colobot/src/math/point.h

// * This file is part of the COLOBOT source code
// * Copyright (C) 2012, Polish Portal of Colobot (PPC)
// *
// * This program is free software: you can redistribute it and/or modify
// * it under the terms of the GNU General Public License as published by
// * the Free Software Foundation, either version 3 of the License, or
// * (at your option) any later version.
// *
// * This program is distributed in the hope that it will be useful,
// * but WITHOUT ANY WARRANTY; without even the implied warranty of
// * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// * GNU General Public License for more details.
// *
// * You should have received a copy of the GNU General Public License
// * along with this program. If not, see  http://www.gnu.org/licenses/.

/** @defgroup MathPointModule math/point.h
   Contains the Point struct and related functions.
 */

#pragma once

#include "const.h"
#include "func.h"

#include <cmath>


/* TODO

 FPOINT    RotatePoint(FPOINT center, float angle, FPOINT p);
 FPOINT    RotatePoint(float angle, FPOINT p);
 FPOINT    RotatePoint(float angle, float dist);
 void      RotatePoint(float cx, float cy, float angle, float &px, float &py);

 float   RotateAngle(FPOINT center, FPOINT p1, FPOINT p2);
 
 */

// Math module namespace
namespace Math
{

/* @{ */ // start of group

/** \struct Point math/point.h
    \brief 2D point

  Represents a 2D point (x, y).
  Contains the required methods for operating on points.

  All methods are made inline to maximize optimization.

 */
struct Point
{
  //! X coord
  float x;
  //! Y coord
  float y;

  //! Constructs a zero point: (0,0)
  inline Point()
  {
    LoadZero();
  }

  //! Constructs a point from given coords: (x,y)
  inline Point(float x, float y)
  {
    this->x = x;
    this->y = y;
  }

  //! Sets the zero point: (0,0)
  inline void LoadZero()
  {
    x = y = 0.0f;
  }

  //! Returns the distance from (0,0) to the point (x,y)
  inline float Length()
  {
    return std::sqrt(x*x + y*y);
  }
};

//! Permutes two points
inline void Swap(Point &a, Point &b)
{
  Point  c;

  c = a;
  a = b;
  b = c;
}

//! Returns the distance between two points
inline float Distance(const Point &a, const Point &b)
{
  return sqrt((a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y));
}

//! Returns py up on the line \a a - \a b
inline float MidPoint(const Point &a, const Point &b, float px)
{
  if (IsEqual(a.x, b.x))
  {
    if (a.y < b.y)
      return HUGE;
    else
      return -HUGE;
  }
  return (b.y-a.y) * (px-a.x) / (b.x-a.x)  + a.y;
}

//! Calculates the parameters a and b of the linear function passing through \a p1 and \a p2
/** Returns \c false if the line is vertical.
  \param p1,p2 points
  \param a,b linear function parameters */
inline bool LinearFunction(const Point &p1, const Point &p2, float &a, float &b)
{
  if ( IsZero(p1.x-p2.x) )
  {
    a = HUGE;
    b = p2.x;
    return false;
  }

  a = (p2.y-p1.y) / (p2.x-p1.x);
  b = p2.y - p2.x*a;

  return true;
}

//! Checks if the point is inside triangle defined by vertices \a a, \a b, \a c
inline bool IsInsideTriangle(Point a, Point b, Point c, const Point &p)
{
  if ( p.x < a.x && p.x < b.x && p.x < c.x )  return false;
  if ( p.x > a.x && p.x > b.x && p.x > c.x )  return false;
  if ( p.y < a.y && p.y < b.y && p.y < c.y )  return false;
  if ( p.y > a.y && p.y > b.y && p.y > c.y )  return false;

  if ( a.x > b.x ) Swap(a,b);
  if ( a.x > c.x ) Swap(a,c);
  if ( c.x < a.x ) Swap(c,a);
  if ( c.x < b.x ) Swap(c,b);

  float n, m;

  n = MidPoint(a, b, p.x);
  m = MidPoint(a, c, p.x);
  if ( (n>p.y || p.y>m) && (n<p.y || p.y<m) )
    return false;

  n = MidPoint(c, b, p.x);
  m = MidPoint(c, a, p.x);
  if ( (n>p.y || p.y>m) && (n<p.y || p.y<m) )
    return false;

  return true;
}

/* @} */ // end of group

}; // namespace Math