#pragma once
#ifndef T_GEOMETRY_INCLUDED
#define T_GEOMETRY_INCLUDED
#include "tutil.h"
#include <cmath>
#undef DVAPI
#undef DVVAR
#ifdef TGEOMETRY_EXPORTS
#define DVAPI DV_EXPORT_API
#define DVVAR DV_EXPORT_VAR
#else
#define DVAPI DV_IMPORT_API
#define DVVAR DV_IMPORT_VAR
#endif
//=============================================================================
inline double logNormalDistribuitionUnscaled(double x, double x0, double w)
{ return exp(-0.5*pow(log(x/x0)/w, 2.0))/x; }
inline double logNormalDistribuition(double x, double x0, double w)
{ return logNormalDistribuitionUnscaled(x, x0, w)/(w*sqrt(2.0*M_PI)); }
//=============================================================================
template <class T> class TPoint4T;
/*
* This is an example of how to use the TPointT, the TRectT and the TAffine
* classes.
*/
/*! The template class TPointT defines the x- and y-coordinates of a point.
*/
template <class T>
class TPointT {
public:
T x, y;
inline TPointT() : x(0), y(0){};
inline TPointT(T _x, T _y) : x(_x), y(_y){};
inline TPointT(const TPointT &point) : x(point.x), y(point.y){};
inline explicit TPointT(const TPoint4T<T> &point);
inline TPointT &operator=(const TPointT &a) {
x = a.x;
y = a.y;
return *this;
};
inline TPointT &operator+=(const TPointT &a) {
x += a.x;
y += a.y;
return *this;
};
inline TPointT &operator-=(const TPointT &a) {
x -= a.x;
y -= a.y;
return *this;
};
inline TPointT operator+(const TPointT &a) const {
return TPointT(x + a.x, y + a.y);
};
inline TPointT operator-(const TPointT &a) const {
return TPointT(x - a.x, y - a.y);
};
inline TPointT operator-() const { return TPointT(-x, -y); };
};
template <class T>
class TPoint4T {
public:
union {
struct { T x, y, z, w; };
T a[4];
};
inline TPoint4T():
x(), y(), z(), w() { };
inline TPoint4T(T x, T y, T z, T w):
x(x), y(y), z(z), w(w) { };
inline explicit TPoint4T(const TPointT<T> &p, T w = (T)1):
x(p.x), y(p.y), z(), w(w) { };
};
template <class T>
inline TPointT<T>::TPointT(const TPoint4T<T> &point) : x(point.x), y(point.y){};
/*! \relates TPointT
* Rotate a point 90 degrees (counterclockwise).
\param p a point.
\return the rotated point
\sa rotate270
*/
template <class T>
inline TPointT<T> rotate90(const TPointT<T> &p) // 90 counterclockwise
{
return TPointT<T>(-p.y, p.x);
}
/*! \relates TPointT
* Rotate a point 270 degrees (clockwise).
\param p a point.
\return the rotated point
\sa rotate90
*/
template <class T>
inline TPointT<T> rotate270(const TPointT<T> &p) // 90 clockwise
{
return TPointT<T>(p.y, -p.x);
}
/*!
\relates TPointT
*/
template <class T> // Scalar(dot) Product
inline T operator*(const TPointT<T> &a, const TPointT<T> &b) {
return a.x * b.x + a.y * b.y;
}
//-----------------------------------------------------------------------------
template <class T>
inline std::ostream &operator<<(std::ostream &out, const TPointT<T> &p) {
return out << "(" << p.x << ", " << p.y << ")";
}
//-----------------------------------------------------------------------------
typedef TPointT<int> TPoint, TPointI;
typedef TPointT<double> TPointD;
typedef TPoint4T<double> TPoint4D;
#ifdef _WIN32
template class DVAPI TPointT<int>;
template class DVAPI TPointT<double>;
#endif
template <class T>
inline bool operator==(const TPointT<T> &p0, const TPointT<T> &p1) {
return p0.x == p1.x && p0.y == p1.y;
}
template<class T>
inline bool operator!=(const TPointT<T> &p0, const TPointT<T> &p1) {
return p0.x != p1.x || p0.y != p1.y;
}
//-----------------------------------------------------------------------------
//!\relates TPointT
inline TPoint operator*(int a, const TPoint &p) {
return TPoint(a * p.x, a * p.y);
}
//!\relates TPointT
inline TPoint operator*(const TPoint &p, int a) {
return TPoint(a * p.x, a * p.y);
}
//!\relates TPointT
inline TPointD operator*(double a, const TPointD &p) {
return TPointD(a * p.x, a * p.y);
}
//!\relates TPointT
inline TPointD operator*(const TPointD &p, double a) {
return TPointD(a * p.x, a * p.y);
}
//-----------------------------------------------------------------------------
/*!
\relates TPointT
This helper function returns the square of the absolute value of the specified
point (a TPointI)
*/
inline int norm2(const TPointI &p) { return p.x * p.x + p.y * p.y; }
//-----------------------------------------------------------------------------
/*!
\relates TPointT
This helper function returns the square of the absolute value of the specified
point (a TPointD)
*/
inline double norm2(const TPointD &p) { return p.x * p.x + p.y * p.y; }
/*!
\relates TPointT
This helper function returns the absolute value of the specified point
*/
inline double norm(const TPointD &p) { return std::sqrt(norm2(p)); }
/*!
\relates TPointT
This helper function returns the normalized version of the specified point
*/
inline TPointD normalize(const TPointD &p) {
double n = norm(p);
assert(n != 0.0);
return (1.0 / n) * p;
}
/*!
\relates TPointT
This helper function converts a TPoint (TPointT<int>) into a TPointD
*/
inline TPointD convert(const TPoint &p) { return TPointD(p.x, p.y); }
/*!
\relates TPointT
This helper function converts a TPointD (TPointT<double>) into a TPoint
*/
inline TPoint convert(const TPointD &p) {
return TPoint(tround(p.x), tround(p.y));
}
/*!
\relates TPointT
This helper function returns the square of the distance between two points
*/
inline double tdistance2(const TPointD &p1, const TPointD &p2) {
return norm2(p2 - p1);
}
inline bool operator==(const TPointD &p0, const TPointD &p1) {
return tdistance2(p0, p1) <= TConsts::epsilon * TConsts::epsilon;
}
inline bool operator!=(const TPointD &p0, const TPointD &p1) {
return !(p0 == p1);
}
/*!
\relates TPointT
This helper function returns the distance between two points
*/
inline double tdistance(const TPointD &p1, const TPointD &p2) {
return norm(p2 - p1);
}
/*!
the cross product
\relates TPointT
*/
inline double cross(const TPointD &a, const TPointD &b) {
return a.x * b.y - a.y * b.x;
}
/*!
the cross product
\relates TPoint
*/
inline int cross(const TPoint &a, const TPoint &b) {
return a.x * b.y - a.y * b.x;
}
/*!
returns the angle of the point p in polar coordinates
n.b atan(-y) = -pi/2, atan(x) = 0, atan(y) = pi/2, atan(-x) = pi
*/
inline double atan(const TPointD &p) { return atan2(p.y, p.x); }
//=============================================================================
template <class T>
class DVAPI T3DPointT {
public:
T x, y, z;
T3DPointT() : x(0), y(0), z(0) {}
T3DPointT(T _x, T _y, T _z) : x(_x), y(_y), z(_z) {}
T3DPointT(const TPointT<T> &_p, T _z) : x(_p.x), y(_p.y), z(_z) {}
T3DPointT(const T3DPointT &_p) : x(_p.x), y(_p.y), z(_p.z) {}
inline T3DPointT &operator=(const T3DPointT &a) {
x = a.x;
y = a.y;
z = a.z;
return *this;
}
inline T3DPointT &operator+=(const T3DPointT &a) {
x += a.x;
y += a.y;
z += a.z;
return *this;
}
inline T3DPointT &operator-=(const T3DPointT &a) {
x -= a.x;
y -= a.y;
z -= a.z;
return *this;
}
inline T3DPointT operator+(const T3DPointT &a) const {
return T3DPointT(x + a.x, y + a.y, z + a.z);
}
inline T3DPointT operator-(const T3DPointT &a) const {
return T3DPointT(x - a.x, y - a.y, z - a.z);
}
inline T3DPointT operator-() const { return T3DPointT(-x, -y, -z); }
bool operator==(const T3DPointT &p) const {
return x == p.x && y == p.y && z == p.z;
}
bool operator!=(const T3DPointT &p) const {
return x != p.x || y != p.y || z != p.z;
}
};
//=============================================================================
template <class T>
inline std::ostream &operator<<(std::ostream &out, const T3DPointT<T> &p) {
return out << "(" << p.x << ", " << p.y << ", " << p.z << ")";
}
typedef T3DPointT<int> T3DPoint, T3DPointI;
typedef T3DPointT<double> T3DPointD;
#ifdef _WIN32
template class DVAPI T3DPointT<int>;
template class DVAPI T3DPointT<double>;
#endif
//-----------------------------------------------------------------------------
//!\relates T3DPointT
template <class T>
inline T3DPointT<T> operator*(T a, const T3DPointT<T> &p) {
return T3DPointT<T>(a * p.x, a * p.y, a * p.z);
}
//!\relates TPointT
template <class T>
inline T3DPointT<T> operator*(const T3DPointT<T> &p, T a) {
return T3DPointT<T>(a * p.x, a * p.y, a * p.z);
}
//-----------------------------------------------------------------------------
/*!
\relates TPointT
This helper function returns the square of the absolute value of the specified
point (a TPointI)
*/
template <class T>
inline T norm2(const T3DPointT<T> &p) {
return p.x * p.x + p.y * p.y + p.z * p.z;
}
/*!
*/
template <class T>
inline T norm(const T3DPointT<T> &p) {
return std::sqrt(norm2(p));
}
/*!
*/
inline T3DPointD normalize(const T3DPointD &p) {
double n = norm(p);
assert(n != 0.0);
return (1.0 / n) * p;
}
/*!
*/
inline T3DPointD convert(const T3DPoint &p) { return T3DPointD(p.x, p.y, p.z); }
/*!
*/
inline T3DPoint convert(const T3DPointD &p) {
return T3DPoint(tround(p.x), tround(p.y), tround(p.z));
}
//!
template <class T>
inline T tdistance(const T3DPointT<T> &p1, const T3DPointT<T> &p2) {
return norm<T>(p2 - p1);
}
//!
template <class T>
inline T tdistance2(const T3DPointT<T> &p1, const T3DPointT<T> &p2) {
return norm2<T>(p2 - p1);
}
//!
template <class T>
inline T3DPointT<T> cross(const T3DPointT<T> &a, const T3DPointT<T> &b) {
return T3DPointT<T>(a.y * b.z - b.y * a.z, a.z * b.x - b.z * a.x,
a.x * b.y - b.x * a.y);
}
//=============================================================================
/*!
TThickPoint describe a thick point.
\relates TThickQuadratic, TThickCubic
*/
class DVAPI TThickPoint final : public TPointD {
public:
double thick;
TThickPoint() : TPointD(), thick(0) {}
TThickPoint(double _x, double _y, double _thick = 0)
: TPointD(_x, _y), thick(_thick) {}
TThickPoint(const TPointD &_p, double _thick = 0)
: TPointD(_p.x, _p.y), thick(_thick) {}
TThickPoint(const T3DPointD &_p) : TPointD(_p.x, _p.y), thick(_p.z) {}
TThickPoint(const TThickPoint &_p) : TPointD(_p.x, _p.y), thick(_p.thick) {}
inline TThickPoint &operator=(const TThickPoint &a) {
x = a.x;
y = a.y;
thick = a.thick;
return *this;
}
inline TThickPoint &operator+=(const TThickPoint &a) {
x += a.x;
y += a.y;
thick += a.thick;
return *this;
}
inline TThickPoint &operator-=(const TThickPoint &a) {
x -= a.x;
y -= a.y;
thick -= a.thick;
return *this;
}
inline TThickPoint operator+(const TThickPoint &a) const {
return TThickPoint(x + a.x, y + a.y, thick + a.thick);
}
inline TThickPoint operator-(const TThickPoint &a) const {
return TThickPoint(x - a.x, y - a.y, thick - a.thick);
}
inline TThickPoint operator-() const { return TThickPoint(-x, -y, -thick); }
bool operator==(const TThickPoint &p) const {
return x == p.x && y == p.y && thick == p.thick;
}
bool operator!=(const TThickPoint &p) const {
return x != p.x || y != p.y || thick != p.thick;
}
};
inline double operator*(const TThickPoint &a, const TThickPoint &b) {
return a.x * b.x + a.y * b.y + a.thick * b.thick;
}
inline TThickPoint operator*(double a, const TThickPoint &p) {
return TThickPoint(a * p.x, a * p.y, a * p.thick);
}
inline TThickPoint operator*(const TThickPoint &p, double a) {
return TThickPoint(a * p.x, a * p.y, a * p.thick);
}
/*!
\relates TPointD
This helper function converts a TThickPoint into a TPointD
*/
inline TPointD convert(const TThickPoint &p) { return TPointD(p.x, p.y); }
/*!
\relates TThickPoint
This helper function returns the square of the distance between two thick points
(only x and y are used)
*/
inline double tdistance2(const TThickPoint &p1, const TThickPoint &p2) {
return norm2(convert(p2 - p1));
}
/*!
\relates TThickPoint
This helper function returns the distance between two thick points
(only x and y are used)
*/
inline double tdistance(const TThickPoint &p1, const TThickPoint &p2) {
return norm(convert(p2 - p1));
}
inline std::ostream &operator<<(std::ostream &out, const TThickPoint &p) {
return out << "(" << p.x << ", " << p.y << ", " << p.thick << ")";
}
//=============================================================================
//! This is a template class representing a generic vector in a plane, i.e.
//! a point.
/*!
It is a data structure with two objects in it representing
coordinate of the point and
the basic operations on it.
*/
template <class T>
class DVAPI TDimensionT {
public:
T lx, ly;
/*!
Constructs a vector of two elements, i.e. a point in a plane.
*/
TDimensionT() : lx(), ly() {}
TDimensionT(T _lx, T _ly) : lx(_lx), ly(_ly) {}
/*!
Copy constructor.
*/
TDimensionT(const TDimensionT &d) : lx(d.lx), ly(d.ly) {}
/*!
Vector addition.
*/
TDimensionT &operator+=(TDimensionT a) {
lx += a.lx;
ly += a.ly;
return *this;
}
/*!
Difference of two vectors.
*/
TDimensionT &operator-=(TDimensionT a) {
lx -= a.lx;
ly -= a.ly;
return *this;
}
/*!
Addition of two vectors.
*/
TDimensionT operator+(TDimensionT a) const {
TDimensionT ris(*this);
return ris += a;
}
/*!
Vector difference.
*/
TDimensionT operator-(TDimensionT a) const {
TDimensionT ris(*this);
return ris -= a;
}
/*!
Compare vectors and returns \e true if are equals element by element.
*/
bool operator==(const TDimensionT &d) const {
return lx == d.lx && ly == d.ly;
}
/*!
Compare vectors and returns \e true if are not equals element by
element.
*/
bool operator!=(const TDimensionT &d) const { return !operator==(d); }
};
//=============================================================================
typedef TDimensionT<int> TDimension, TDimensionI;
typedef TDimensionT<double> TDimensionD;
//=============================================================================
template <class T>
inline std::ostream &operator<<(std::ostream &out, const TDimensionT<T> &p) {
return out << "(" << p.lx << ", " << p.ly << ")";
}
#ifdef _WIN32
template class DVAPI TDimensionT<int>;
template class DVAPI TDimensionT<double>;
#endif
//=============================================================================
//! Specifies the corners of a rectangle.
/*!
x0 specifies the x-coordinate of the bottom-left corner of a rectangle.
y0 specifies the y-coordinate of the bottom-left corner of a rectangle.
x1 specifies the x-coordinate of the upper-right corner of a rectangle.
y1 specifies the y-coordinate of the upper-right corner of a rectangle.
*/
template <class T>
class DVAPI TRectT {
public:
/*! if x0>x1 || y0>y1 then rect is empty
if x0==y1 && y0==y1 and rect is a TRectD then rect is empty */
T x0, y0;
T x1, y1;
/*! makes an empty rect */
TRectT();
TRectT(T _x0, T _y0, T _x1, T _y1) : x0(_x0), y0(_y0), x1(_x1), y1(_y1){};
TRectT(const TRectT &rect)
: x0(rect.x0), y0(rect.y0), x1(rect.x1), y1(rect.y1){};
TRectT(const TPointT<T> &p0, const TPointT<T> &p1) // non importa l'ordine
: x0(std::min((T)p0.x, (T)p1.x)),
y0(std::min((T)p0.y, (T)p1.y)),
x1(std::max((T)p0.x, (T)p1.x)),
y1(std::max((T)p0.y, (T)p1.y)){};
TRectT(const TPointT<T> &bottomLeft, const TDimensionT<T> &d);
TRectT(const TDimensionT<T> &d);
void empty();
/*! TRectD is empty if and only if (x0>x1 || y0>y1) || (x0==y1 && y0==y1);
TRectI is empty if x0>x1 || y0>y1 */
bool isEmpty() const;
T getLx() const;
T getLy() const;
TDimensionT<T> getSize() const { return TDimensionT<T>(getLx(), getLy()); };
TPointT<T> getP00() const { return TPointT<T>(x0, y0); };
TPointT<T> getP10() const { return TPointT<T>(x1, y0); };
TPointT<T> getP01() const { return TPointT<T>(x0, y1); };
TPointT<T> getP11() const { return TPointT<T>(x1, y1); };
//! Returns the union of two source rectangles.
//!The union is the smallest rectangle that contains both source rectangles.
TRectT<T> operator+(const TRectT<T> &rect) const { // unione
if (isEmpty())
return rect;
else if (rect.isEmpty())
return *this;
else
return TRectT<T>(std::min((T)x0, (T)rect.x0),
std::min((T)y0, (T)rect.y0),
std::max((T)x1, (T)rect.x1),
std::max((T)y1, (T)rect.y1));
};
TRectT<T> &operator+=(const TRectT<T> &rect) { // unione
return *this = *this + rect;
};
TRectT<T> &operator*=(const TRectT<T> &rect) { // intersezione
return *this = *this * rect;
};
//!Returns the intersection of two existing rectangles.
//The intersection is the largest rectangle contained in both existing rectangles.
TRectT<T> operator*(const TRectT<T> &rect) const { // intersezione
if (isEmpty() || rect.isEmpty())
return TRectT<T>();
else if (rect.x1 < x0 || x1 < rect.x0 || rect.y1 < y0 || y1 < rect.y0)
return TRectT<T>();
else
return TRectT<T>(std::max((T)x0, (T)rect.x0), std::max((T)y0, (T)rect.y0),
std::min((T)x1, (T)rect.x1),
std::min((T)y1, (T)rect.y1));
};
TRectT<T> &operator+=(const TPointT<T> &p) { // shift
x0 += p.x;
y0 += p.y;
x1 += p.x;
y1 += p.y;
return *this;
};
TRectT<T> &operator-=(const TPointT<T> &p) {
x0 -= p.x;
y0 -= p.y;
x1 -= p.x;
y1 -= p.y;
return *this;
};
TRectT<T> operator+(const TPointT<T> &p) const {
TRectT<T> ris(*this);
return ris += p;
};
TRectT<T> operator-(const TPointT<T> &p) const {
TRectT<T> ris(*this);
return ris -= p;
};
bool operator==(const TRectT<T> &r) const {
return x0 == r.x0 && y0 == r.y0 && x1 == r.x1 && y1 == r.y1;
};
bool operator!=(const TRectT<T> &r) const {
return x0 != r.x0 || y0 != r.y0 || x1 != r.x1 || y1 != r.y1;
};
bool contains(const TPointT<T> &p) const {
return x0 <= p.x && p.x <= x1 && y0 <= p.y && p.y <= y1;
};
bool contains(const TRectT<T> &b) const {
return x0 <= b.x0 && x1 >= b.x1 && y0 <= b.y0 && y1 >= b.y1;
};
bool overlaps(const TRectT<T> &b) const {
return x0 <= b.x1 && x1 >= b.x0 && y0 <= b.y1 && y1 >= b.y0;
};
TRectT<T> enlarge(T dx, T dy) const {
if (isEmpty()) return *this;
return TRectT<T>(x0 - dx, y0 - dy, x1 + dx, y1 + dy);
};
TRectT<T> enlarge(T d) const { return enlarge(d, d); };
TRectT<T> enlarge(TDimensionT<T> d) const { return enlarge(d.lx, d.ly); };
};
//-----------------------------------------------------------------------------
typedef TRectT<int> TRect, TRectI;
typedef TRectT<double> TRectD;
#ifdef _WIN32
template class DVAPI TRectT<int>;
template class DVAPI TRectT<double>;
#endif
//=============================================================================
// check this, not final version
/*!
\relates TRectT
Convert a TRectD into a TRect
*/
inline TRect convert(const TRectD &r) {
return TRect((int)(r.x0 + 0.5), (int)(r.y0 + 0.5), (int)(r.x1 + 0.5),
(int)(r.y1 + 0.5));
}
/*!
\relates TRectT
Convert a TRect into a TRectD
*/
inline TRectD convert(const TRect &r) { return TRectD(r.x0, r.y0, r.x1, r.y1); }
// template?
/*!
\relates TRectT
\relates TPointT
*/
inline TRectD boundingBox(const TPointD &p0, const TPointD &p1) {
return TRectD(std::min(p0.x, p1.x), std::min(p0.y, p1.y), // bottom left
std::max(p0.x, p1.x), std::max(p0.y, p1.y)); // top right
}
/*!
\relates TRectT
\relates TPointT
*/
inline TRectD boundingBox(const TPointD &p0, const TPointD &p1,
const TPointD &p2) {
return TRectD(std::min({p0.x, p1.x, p2.x}), std::min({p0.y, p1.y, p2.y}),
std::max({p0.x, p1.x, p2.x}), std::max({p0.y, p1.y, p2.y}));
}
/*!
\relates TRectT
\relates TPointT
*/
inline TRectD boundingBox(const TPointD &p0, const TPointD &p1,
const TPointD &p2, const TPointD &p3) {
return TRectD(
std::min({p0.x, p1.x, p2.x, p3.x}), std::min({p0.y, p1.y, p2.y, p3.y}),
std::max({p0.x, p1.x, p2.x, p3.x}), std::max({p0.y, p1.y, p2.y, p3.y}));
}
//-----------------------------------------------------------------------------
// TRectT is a rectangle that uses thick points
template <>
inline TRectT<int>::TRectT() : x0(0), y0(0), x1(-1), y1(-1) {}
template <>
inline TRectT<int>::TRectT(const TPointT<int> &bottomLeft,
const TDimensionT<int> &d)
: x0(bottomLeft.x)
, y0(bottomLeft.y)
, x1(bottomLeft.x + d.lx - 1)
, y1(bottomLeft.y + d.ly - 1){};
template <>
inline TRectT<int>::TRectT(const TDimensionT<int> &d)
: x0(0), y0(0), x1(d.lx - 1), y1(d.ly - 1){};
template <>
inline bool TRectT<int>::isEmpty() const {
return x0 > x1 || y0 > y1;
}
template <>
inline void TRectT<int>::empty() {
x0 = y0 = 0;
x1 = y1 = -1;
}
// Is the adding of one here to account for the thickness?
template <>
inline int TRectT<int>::getLx() const {
return x1 >= x0 ? x1 - x0 + 1 : 0;
}
template <>
inline int TRectT<int>::getLy() const {
return y1 >= y0 ? y1 - y0 + 1 : 0;
}
template <>
inline TRectT<double>::TRectT() : x0(0), y0(0), x1(0), y1(0) {}
template <>
inline TRectT<double>::TRectT(const TPointT<double> &bottomLeft,
const TDimensionT<double> &d)
: x0(bottomLeft.x)
, y0(bottomLeft.y)
, x1(bottomLeft.x + d.lx)
, y1(bottomLeft.y + d.ly){};
template <>
inline TRectT<double>::TRectT(const TDimensionT<double> &d)
: x0(0.0), y0(0.0), x1(d.lx), y1(d.ly){};
template <>
inline bool TRectT<double>::isEmpty() const {
return (x0 == x1 && y0 == y1) || x0 > x1 || y0 > y1;
}
template <>
inline void TRectT<double>::empty() {
x0 = y0 = x1 = y1 = 0;
}
template <>
inline double TRectT<double>::getLx() const {
return x1 >= x0 ? x1 - x0 : 0;
}
template <>
inline double TRectT<double>::getLy() const {
return y1 >= y0 ? y1 - y0 : 0;
}
//-----------------------------------------------------------------------------
inline TRectD &operator*=(TRectD &rect, double factor) {
rect.x0 *= factor;
rect.y0 *= factor;
rect.x1 *= factor;
rect.y1 *= factor;
return rect;
}
//-----------------------------------------------------------------------------
inline TRectD operator*(const TRectD &rect, double factor) {
TRectD result(rect);
return result *= factor;
}
//-----------------------------------------------------------------------------
inline TRectD &operator/=(TRectD &rect, double factor) {
assert(factor != 0.0);
return rect *= (1.0 / factor);
}
//-----------------------------------------------------------------------------
inline TRectD operator/(const TRectD &rect, double factor) {
assert(factor != 0.0);
TRectD result(rect);
return result *= 1.0 / factor;
}
//-----------------------------------------------------------------------------
template <class T>
inline std::ostream &operator<<(std::ostream &out, const TRectT<T> &r) {
return out << "(" << r.x0 << "," << r.y0 << ";" << r.x1 << "," << r.y1 << ")";
}
//=============================================================================
namespace TConsts {
extern DVVAR const TPointD napd;
extern DVVAR const TPoint nap;
extern DVVAR const T3DPointD nap3d;
extern DVVAR const TThickPoint natp;
extern DVVAR const TRectD infiniteRectD;
extern DVVAR const TRectI infiniteRectI;
}
//=============================================================================
//! This is the base class for the affine transformations.
/*!
This class performs basic manipulations of affine transformations.
An affine transformation is a linear transformation followed by a translation.
[a11, a12, a13]
[a21, a22, a23]
a13 and a23 represent translation (moving sideways or up and down)
the other 4 handle rotation, scale and shear
*/
class DVAPI TAffine {
public:
double a11, a12, a13;
double a21, a22, a23;
/*!
By default the object is initialized with a null matrix and a null
translation vector.
*/
TAffine() : a11(1.0), a12(0.0), a13(0.0), a21(0.0), a22(1.0), a23(0.0){};
/*!
Initializes the internal matrix and vector of translation with the
user values.
*/
TAffine(double p11, double p12, double p13, double p21, double p22,
double p23)
: a11(p11), a12(p12), a13(p13), a21(p21), a22(p22), a23(p23){};
/*!
Copy constructor.
*/
TAffine(const TAffine &a)
: a11(a.a11)
, a12(a.a12)
, a13(a.a13)
, a21(a.a21)
, a22(a.a22)
, a23(a.a23){};
/*!
Assignment operator.
*/
TAffine &operator=(const TAffine &a);
/*Moved to tgeometry.cpp
{
a11 = a.a11; a12 = a.a12; a13 = a.a13;
a21 = a.a21; a22 = a.a22; a23 = a.a23;
return *this;
};
*/
/*!
Matrix multiplication.
<p>\f$\left(\begin{array}{cc}\bf{A}&\vec{a}\\\vec{0}&1\end{array}\right)
\left(\begin{array}{cc}\bf{B}&\vec{b}\\\vec{0}&1\end{array}\right)\f$</p>
*/
TAffine operator*(const TAffine &b) const;
/*Moved to in tgeometry.cpp
{
return TAffine (
a11 * b.a11 + a12 * b.a21,
a11 * b.a12 + a12 * b.a22,
a11 * b.a13 + a12 * b.a23 + a13,
a21 * b.a11 + a22 * b.a21,
a21 * b.a12 + a22 * b.a22,
a21 * b.a13 + a22 * b.a23 + a23);
};
*/
TAffine operator*=(const TAffine &b);
/*Moved to tgeometry.cpp
{
return *this = *this * b;
};
*/
/*!
Returns the inverse tansformation as:
<p>\f$\left(\begin{array}{ccc}\bf{A}^{-1}&-\bf{A}^{-1}&\vec{b}\\\vec{0}&\vec{0}&1\end{array}\right)\f$</p>
*/
TAffine inv() const;
/*Moved to tgeometry.cpp
{
if(a12 == 0.0 && a21 == 0.0)
{
assert(a11 != 0.0);
assert(a22 != 0.0);
double inv_a11 = 1.0/a11;
double inv_a22 = 1.0/a22;
return TAffine(inv_a11,0, -a13 * inv_a11,
0,inv_a22, -a23 * inv_a22);
}
else if(a11 == 0.0 && a22 == 0.0)
{
assert(a12 != 0.0);
assert(a21 != 0.0);
double inv_a21 = 1.0/a21;
double inv_a12 = 1.0/a12;
return TAffine(0, inv_a21, -a23 * inv_a21,
inv_a12, 0, -a13 * inv_a12);
}
else
{
double d = 1./det();
return TAffine(a22*d,-a12*d, (a12*a23-a22*a13)*d,
-a21*d, a11*d, (a21*a13-a11*a23)*d);
}
};
*/
double det() const;
/*Sposto in tgeometry.cpp{
return a11*a22-a12*a21;
};
*/
/*!
Returns \e true if all elements are equals.
*/
bool operator==(const TAffine &a) const;
/*Sposto in tgeometry.cpp
{
return a11==a.a11 && a12==a.a12 && a13==a.a13 &&
a21==a.a21 && a22==a.a22 && a23==a.a23;
};
*/
/*!
Returns \e true if at least one element is different.
*/
bool operator!=(const TAffine &a) const;
/*Sposto in tgeometry.cpp
{
return a11!=a.a11 || a12!=a.a12 || a13!=a.a13 ||
a21!=a.a21 || a22!=a.a22 || a23!=a.a23;
};
*/
/*!
Returns \e true if the transformation is an identity,
i.e in the error limit \e err leaves the vectors unchanged.
*/
bool isIdentity(double err = 1.e-8) const;
/*Sposto in tgeometry.cpp
{
return ((a11-1.0)*(a11-1.0)+(a22-1.0)*(a22-1.0)+
a12*a12+a13*a13+a21*a21+a23*a23) < err;
};
*/
/*!
Returns \e true if in the error limits \e err \f$\bf{A}\f$ is the
identity matrix.
*/
bool isZero(double err = 1.e-8) const;
bool isTranslation(double err = 1.e-8) const;
/*Sposto in tgeometry.cpp
{
return ((a11-1.0)*(a11-1.0)+(a22-1.0)*(a22-1.0)+
a12*a12+a21*a21) < err;
};
*/
/*!
Returns \e true if in the error limits the matrix \f$\bf{A}\f$ is of
the form:
<p>\f$\left(\begin{array}{cc}a&b\\-b&a\end{array}\right)\f$</p>.
*/
bool isIsotropic(double err = 1.e-8) const;
/*Sposto in tgeometry.cpp
{
return areAlmostEqual(a11, a22, err) && areAlmostEqual(a12, -a21, err);
};
*/
/*!
Returns the transformed point.
*/
TPointD operator*(const TPointD &p) const;
/*Sposto in tgeometry.cpp
{
return TPointD(p.x*a11+p.y*a12+a13, p.x*a21+p.y*a22+a23);
};
*/
/*!
Transform point without translation
*/
TPointD transformDirection(const TPointD &p) const;
/*!
Retruns the transformed box of the bounding box.
*/
TRectD operator*(const TRectD &rect) const;
/*!
Returns a translated matrix that change the vector (u,v) in (x,y).
\n It returns a matrix of the form:
<p>\f$\left(\begin{array}{ccc}\bf{A}&\vec{x}-\bf{A} \vec{u}\\
\vec{0}&1\end{array}\right)\f$</p>
*/
TAffine place(double u, double v, double x, double y) const;
/*!
See above.
*/
TAffine place(const TPointD &pIn, const TPointD &pOut) const;
inline static TAffine identity()
{ return TAffine(); }
inline static TAffine zero()
{ return TAffine(0, 0, 0, 0, 0, 0); }
inline static TAffine translation(double x, double y)
{ return TAffine(1, 0, x, 0, 1, y); }
inline static TAffine translation(const TPointD &p)
{ return translation(p.x, p.y); }
inline static TAffine scale(double sx, double sy)
{ return TAffine(sx, 0, 0, 0, sy, 0); }
inline static TAffine scale(double s)
{ return scale(s, s); }
inline static TAffine scale(const TPointD ¢er, double sx, double sy)
{ return translation(center)*scale(sx, sy)*translation(-center); }
inline static TAffine scale(const TPointD ¢er, double s)
{ return scale(center, s, s); }
static TAffine rotation(double angle);
inline static TAffine rotation(const TPointD ¢er, double angle)
{ return translation(center)*rotation(angle)*translation(-center); }
inline static TAffine shear(double sx, double sy)
{ return TAffine(1, sx, 0, sy, 1, 0); }
};
//-----------------------------------------------------------------------------
// template <>
inline bool areAlmostEqual(const TPointD &a, const TPointD &b,
double err = TConsts::epsilon) {
return tdistance2(a, b) < err * err;
}
// template <>
inline bool areAlmostEqual(const TRectD &a, const TRectD &b,
double err = TConsts::epsilon) {
return areAlmostEqual(a.getP00(), b.getP00(), err) &&
areAlmostEqual(a.getP11(), b.getP11(), err);
}
const TAffine AffI = TAffine();
//-----------------------------------------------------------------------------
class DVAPI TTranslation final : public TAffine {
public:
TTranslation(){};
TTranslation(double x, double y) : TAffine(1, 0, x, 0, 1, y){};
TTranslation(const TPointD &p) : TAffine(1, 0, p.x, 0, 1, p.y){};
};
//-----------------------------------------------------------------------------
class DVAPI TRotation final : public TAffine {
public:
TRotation(){};
/*! makes a rotation matrix of "degrees" degrees counterclockwise
on the origin */
TRotation(double degrees);
/*Sposto in tgeometry.cpp
{
double rad, sn, cs;
int idegrees = (int)degrees;
if ((double)idegrees == degrees && idegrees % 90 == 0)
{
switch ((idegrees / 90) & 3)
{
case 0: sn = 0; cs = 1; break;
case 1: sn = 1; cs = 0; break;
case 2: sn = 0; cs = -1; break;
case 3: sn = -1; cs = 0; break;
default: sn = 0; cs = 0; break;
}
}
else
{
rad = degrees * (TConsts::pi_180);
sn = sin (rad);
cs = cos (rad);
if (sn == 1 || sn == -1)
cs = 0;
if (cs == 1 || cs == -1)
sn = 0;
}
a11=cs;a12= -sn;a21= -a12;a22=a11;
};
*/
/*! makes a rotation matrix of "degrees" degrees counterclockwise
on the given center */
TRotation(const TPointD ¢er, double degrees);
/*Sposto in tgeometry.cpp
{
TAffine a = TTranslation(center) * TRotation(degrees) * TTranslation(-center);
a11 = a.a11; a12 = a.a12; a13 = a.a13;
a21 = a.a21; a22 = a.a22; a23 = a.a23;
};
*/
};
//-----------------------------------------------------------------------------
class DVAPI TScale final : public TAffine {
public:
TScale(){};
TScale(double sx, double sy) : TAffine(sx, 0, 0, 0, sy, 0){};
TScale(double s) : TAffine(s, 0, 0, 0, s, 0) {}
TScale(const TPointD ¢er, double sx, double sy);
/*Sposto in tgeometry.cpp
{
TAffine a = TTranslation(center) * TScale(sx,sy) * TTranslation(-center);
a11 = a.a11; a12 = a.a12; a13 = a.a13;
a21 = a.a21; a22 = a.a22; a23 = a.a23;
}
*/
TScale(const TPointD ¢er, double s);
/*Sposto in tgeometry.cpp
{
TAffine a = TTranslation(center) * TScale(s) * TTranslation(-center);
a11 = a.a11; a12 = a.a12; a13 = a.a13;
a21 = a.a21; a22 = a.a22; a23 = a.a23;
}
*/
};
//-----------------------------------------------------------------------------
class DVAPI TShear final : public TAffine {
public:
TShear(){};
TShear(double sx, double sy) : TAffine(1, sx, 0, sy, 1, 0){};
};
//-----------------------------------------------------------------------------
inline bool areEquals(const TAffine &a, const TAffine &b, double err = 1e-8) {
return fabs(a.a11 - b.a11) < err && fabs(a.a12 - b.a12) < err &&
fabs(a.a13 - b.a13) < err && fabs(a.a21 - b.a21) < err &&
fabs(a.a22 - b.a22) < err && fabs(a.a23 - b.a23) < err;
}
//-----------------------------------------------------------------------------
inline TAffine inv(const TAffine &a) { return a.inv(); }
//-----------------------------------------------------------------------------
inline std::ostream &operator<<(std::ostream &out, const TAffine &a) {
return out << "(" << a.a11 << ", " << a.a12 << ", " << a.a13 << ";" << a.a21
<< ", " << a.a22 << ", " << a.a23 << ")";
}
//=============================================================================
//! This class performs basic manipulations of affine transformations in 3D space.
//! the matrix is transposed to TAffine and equal to OpenGL
class DVAPI TAffine4 {
public:
union {
struct {
double a11, a12, a13, a14;
double a21, a22, a23, a24;
double a31, a32, a33, a34;
double a41, a42, a43, a44;
};
double m[4][4];
double a[16];
};
inline TAffine4():
a11(1.0), a12(0.0), a13(0.0), a14(0.0),
a21(0.0), a22(1.0), a23(0.0), a24(0.0),
a31(0.0), a32(0.0), a33(1.0), a34(0.0),
a41(0.0), a42(0.0), a43(0.0), a44(1.0) { }
inline explicit TAffine4(const TAffine &a):
a11(a.a11), a12(a.a21), a13(0.0), a14(0.0),
a21(a.a12), a22(a.a22), a23(0.0), a24(0.0),
a31( 0.0 ), a32( 0.0 ), a33(1.0), a34(0.0),
a41(a.a13), a42(a.a23), a43(0.0), a44(1.0) { }
inline TAffine4(
const TPoint4D &rowX,
const TPoint4D &rowY,
const TPoint4D &rowZ,
const TPoint4D &rowW
):
a11(rowX.x), a12(rowX.y), a13(rowX.z), a14(rowX.w),
a21(rowY.x), a22(rowY.y), a23(rowY.z), a24(rowY.w),
a31(rowZ.x), a32(rowZ.y), a33(rowZ.z), a34(rowZ.w),
a41(rowW.x), a42(rowW.y), a43(rowW.z), a44(rowW.w) { }
inline TPoint4D& row(int index)
{ return *(TPoint4D*)(m[index]); }
inline const TPoint4D& row(int index) const
{ return *(const TPoint4D*)(m[index]); }
inline TPoint4D& rowX() { return row(0); }
inline TPoint4D& rowY() { return row(1); }
inline TPoint4D& rowZ() { return row(2); }
inline TPoint4D& rowW() { return row(3); }
inline const TPoint4D& rowX() const { return row(0); }
inline const TPoint4D& rowY() const { return row(1); }
inline const TPoint4D& rowZ() const { return row(2); }
inline const TPoint4D& rowW() const { return row(3); }
TPoint4D operator*(const TPoint4D &b) const;
TAffine4 operator*(const TAffine4 &b) const;
TAffine4 operator*=(const TAffine4 &b);
TAffine4 inv() const;
TAffine get2d(double z = 0.0) const;
inline static TAffine4 identity() { return TAffine4(); }
static TAffine4 translation(double x, double y, double z);
static TAffine4 scale(double x, double y, double z);
static TAffine4 rotation(double x, double y, double z, double angle);
static TAffine4 rotationX(double angle);
static TAffine4 rotationY(double angle);
static TAffine4 rotationZ(double angle);
static TAffine4 perspective(double near, double far, double tangent);
};
//=============================================================================
//! This class performs binary manipulations with angle ranges
typedef unsigned int TAngleI;
class DVAPI TAngleRangeSet {
public:
typedef TAngleI Type;
typedef std::vector<Type> List;
static const Type min = Type();
static const Type max = Type() - Type(1);
static const Type half = ((Type() - Type(1)) >> 1) + Type(1);
static Type fromDouble(double a)
{ return Type(round((a/M_2PI + 0.5)*max)); }
static double toDouble(Type a)
{ return ((double)a/(double)max - 0.5)*M_2PI; }
static List::const_iterator empty_iterator()
{ static List list; return list.end(); }
struct Range {
Type a0, a1;
Range(): a0(), a1() { }
Range(Type a0, Type a1): a0(a0), a1(a1) { }
inline bool isEmpty() const { return a0 == a1; }
inline Range flip() const { return Range(a1, a0); }
};
struct Iterator {
private:
bool m_flip;
List::const_iterator m_prebegin;
List::const_iterator m_begin;
List::const_iterator m_end;
List::const_iterator m_current;
bool m_lapped;
public:
inline Iterator(): m_flip(), m_lapped(true)
{ reset(); }
inline explicit Iterator(const List &list, bool flip = false, bool reverse = false)
{ set(list, flip, reverse); }
inline explicit Iterator(const TAngleRangeSet &ranges, bool flip = false, bool reverse = false)
{ set(ranges, flip, reverse); }
inline Iterator& set(bool full) {
m_flip = full; m_lapped = !m_flip;
m_current = m_prebegin = m_begin = m_end = empty_iterator();
return *this;
}
inline Iterator& reset()
{ return set(false); }
inline Iterator& set(const List &list, bool flip = false, bool reverse = false) {
assert(list.size()%2 == 0);
if (list.empty()) {
set(flip);
} else {
m_flip = flip;
m_lapped = false;
if (flip) {
m_prebegin = list.end() - 1;
m_begin = list.begin();
m_end = m_prebegin - 1;
} else {
m_prebegin = list.begin();
m_begin = m_prebegin + 1;
m_end = list.end() - 1;
}
}
m_current = reverse ? m_end : m_begin;
return *this;
}
inline Iterator& set(const TAngleRangeSet &ranges, bool flip = false, bool reverse = false)
{ return set(ranges.angles(), ranges.isFlipped() != flip, reverse); }
inline const Type a0() const
{ return valid() ? *(m_current == m_begin ? m_prebegin : m_current - 1) : Type(); }
inline const Type a1() const
{ return valid() ? *m_current : Type(); }
inline double d0() const
{ return toDouble(a0()); }
inline double d1() const
{ return toDouble(a1()); }
inline double d1greater() const {
return !valid() ? (m_flip ? M_PI : -M_PI)
: m_current == m_begin && m_prebegin > m_begin
? toDouble(*m_current) + M_2PI : toDouble(*m_current);
}
inline Range range() const
{ return Range(a0(), a1()); }
inline int size() const
{ return (m_end - m_begin)/2 + 1; }
inline int index() const
{ return (m_current - m_begin)/2; }
inline int reverseIndex() const
{ int i = index(); return i == 0 ? 0 : size() - i; }
inline bool lapped() const
{ return m_lapped; }
inline bool valid() const
{ return m_prebegin != m_begin; }
inline bool isFull() const
{ return !valid() && m_flip; }
inline bool isEmpty() const
{ return !valid() && !m_flip; }
inline operator bool() const
{ return !m_lapped; }
inline Iterator& operator++() {
if (!valid()) { m_lapped = true; return *this; }
m_lapped = (m_current == m_end);
if (m_lapped) m_current = m_begin; else m_current += 2;
return *this;
}
inline Iterator& operator--() {
if (!valid()) { m_lapped = true; return *this; }
m_lapped = (m_current == m_end);
if (m_lapped) m_current = m_end; else m_current -= 2;
return *this;
}
inline Iterator& operator += (int i) {
if (i == 0) { m_lapped = isEmpty(); return *this; }
if (!valid()) { m_lapped = true; return *this; }
int ii = index();
int s = size();
if (ii + i >= 0 && ii + i < s) {
m_current += i*2;
m_lapped = false;
} else {
m_current = m_begin + ((ii + s + i%s)%s)*2;
m_lapped = true;
}
return *this;
}
inline int operator-(const Iterator &i) const {
assert(m_flip == i.m_flip && m_begin == i.m_begin && m_end == i.m_end && m_prebegin == i.m_prebegin);
int ii = (int)(m_current - i.m_current);
return ii < 0 ? ii + size() : ii;
}
inline Iterator operator++() const
{ Iterator copy(*this); ++(*this); return copy; }
inline Iterator operator--() const
{ Iterator copy(*this); --(*this); return copy; }
inline Iterator& operator -= (int i)
{ return (*this) += -i; }
inline Iterator operator+(int i) const
{ Iterator ii(*this); return ii += i; }
inline Iterator operator-(int i) const
{ Iterator ii(*this); return ii -= i; }
};
private:
bool m_flip;
List m_angles;
int find(Type a) const;
void insert(Type a);
void doAdd(Type a0, Type a1);
public:
inline explicit TAngleRangeSet(bool fill = false): m_flip(fill) { }
inline TAngleRangeSet(const TAngleRangeSet &x, bool flip = false):
m_flip(x.isFlipped() != flip), m_angles(x.angles()) { }
inline const List& angles() const { return m_angles; }
inline bool isFlipped() const { return m_flip; }
inline bool isEmpty() const { return !m_flip && m_angles.empty(); }
inline bool isFull() const { return m_flip && m_angles.empty(); }
bool contains(Type a) const;
bool check() const;
inline void clear() { m_flip = false; m_angles.clear(); }
inline void fill() { m_flip = true; m_angles.clear(); }
inline void invert() { m_flip = !m_flip; }
void set(Type a0, Type a1);
void set(const TAngleRangeSet &x, bool flip = false);
//! also known as 'xor'
void invert(Type a0, Type a1);
inline void invert(const Range &x) { invert(x.a0, x.a1); }
void invert(const TAngleRangeSet &x);
void add(Type a0, Type a1);
inline void add(const Range &x) { add(x.a0, x.a1); }
void add(const TAngleRangeSet &x);
void subtract(Type a0, Type a1);
inline void subtract(const Range &x) { subtract(x.a0, x.a1); }
void subtract(const TAngleRangeSet &x);
void intersect(Type a0, Type a1);
inline void intersect(const Range &x) { intersect(x.a0, x.a1); }
void intersect(const TAngleRangeSet &x);
};
#endif // __T_GEOMETRY_INCLUDED__