point = Point2f #: 圆对应的同类型点

using Rect = Rect2f #: 圆对应的同类型矩形 envelope()

Public Functions

Circle2f() = default#: Default constructor,no initialization.

Circle2f(const Point &center, const float &radius)#: Constructor to set center and radius.

float area() const#: 圆面积

float perimeter() const#: 圆周长

Public Members

Point center#: 圆心

float radius = 0#: 半径

struct Circle2i#

整型圆

Public Types

using Point = Point2i #: 圆对应的同类型点

using Rect = Rect2i #: 圆对应的同类型矩形 envelope()

Public Functions

Circle2i() = default#: Default constructor,no initialization.

Circle2i(const Point &center, const float &radius)#: Constructor to set center and radius.

float area() const#: 圆面积

float perimeter() const#: 圆周长

Public Members

Point center#: 圆心

float radius = 0#: 半径

struct MultiPoint2f : public std::vector<Point2f>#

浮点型点集

Warning

算法实现中不会清空原有数据,导致结果产生错误.

Public Functions

MultiPoint2f() = default#: Default constructor,no initialization.

MultiPoint2f(const std::initializer_list<Point> &rhs)#: Constructor taking std::initializer_list,filling the MultiPoint.

struct MultiPoint2i : public std::vector<Point2i>#

整型点集

Warning

算法实现中不会清空原有数据,导致结果产生错误.

Public Functions

MultiPoint2i() = default#: Default constructor,no initialization.

MultiPoint2i(const std::initializer_list<Point> &rhs)#: Constructor taking std::initializer_list,filling the MultiPoint.

struct MultiPolygon2f : public std::vector<Polygon2f>#

浮点型多多边形

Warning

算法实现中不会清空原有数据,导致结果产生错误.

Public Functions

MultiPolygon2f() = default#: Default constructor,no initialization.

MultiPolygon2f(const std::initializer_list<Polygon> &rhs)#: Constructor taking std::initializer_list,filling the MultiPolygon.

struct MultiPolygon2i : public std::vector<Polygon2i>#

整型多多边形

Warning

算法实现中不会清空原有数据,导致结果产生错误.

Public Functions

MultiPolygon2i() = default#: Default constructor,no initialization.

MultiPolygon2i(const std::initializer_list<Polygon> &rhs)#: Constructor taking std::initializer_list,filling the MultiPolygon.

class Matrix3f#

3x3 float matrix.

Transformation matrix.

Public Functions

explicit Matrix3f(float diag = 1)#

Construct a 3*3 float matrix.

The value of the principal diagonal is diag, the rest are 0.

Parameters:: diag – The principal diagonal value. If rhs is 1(As default), it will construct a identity matrix.

Matrix3f(float mat_0_0, float mat_0_1, float mat_0_2, float mat_1_0, float mat_1_1, float mat_1_2, float mat_2_0, float mat_2_1, float mat_2_2)#

Construct a 3*3 float matrix.

Read parameters in first row the col order.

Matrix3f(const Matrix3f &rhs)#

Deep copy constructor.

It will not share the same references as the source object.

Parameters:: rhs – other Matrix3f.

Matrix3f(Matrix3f &&rhs) noexcept#

Move constructor.

Parameters:: rhs – other rvalue Matrix3f.

Matrix3f operator*(const Matrix3f &rhs) const#

Matrix multiplication.

A * B = C.

Parameters:: rhs – B matrix.
Returns:: Matrix3f C matrix.

float &at(size_t row, size_t col)#

Return a reference to the specified array element.

if row or col out of range, an aidi::excepts::InvalidArgument will be thrown.

Parameters:

row – Index along the dimension 1.
col – Index along the dimension 2.

Throws:

aidi::excepts::InvalidArgument – if row or col out of range.

Returns:

NO_DISCARD float& array element.

float at(size_t row, size_t col) const#

Return the specified array element.

if row or col out of range, an aidi::excepts::InvalidArgument will be thrown.

Parameters:

row – Index along the dimension 1.
col – Index along the dimension 2.

Throws:

aidi::excepts::InvalidArgument – if row or col out of range.

Returns:

NO_DISCARD float array element.

enum aidi::geometry::GeoIsSampleFailType#

The enumeration GeoIsSampleFailType enumerates the possible reasons for which a geometry may be found as not simple or invalid by the is_simple() and is_valid() algorithms.

Values:

enumerator kNoFailure = 0#: The geometry is simple/valid.

enumerator kEmpty = 1#: The geometry is empty.

enumerator kDuplicatePoints = 2#: The geometry has (consecutive) duplicate points.

enumerator kSpikes = 4#: The geometry contains spikes.

enumerator kSelfIntersections = 8#: The geometry has self-intersections.

enumerator kPolygonOuterFailure = 16#: The exterior ring of geometry is not simple/valid.

enumerator kPolygonInnersFailure = 32#: The interior rings of geometry is not simple/valid.

enumerator kFewPoints = 64#: The geometry has a very small number of points.

enumerator kWrongTopologicalDimension = 128#: The topological dimension of the geometry is smaller than its dimension.

enumerator kInvalidCoordinate = 256#: The geometry has at least one point with an invalid coordinate.

enumerator kWrongOrientation = 512#: The actual orientation of the geometry is different from the one defined.

enumerator kInteriorRingsOutside = 1024#: The geometry contains interior rings that lie outside the exterior ring.

enumerator kNestedInteriorRings = 2048#: The geometry has nested interior rings.

Geometry algorithms#

template<typename LinearOrAreal, typename MultiPointOrPoint> void aidi::geometry::append(LinearOrAreal &lhs, const MultiPointOrPoint &rhs)#

几何图形的数据扩展

LinearOrAreal	MultiPointOrPoint
LineString	点集或单点
Ring	点集或单点
Polygon	体现在外环和内环上
MultiPoint	点集或单点

Template Parameters:

LinearOrAreal – 可扩展的几何图形
MultiPointOrPoint – 点集或单点

Parameters:

lhs – [inout]
rhs –

template<typename Areal> float aidi::geometry::area(const Areal &rhs)#

多边形的面积

Warning

多边形的内环方向以及数据是否遵循约定方向等会对结果产生影响.

Template Parameters:

Areal – 多边形,矩形以及圆

Parameters:

rhs –

Areal
Ring
Polygon
Rect
RotateRect
Circle
MultiPolygon

Returns:

NO_DISCARD float 浮点型面积

int32_t aidi::geometry::area(const Rect2i &rhs)#

整型矩形面积

Parameters:: rhs – Rect2i
Returns:: NO_DISCARD int32_t 整型面积

template<typename Point> bool aidi::geometry::operator==(const typename Point::Vector &lhs, const Point &rhs)#

点和向量之间的数值比较

Template Parameters:

Point – 任意类型的点

Parameters:

lhs – 点对应的同类型向量
rhs – 点

Returns:

true 点与向量数值上相等.

Returns:

false 点与向量数值上不等.

template<typename Point> Point aidi::geometry::operator+(const typename Point::Vector &lhs, const Point &rhs)#

向量+点=点

Template Parameters:

Point – 任意类型的点

Parameters:

lhs – 点对应的同类型向量
rhs – 点

Returns:

Point 结果不改变点的类型

Point2f aidi::geometry::operator+(const Point2i &lhs, const Vector2f &rhs)#

整型点+浮点型向量=浮点型点

Parameters:

lhs – 整型点
rhs – 浮点型向量

Returns:

Point2f 浮点型点

template<typename Point> Point::Vector aidi::geometry::operator-(const Point &lhs, const Point &rhs)#

点-点=向量

Template Parameters:

Point – 任意类型的点

Parameters:

lhs – 被减点
rhs – 减点

Returns:

Point::Vector 点对应的同类型向量

Point2f aidi::geometry::operator-(const Point2i &lhs, const Vector2f &rhs)#

整型点-浮点型向量=浮点型点

Parameters:

lhs – 整型点
rhs – 浮点型向量

Returns:

Point2f 浮点型点

Vector2f aidi::geometry::operator-(const Point2i &lhs, const Point2f &rhs)#

整型点-浮点型点=浮点型向量

Parameters:

lhs – 整型点
rhs – 浮点型点

Returns:

Vector2f 浮点型向量

Vector2f aidi::geometry::operator-(const Point2f &lhs, const Point2i &rhs)#

浮点型-整形点=浮点型向量

Parameters:

lhs – 浮点型点
rhs – 整形点

Returns:

Vector2f 浮点型向量

template<typename PointLike> PointLike aidi::geometry::operator*(const typename PointLike::Elem &lhs, const PointLike &rhs)#

点和向量的放大

Template Parameters:

PointLike – 任意类型的点或向量

Parameters:

lhs – 点或向量的Elem
rhs – 点或向量

Returns:

PointLike 结果不改变点或向量的类型

Point2f aidi::geometry::operator*(const Point2i &lhs, const float &rhs)#

整型点*浮点数=浮点型点

Parameters:

lhs – 整形点
rhs – 浮点数

Returns:

Point2f 浮点型点

Vector2f aidi::geometry::operator*(const Vector2i &lhs, const float &rhs)#

整型向量*浮点数=浮点型向量

Parameters:

lhs – 整型向量
rhs – 浮点数

Returns:

Vector2f 浮点型向量

template<typename Point> void aidi::geometry::add_point(Point &lhs, const Point &rhs)#

将第一个点的值加上第二个

Template Parameters:

Point – 任意类型的点

Parameters:

lhs – 被改变的第一个点
rhs – 同类型的第二个点不发生变化

template<typename Point> void aidi::geometry::add_value(Point &lhs, const typename Point::Elem &rhs)#

将一个点的坐标加上相同值

Template Parameters:

Point – 任意类型的点

Parameters:

lhs – 被改变的点
rhs – 点对应的同类型值

template<typename Point> Point::Elem aidi::geometry::cross_product(const Point &lhs, const Point &rhs)#

向量积,叉积

Template Parameters:

Point – 任意类型的点

Parameters:

lhs – 点
rhs – 同类型的点

Returns:

NO_DISCARD 点对应的同类型值

template<typename Point> void aidi::geometry::divide_point(Point &lhs, const Point &rhs)#

将第一个点除以第二个点

Note

注意int和float不同产生的结果.

Template Parameters:

Point – 任意类型的点

Parameters:

lhs – 被改变的第一个点
rhs – 同类型的第二个点不发生变化

template<typename Point> void aidi::geometry::divide_value(Point &lhs, const typename Point::Elem &rhs)#

将一个点的坐标除以相同值

Template Parameters:

Point – 任意类型的点

Parameters:

lhs – 被改变的点
rhs – 点对应的同类型值

template<typename PointLike> PointLike::Elem aidi::geometry::dot_product(const PointLike &lhs, const PointLike &rhs)#

数量积,点积

Template Parameters:

PointLike – 任意类型的点或向量

Parameters:

lhs – 点或向量
rhs – 同类型的点或向量

Returns:

NO_DISCARD 点或向量对应的同类型的值

template<typename Point> void aidi::geometry::multiply_point(Point &lhs, const Point &rhs)#

将第一个点乘以第二个点

Template Parameters:

Point – 任意类型的点

Parameters:

lhs – 被改变的第一个点
rhs – 同类型的第二个点不发生变化

template<typename Point> void aidi::geometry::multiply_value(Point &lhs, const typename Point::Elem &rhs)#

将一个点的坐标乘以相同值

Template Parameters:

Point – 任意类型的点

Parameters:

lhs – 被改变的点
rhs – 点对应的同类型值

template<typename Point> void aidi::geometry::subtract_point(Point &lhs, const Point &rhs)#

将第一个点减去第二个点

Template Parameters:

Point – 任意类型的点

Parameters:

lhs – 被改变的第一个点
rhs – 同类型的第二个点不发生改变

template<typename Point> void aidi::geometry::subtract_value(Point &lhs, const typename Point::Elem &rhs)#

将一个点的坐标减去相同值

Template Parameters:

Point – 任意类型的点

Parameters:

lhs – 被改变的点
rhs – 点对应的同类型值

template<typename PointLike> Radian aidi::geometry::azimuth(const PointLike &lhs, const PointLike &rhs)#

线段的方位角

Template Parameters:

PointLike – 任意类型的点或向量

Parameters:

lhs – 点或向量
rhs – 同类型的点或向量

Returns:

NO_DISCARD 两点形成线段从x轴正方向向y轴正方向旋转的弧度(±𝝅)

template<typename Vector> Radian aidi::geometry::azimuth(const Vector &rhs)#

向量的方位角

Template Parameters:: Vector – 任意类型的向量
Parameters:: rhs – 向量
Returns:: NO_DISCARD 原点(0,0)到向量所形成线段的方位角弧度(±𝝅)

template<typename Areal> Point2f aidi::geometry::center(const Areal &rhs)#

多边形中心,即外接平行矩形的中心

Template Parameters:

Areal – 多边形,矩形和圆.

Parameters:

rhs –

Areal
Ring
Polygon
Rect
RotateRect
Circle

Returns:

NO_DISCARD 浮点型点

Point2i aidi::geometry::center(const Circle2i &rhs)#

整型圆的中心

Parameters:: rhs – 整型圆
Returns:: NO_DISCARD 整型点,即圆心.

template<typename Areal> Point2f aidi::geometry::centroid(const Areal &rhs)#

多边形质心

Template Parameters:

Areal – 多边形,矩形和圆

Parameters:

rhs –

Areal
Ring
Polygon
Rect
RotateRect
Circle

Returns:

NO_DISCARD 浮点型点

Point2i aidi::geometry::centroid(const Circle2i &rhs)#

整型圆质心

Parameters:: rhs – 整型圆
Returns:: NO_DISCARD 整形点,即圆心

template<typename LinearOrAreal> void aidi::geometry::clear(LinearOrAreal &rhs)#

清空几何图形数据

Template Parameters:

LinearOrAreal – 线或多边形

Parameters:

rhs –

LinearOrAreal
LineString
Ring
Polygon
MultiPoint
MultiPolygon

template<typename Geometry1, typename Geometry2> void aidi::geometry::convert(const Geometry1 &lhs, Geometry2 &rhs)#

几何图形之间的转换

Template Parameters:

Geometry1 – 几何图形
Geometry2 – 同类型的几何图形

Parameters:

lhs, rhs –

lhs/rhs	Point	LineString	Ring	Polygon	Rect	RotateRect	Arc	Circle	Vector
Point	√	×	×	×	×	×	×	×	√
LineString	×	√	√	√	×	×	×	×	×
Ring	×	√	√	√	×	×	×	×	×
Polygon	×	×	×	√	×	×	×	×	×
Rect	×	×	√	√	√	×	×	×	×
RotateRect	×	×	√	√	×	×	×	×	×
Arc	×	×	×	×	×	×	×	√	×
Circle	×	×	×	×	×	×	×	×	×
Vector	×	×	×	×	×	×	×	×	×

template<typename Areal> void aidi::geometry::convex_hull(const Areal &lhs, typename Areal::Ring &rhs)#

多边形的凸包

Note

新的凸包将以x最小的点为起点,从x轴正方向向y轴正方向顺序排列.

Template Parameters:

Areal – 多边形

Parameters:

lhs, rhs –

Areal
Ring
Polygon

template<typename Areal> Areal::Ring aidi::geometry::return_convex_hull(const Areal &lhs)#

多边形的凸包

See also

convex_hull()

template<typename Areal> void aidi::geometry::correct(Areal &rhs)#

修正多边形的约定顺序和约定开闭包形式.

Template Parameters:

Areal – 多边形

Parameters:

rhs –

Areal
Ring
Polygon

template<typename Areal> Areal aidi::geometry::return_correct(const Areal &rhs)#

修正多边形的约定顺序和约定开闭包形式.

See also

correct()

template<typename Geometry1, typename Geometry2> bool aidi::geometry::covered_by(const Geometry1 &lhs, const Geometry2 &rhs)#

第一个几何图形是否被第二个几何图形覆盖

The difference with the within algorithm is that this algorithm checks the border by default.

See also

within()

Note

边界有交集仍然会被认为是覆盖.

Template Parameters:

Geometry1 – 几何图形
Geometry2 – 同类型的几何图形

Parameters:

lhs, rhs –

lhs/rhs	Point	LineString	Ring	Polygon	Rect	RotateRect	Arc	Circle	Vector
Point	√	√	√	√	√	√	×	√	×
LineString	×	√	√	√	√	√	×	×	×
Ring	×	×	√	√	√	√	×	×	×
Polygon	×	×	√	√	√	√	×	×	×
Rect	×	×	√	√	√	√	×	×	×
RotateRect	×	×	√	√	√	√	×	×	×
Arc	×	×	×	×	×	×	×	×	×
Circle	×	×	×	×	×	×	×	√	×
Vector	×	×	×	×	×	×	×	×	×

Returns:

NO_DISCARD bool

template<typename Linear, typename Geometry> bool aidi::geometry::crosses(const Linear &lhs, const Geometry &rhs)#

第一个线是否穿过第二个几何图形

See also

covered_by()

Note

如果没能穿过边界,则会被视为覆盖.

Template Parameters:

Linear – 线
Geometry – 几何图形

Parameters:

lhs, rhs –

Geometry
Point
LineString
Ring
Polygon
Rect
RotateRect
Circle

Returns:

NO_DISCARD bool

template<typename Areal1, typename Areal2, typename MultiPolygon> void aidi::geometry::difference(const Areal1 &lhs, const Areal2 &rhs, MultiPolygon &result)#

多边形之间的差集

Note

算法并不会清空MultiPolygon中已有的数据,而是将结果添加进MultiPolygon.

Warning

对于整型几何图形的差集结果存在交点为浮点型时,会产生一定的问题.

Template Parameters:

Areal1 – 多边形,矩形
Areal2 – 多边形,矩形
MultiPolygon – 多多边形

Parameters:

lhs, rhs –

lhs/rhs	Point	LineString	Ring	Polygon	Rect	RotateRect	Arc	Circle	Vector
Point	×	×	×	×	×	×	×	×	×
LineString	×	×	×	×	×	×	×	×	×
Ring	×	×	√	√	√	√	×	×	×
Polygon	×	×	√	√	√	√	×	×	×
Rect	×	×	√	√	√	√	×	×	×
RotateRect	×	×	√	√	√	√	×	×	×
Arc	×	×	×	×	×	×	×	×	×
Circle	×	×	×	×	×	×	×	×	×
Vector	×	×	×	×	×	×	×	×	×

result – 多多边形,多边形之间的差集.

template<typename Linear1, typename Linear2> float aidi::geometry::discrete_frechet_distance(const Linear1 &lhs, const Linear2 &rhs)#

线之间的frechet距离

几何图形之间最大的最短距离,用于描述相似度.

Template Parameters:

Linear1 – 线
Linear2 – 同类型的线

Returns:

NO_DISCARD float

template<typename Geometry1, typename Geometry2> bool aidi::geometry::disjoint(const Geometry1 &lhs, const Geometry2 &rhs)#

几何图形是否相离

Template Parameters:

Geometry1 – 几何图形
Geometry2 – 同类型的几何图形

Parameters:

lhs, rhs –

lhs/rhs	Point	LineString	Ring	Polygon	Rect	RotateRect	Arc	Circle	Vector
Point	√	√	√	√	√	√	×	√	×
LineString	√	√	√	√	√	√	×	√	×
Ring	√	√	√	√	√	√	×	√	×
Polygon	√	√	√	√	√	√	×	√	×
Rect	√	√	√	√	√	√	×	√	×
RotateRect	√	√	√	√	√	√	×	√	×
Arc	×	×	×	×	×	×	×	×	×
Circle	√	√	√	√	√	√	×	√	×
Vector	×	×	×	×	×	×	×	×	×

Returns:

NO_DISCARD bool

template<typename Geometry1, typename Geometry2> float aidi::geometry::distance(const Geometry1 &lhs, const Geometry2 &rhs)#

几何图形之间的距离

Template Parameters:

Geometry1 – 几何图形
Geometry2 – 同类型的几何图形

Parameters:

lhs, rhs –

lhs/rhs	Point	LineString	Ring	Polygon	Rect	RotateRect	Arc	Circle	Vector
Point	√	√	√	√	√	√	×	√	×
LineString	√	√	√	√	√	√	×	√	×
Ring	√	√	√	√	√	√	×	√	×
Polygon	√	√	√	√	√	√	×	√	×
Rect	√	√	√	√	√	√	×	√	×
RotateRect	√	√	√	√	√	√	×	√	×
Arc	×	×	×	×	×	×	×	×	×
Circle	√	√	√	√	√	√	×	√	×
Vector	×	×	×	×	×	×	×	×	×

Returns:

NO_DISCARD float

template<typename LinearOrAreal> void aidi::geometry::envelope(const LinearOrAreal &lhs, typename LinearOrAreal::Rect &rhs)#

最小外接矩形

Template Parameters:

LinearOrAreal – 线或多边形

Parameters:

lhs, rhs –

LinearOrAreal
LineString
Ring
Polygon
RotateRect

template<typename LinearOrAreal> LinearOrAreal::Rect aidi::geometry::return_envelope(const LinearOrAreal &rhs)#

最小外接矩形

See also

envelope()

template<typename Geometry1, typename Geometry2> bool aidi::geometry::equals(const Geometry1 &lhs, const Geometry2 &rhs)#

几何图形是否相等

Template Parameters:

Geometry1 – 几何图形
Geometry2 – 同类型的几何图形

Parameters:

lhs, rhs –

lhs/rhs	Point	LineString	Ring	Polygon	Rect	RotateRect	Arc	Circle	Vector
Point	√	×	×	×	×	×	×	×	√
LineString	×	√	×	×	×	×	×	×	×
Ring	×	×	√	√	√	√	×	×	×
Polygon	×	×	√	√	√	√	×	×	×
Rect	×	×	√	√	√	√	×	×	×
RotateRect	×	×	√	√	√	√	×	×	×
Arc	×	×	×	×	×	×	×	×	×
Circle	×	×	×	×	×	×	×	√	×
Vector	√	×	×	×	×	×	×	×	√

Returns:

NO_DISCARD bool

template<typename Geometry1, typename Geometry2, typename GeometryOut> void aidi::geometry::intersection(const Geometry1 &lhs, const Geometry2 &rhs, GeometryOut &result)#

几何图形之间的交集

Warning

对于整型几何图形的交集结果存在交点为浮点型时,会产生一定的问题.

Template Parameters:

Geometry1 – 几何图形
Geometry2 – 同类型的几何图形
GeometryOut – 点集或多多边形

Parameters:

lhs, rhs – [in]

result – [out] The intersection of geo1 and geo2

lhs/rhs	Point	LineString	Ring	Polygon	Rect	RotateRect	Arc	Circle	Vector
Point	√	√	√	√	√	√	×	×	×
LineString	√	√	√	√	×	√	×	×	×
Ring	√	√	√	√	×	√	×	×	×
Polygon	√	√	√	√	×	√	×	×	×
Rect	×	×	×	×	×	×	×	×	×
RotateRect	×	×	×	×	×	×	×	×	×
Arc	×	×	×	×	×	×	×	×	×
Circle	×	×	×	×	×	×	×	×	×
Vector	×	×	×	×	×	×	×	×	×

template<typename Geometry1, typename Geometry2> bool aidi::geometry::intersects(const Geometry1 &lhs, const Geometry2 &rhs)#

几何图形是否相交(存在至少一个交点)

Template Parameters:

Geometry1 – 几何图形
Geometry2 – 同类型的几何图形

Parameters:

lhs, rhs –

lhs/rhs	Point	LineString	Ring	Polygon	Rect	RotateRect	Arc	Circle	Vector
Point	√	√	√	√	√	√	×	√	×
LineString	√	√	√	√	√	√	×	√	×
Ring	√	√	√	√	√	√	×	√	×
Polygon	√	√	√	√	√	√	×	√	×
Rect	√	√	√	√	√	√	×	√	×
RotateRect	√	√	√	√	√	√	×	√	×
Arc	×	×	×	×	×	×	×	×	×
Circle	√	√	√	√	√	√	×	√	×
Vector	×	×	×	×	×	×	×	×	×

template<typename LinearOrAreal> bool aidi::geometry::is_empty(const LinearOrAreal &rhs)#

判断几何图形是否为空

Template Parameters:

LinearOrAreal – 线或多边形

Parameters:

rhs –

LinearOrAreal
LineString
Ring
Polygon
MultiPoint
MultiPolygon

template<typename LinearOrAreal> bool aidi::geometry::is_simple(const LinearOrAreal &rhs)#

判断几何图形是否是简单几何图形

Template Parameters:

LinearOrAreal – 线或多边形

Parameters:

rhs –

LinearOrAreal
LineString
Ring
Polygon

Returns:

Linear:非空,没有重复点,不自交,没有尖峰.

Returns:

Areal:非空,没有重复点.

template<typename LinearOrAreal> GeoIsSampleFailType aidi::geometry::return_is_simple(const LinearOrAreal &rhs)#

判断几何图形是否是简单几何图形

See also

is_simple()

See also

GeoIsSampleFailType

Template Parameters:: LinearOrAreal – 线或多边形
Returns:: NO_DISCARD GeoIsSampleFailType 几何图形不为简单几何图形的错误信息

template<typename LinearOrAreal> bool aidi::geometry::is_valid(const LinearOrAreal &rhs)#

判断几何图形数据是否有效

Template Parameters:

LinearOrAreal – 线或多边形

Parameters:

rhs –

LinearOrAreal
LineString
Ring
Polygon

Returns:

Linear:没有无效点,至少有两个点,满足拓扑维数(存在至少两个不相同点),可以有尖峰.

Returns:

Ring:没有无效点,至少有三个点(闭包四个点),满足拓扑维数(存在至少三个不相同点), 可以有重复点,没有尖峰,没有自交,满足数据顺序定义.

Returns:

Polygon:外环内环都是有效的,多边形不自交,内环在外环内,内环不存在嵌套.

template<typename LinearOrAreal> int32_t aidi::geometry::return_is_valid(const LinearOrAreal &rhs)#

判断几何图形数据是否有效

See also

is_valid()

See also

failure_type

Template Parameters:: LinearOrAreal – 线或多边形
Returns:: NO_DISCARD int32_t 几何图形数据失效的错误信息

template<typename LinearOrVector> float aidi::geometry::length(const LinearOrVector &rhs)#

几何图形的长度

Template Parameters:

LinearOrVector – 线或向量

Parameters:

rhs –

LinearOrVector
LineString
Vector

Returns:

NO_DISCARD float

template<typename Linear, typename MultiPointOrPoint> void aidi::geometry::line_interpolate(const Linear &lhs, const float &rhs, MultiPointOrPoint &result)#

线上的线性插值

Warning

对于整型线的插值结果存在浮点型时,会产生一定的问题.

Template Parameters:

Linear – 线
MultiPointOrPoint – 点集或单点

Parameters:

lhs – 线
rhs – 插值点之间的距离
result – 单点则为起点起插值的第一个点,点集则是全部点.

template<typename Areal> void aidi::geometry::min_area_rect(const Areal &lhs, RotateRect2f &rhs)#

最小面积外接矩形

Template Parameters:

Areal – 多边形
RotateRect – 同类型的旋转矩形

Parameters:

lhs, rhs –

Areal
Ring
Polygon

template<typename Areal> RotateRect2f aidi::geometry::return_min_area_rect(const Areal &rhs)#

最小面积外接矩形

See also

min_area_rect()

template<typename Areal1, typename Areal2> bool aidi::geometry::overlaps(const Areal1 &lhs, const Areal2 &rhs)#

多边形是否有重叠部分

Template Parameters:

Areal1 – 多边形
Areal2 – 同类型的多边形

Parameters:

lhs, rhs –

lhs/rhs	Point	LineString	Ring	Polygon	Rect	RotateRect	Arc	Circle	Vector
Point	×	×	×	×	×	×	×	×	×
LineString	×	×	×	×	×	×	×	×	×
Ring	×	×	√	√	×	×	×	×	×
Polygon	×	×	√	√	×	×	×	×	×
Rect	×	×	×	×	√	×	×	×	×
RotateRect	×	×	×	×	×	×	×	×	×
Arc	×	×	×	×	×	×	×	×	×
Circle	×	×	×	×	×	×	×	×	×
Vector	×	×	×	×	×	×	×	×	×

Returns:

NO_DISCARD bool

template<typename Areal> float aidi::geometry::perimeter(const Areal &rhs)#

几何图形的周长

Template Parameters:

Areal – 多边形的周长

Parameters:

rhs –

Areal
Ring
Polygon
Rect
RotateRect
Circle

int32_t aidi::geometry::perimeter(const Rect2i &rhs)#

整型矩形的周长

Parameters:: rhs – 整型矩形
Returns:: NO_DISCARD int32_t 整型周长

template<typename LinearOrAreal> void aidi::geometry::reverse(LinearOrAreal &rhs)#

翻转几何图形数据顺序

Note

The reverse of a (multi)polygon or ring might make a valid geometry invalid because the (counter)clockwise orientation reverses.

Template Parameters:

LinearOrAreal – 线或多边形

Parameters:

rhs –

LinearOrAreal
LineString
Ring
Polygon

template<typename LinearOrAreal> LinearOrAreal aidi::geometry::return_reverse(const LinearOrAreal &rhs)#

翻转几何图形数据顺序

See also

reverse()

template<typename LinearOrAreal> void aidi::geometry::simplify(LinearOrAreal &lhs, const float &rhs)#

简化几何图形

采用Douglas-Peucker算法进行多边形逼近,小于阈值则被删除.

Warning

结果会被强制改为闭包.

Template Parameters:

LinearOrAreal – 线或多边形

Parameters:

lhs – 线或多边形
rhs – 阈值

template<typename LinearOrAreal> LinearOrAreal aidi::geometry::return_simplify(const LinearOrAreal &lhs, const float &rhs)#

简化几何图形

See also

simplify()

template<typename Areal1, typename Areal2, typename ArealOut> void aidi::geometry::sym_difference(const Areal1 &lhs, const Areal2 &rhs, ArealOut &result)#

几何图形之间的对称差

Warning

对于整型几何图形的对称差结果存在交点为浮点型时,会产生一定的问题.

Warning

几何结构不遵守约定顺序可能会产生一定的问题.

Template Parameters:

Areal1 – 多边形
Areal2 – 同类型的多边形
ArealOut – 多多边形

Parameters:

lhs, rhs –

lhs/rhs	Point	LineString	Ring	Polygon	Rect	RotateRect	Arc	Circle	Vector
Point	×	×	×	×	×	×	×	×	×
LineString	×	×	×	×	×	×	×	×	×
Ring	×	×	√	√	×	×	×	×	×
Polygon	×	×	√	√	×	×	×	×	×
Rect	×	×	×	×	×	×	×	×	×
RotateRect	×	×	×	×	×	×	×	×	×
Arc	×	×	×	×	×	×	×	×	×
Circle	×	×	×	×	×	×	×	×	×
Vector	×	×	×	×	×	×	×	×	×

result – 同类型的多多边形

template<typename Areal1, typename Areal2> bool aidi::geometry::touches(const Areal1 &lhs, const Areal2 &rhs)#

几何图形之间是否触及(相切,不重叠)

Template Parameters:

Areal1 – 多边形
Areal2 – 同类型的多边形

Parameters:

lhs, rhs –

lhs/rhs	Point	LineString	Ring	Polygon	Rect	RotateRect	Arc	Circle	Vector
Point	×	×	×	×	×	×	×	×	×
LineString	×	×	×	×	×	×	×	×	×
Ring	×	×	√	√	×	×	×	×	×
Polygon	×	×	√	√	×	×	×	×	×
Rect	×	×	×	×	×	×	×	×	×
RotateRect	×	×	×	×	×	×	×	×	×
Arc	×	×	×	×	×	×	×	×	×
Circle	×	×	×	×	×	×	×	×	×
Vector	×	×	×	×	×	×	×	×	×

Returns:

NO_DISCARD bool

template<typename Areal1, typename Areal2, typename ArealOut> void aidi::geometry::union_areal(const Areal1 &lhs, const Areal2 &rhs, ArealOut &result)#

多边形之间的并集

Warning

对于整型几何图形的并集结果存在交点为浮点型时,会产生一定的问题.

Template Parameters:

Areal1 – 多边形
Areal2 – 同类型的多边形
ArealOut – 多多边形

Parameters:

lhs, rhs –

lhs/rhs	Point	LineString	Ring	Polygon	Rect	RotateRect	Arc	Circle	Vector
Point	×	×	×	×	×	×	×	×	×
LineString	×	×	×	×	×	×	×	×	×
Ring	×	×	√	√	×	×	×	×	×
Polygon	×	×	√	√	×	×	×	×	×
Rect	×	×	×	×	×	×	×	×	×
RotateRect	×	×	×	×	×	×	×	×	×
Arc	×	×	×	×	×	×	×	×	×
Circle	×	×	×	×	×	×	×	×	×
Vector	×	×	×	×	×	×	×	×	×

result – 同类型的多多边形

template<typename LinearOrAreal> void aidi::geometry::unique(LinearOrAreal &rhs)#

去除几何图形中重复节点

Template Parameters:

LinearOrAreal – 线或多边形

Parameters:

rhs –

LinearOrAreal
LineString
Ring
Polygon

template<typename LinearOrAreal> LinearOrAreal aidi::geometry::return_unique(const LinearOrAreal &rhs)#

去除几何图形中重复节点

See also

unique()

template<typename Geometry1, typename Geometry2> bool aidi::geometry::within(const Geometry1 &lhs, const Geometry2 &rhs)#

第一个几何图形是否在第二个几何图形内部

Template Parameters:

Geometry1 – 几何图形
Geometry2 –

Parameters:

lhs, rhs –

lhs/rhs	Point	LineString	Ring	Polygon	Rect	RotateRect	Arc	Circle	Vector
Point	√	√	√	√	√	√	×	√	×
LineString	×	√	√	√	√	√	×	√	×
Ring	×	×	√	√	√	√	×	√	×
Polygon	×	×	√	√	√	√	×	√	×
Rect	×	×	√	√	√	√	×	√	×
RotateRect	×	×	√	√	√	√	×	√	×
Arc	×	×	×	×	×	×	×	×	×
Circle	×	×	√	√	√	√	×	√	×
Vector	×	×	×	×	×	×	×	×	×

Returns:

NO_DISCARD bool

template<typename Geometry> Geometry aidi::geometry::transform_rotate(const Geometry &geometry, Radian radian)#

Geometry rotate transform.

Cartesian coordinate system(the origin of the first quadrant is in

the lower left corner), the matrix is rotated clockwise in radians.

Parameters:

geometry – Geometry.

Geometry

Point

LineString

Ring

Polygon

RotateRect

Vector

Segment

MultiPoint

MultiPolygon
radian – Rotation radian.

Returns:

NO_DISCARD the result is consistent with the input geometry.

RotateRect2f aidi::geometry::transform_rotate(const Rect2f &rect, Radian radian)#

Geometry rotate transform.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters:

rect – Rect.
radian – Rotation radian.

Returns:

NO_DISCARD the result is RotateRect.

template<typename Geometry> Geometry aidi::geometry::transform_scale(const Geometry &geometry, float ratiox, float ratioy)#

Geometry scale transform.

Parameters:

geometry – Geometry.

Geometry

Point

LineString

Ring

Polygon

Rect

Vector

Segment

MultiPoint

MultiPolygon
ratiox – Scaling ratio direction-x.
ratioy – Scaling ratio direction-y.

Returns:

NO_DISCARD the result is consistent with the input geometry.

Ring2f aidi::geometry::transform_scale(const RotateRect2f &rotate_rect, float ratiox, float ratioy)#

Geometry scale transform.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters:

rotate_rect – RotateRect.
ratiox – Scaling ratio direction-x.
ratioy – Scaling ratio direction-y.

Returns:

NO_DISCARD the result is Ring.

template<typename Geometry> Geometry aidi::geometry::transform_translate(const Geometry &geometry, float directx, float directy)#

Geometry translate transform.

Parameters:

geometry – Geometry.

Geometry

Point

LineString

Ring

Polygon

Rect

RotateRect

Vector

Segment

MultiPoint

MultiPolygon
directx – Translation transform direction-x.
directy – Translation transform direction-y.

Returns:

NO_DISCARD the result is consistent with the input geometry.

template<typename Geometry> Geometry aidi::geometry::transform(const Geometry &geometry, const Matrix3f &mat)#

Geometry transform.

transform(geometry, step1), transform(geometry, step2) -> transform(geometry, step2 * step1).

Parameters:

geometry – Geometry.

Geometry

Point

LineString

Ring

Polygon

Vector

Segment

MultiPoint

MultiPolygon
mat – Transformation matrix.

Returns:

NO_DISCARD the result is consistent with the input geometry.

Ring2f aidi::geometry::transform(const Rect2f &rect, const Matrix3f &mat)#

Geometry transform.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters:

rect – Rect.
mat – Transformation matrix.

Returns:

NO_DISCARD the result is Ring.

Ring2f aidi::geometry::transform(const RotateRect2f &rotate_rect, const Matrix3f &mat)#

Geometry transform.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Parameters:

rotate_rect – RotateRect.
mat – Transformation matrix.

Returns:

NO_DISCARD the result is Ring.

Matrix3f aidi::geometry::get_affine_transform(const std::vector<Point2f> &src, const std::vector<Point2f> &dst)#

Calculate an affine transform from three pairs of the corresponding points.

If the number of point pairs is less than 3, an aidi::excepts::InvalidArgument will be thrown.

Parameters:

src – Coordinate of triangle vertices in the source image.
dst – Coordinate of the corresponding triangle vertices in the destination image.

Throws:

aidi::excepts::InvalidArgument – if the number of point pairs is less than requirement.

Returns:

NO_DISCARD transformation matrix.

Matrix3f aidi::geometry::get_perspective_transform(const std::vector<Point2f> &src, const std::vector<Point2f> &dst)#

Calculate a perspective transform from four pairs of the corresponding points.

If the number of point pairs is less than 4, an aidi::excepts::InvalidArgument will be thrown.

Parameters:

src – Coordinate of quadrangle vertices in the source image.
dst – Coordinate of the corresponding quadrangle vertices in the destination image.

Throws:

aidi::excepts::InvalidArgument – if the number of point pairs is less than requirement.

Returns: