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csgeom/math3d_d.h

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/*
    Copyright (C) 1998,1999,2000 by Jorrit Tyberghein
    Largely rewritten by Ivan Avramovic <[email protected]>
    Converted to double by Thomas Hieber

    This library is free software; you can redistribute it and/or
    modify it under the terms of the GNU Library General Public
    License as published by the Free Software Foundation; either
    version 2 of the License, or (at your option) any later version.

    This library 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
    Library General Public License for more details.

    You should have received a copy of the GNU Library General Public
    License along with this library; if not, write to the Free
    Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
*/

#ifndef __CS_MATH3D_D_H__
#define __CS_MATH3D_D_H__

#include "csextern.h"

#include "cstypes.h"

#ifndef ABS
#define ABS(x) ((x)<0?-(x):(x))
#endif

class csDVector3;
class csDMatrix3;
class csVector3;

inline double dSqr (double d)
{
  return d * d;
}

class CS_CRYSTALSPACE_EXPORT csDVector3
{
public:
  double x;
  double y;
  double z;

  csDVector3 () {}

  csDVector3 (double m) : x(m), y(m), z(m) {}

  csDVector3 (double ix, double iy, double iz = 0) { x = ix; y = iy; z = iz; }

  csDVector3 (const csDVector3& v) { x = v.x; y = v.y; z = v.z; }

  csDVector3 (const csVector3&);

  inline friend
  csDVector3 operator+ (const csDVector3& v1, const csDVector3& v2)
  { return csDVector3(v1.x+v2.x, v1.y+v2.y, v1.z+v2.z); }

  inline friend
  csDVector3 operator- (const csDVector3& v1, const csDVector3& v2)
  { return csDVector3(v1.x-v2.x, v1.y-v2.y, v1.z-v2.z); }

  inline friend double operator* (const csDVector3& v1, const csDVector3& v2)
  { return v1.x*v2.x + v1.y*v2.y + v1.z*v2.z; }

  inline friend
  csDVector3 operator% (const csDVector3& v1, const csDVector3& v2)
  {
    return csDVector3 (v1.y*v2.z-v1.z*v2.y,
                       v1.z*v2.x-v1.x*v2.z,
                       v1.x*v2.y-v1.y*v2.x);
  }

  void Cross (const csDVector3 & px, const csDVector3 & py)
  {
    x = px.y*py.z - px.z*py.y;
    y = px.z*py.x - px.x*py.z;
    z = px.x*py.y - px.y*py.x;
  }

  inline friend csDVector3 operator* (const csDVector3& v, double f)
  { return csDVector3(v.x*f, v.y*f, v.z*f); }

  inline friend csDVector3 operator* (double f, const csDVector3& v)
  { return csDVector3(v.x*f, v.y*f, v.z*f); }

  inline friend csDVector3 operator/ (const csDVector3& v, double f)
  { f = 1.0f/f; return csDVector3(v.x*f, v.y*f, v.z*f); }

  inline friend bool operator== (const csDVector3& v1, const csDVector3& v2)
  { return v1.x==v2.x && v1.y==v2.y && v1.z==v2.z; }

  inline friend bool operator!= (const csDVector3& v1, const csDVector3& v2)
  { return v1.x!=v2.x || v1.y!=v2.y || v1.z!=v2.z; }

  inline friend
  csDVector3 operator>> (const csDVector3& v1, const csDVector3& v2)
  { return v2*(v1*v2)/(v2*v2); }

  inline friend
  csDVector3 operator<< (const csDVector3& v1, const csDVector3& v2)
  { return v1*(v1*v2)/(v1*v1); }

  inline friend bool operator< (const csDVector3& v, double f)
  { return ABS(v.x)<f && ABS(v.y)<f && ABS(v.z)<f; }

  inline friend bool operator> (double f, const csDVector3& v)
  { return ABS(v.x)<f && ABS(v.y)<f && ABS(v.z)<f; }

  inline double operator[](int n) const {return !n?x:n&1?y:z;}

  inline double & operator[](int n){return !n?x:n&1?y:z;}

  inline csDVector3& operator+= (const csDVector3& v)
  {
    x += v.x;
    y += v.y;
    z += v.z;

    return *this;
  }

  inline csDVector3& operator-= (const csDVector3& v)
  {
    x -= v.x;
    y -= v.y;
    z -= v.z;

    return *this;
  }

  inline csDVector3& operator*= (double f)
  { x *= f; y *= f; z *= f; return *this; }

  inline csDVector3& operator/= (double f)
  { x /= f; y /= f; z /= f; return *this; }

  inline csDVector3 operator+ () const { return *this; }

  inline csDVector3 operator- () const { return csDVector3(-x,-y,-z); }

  inline void Set (double sx, double sy, double sz) { x = sx; y = sy; z = sz; }

  double Norm () const;

  double SquaredNorm () const;

  csDVector3 Unit () const { return (*this)/(this->Norm()); }

  inline static double Norm (const csDVector3& v) { return v.Norm(); }

  inline static csDVector3 Unit (const csDVector3& v) { return v.Unit(); }

  void Normalize();
};


class CS_CRYSTALSPACE_EXPORT csDMatrix3
{
public:
  double m11, m12, m13;
  double m21, m22, m23;
  double m31, m32, m33;

public:
  csDMatrix3 ();

  csDMatrix3 (double m11, double m12, double m13,
            double m21, double m22, double m23,
            double m31, double m32, double m33);

  inline csDVector3 Row1() const { return csDVector3 (m11,m12,m13); }

  inline csDVector3 Row2() const { return csDVector3 (m21,m22,m23); }

  inline csDVector3 Row3() const { return csDVector3 (m31,m32,m33); }

  inline csDVector3 Col1() const { return csDVector3 (m11,m21,m31); }

  inline csDVector3 Col2() const { return csDVector3 (m12,m22,m32); }

  inline csDVector3 Col3() const { return csDVector3 (m13,m23,m33); }

  inline void Set (double m11, double m12, double m13,
                   double m21, double m22, double m23,
                   double m31, double m32, double m33)
  {
    csDMatrix3::m11 = m11; csDMatrix3::m12 = m12; csDMatrix3::m13 = m13;
    csDMatrix3::m21 = m21; csDMatrix3::m22 = m22; csDMatrix3::m23 = m23;
    csDMatrix3::m31 = m31; csDMatrix3::m32 = m32; csDMatrix3::m33 = m33;
  }

  csDMatrix3& operator+= (const csDMatrix3& m);

  csDMatrix3& operator-= (const csDMatrix3& m);

  csDMatrix3& operator*= (const csDMatrix3& m);

  csDMatrix3& operator*= (double s);

  csDMatrix3& operator/= (double s);

  inline csDMatrix3 operator+ () const { return *this; }
  inline csDMatrix3 operator- () const
  {
   return csDMatrix3(-m11,-m12,-m13,
                    -m21,-m22,-m23,
                    -m31,-m32,-m33);
  }

  void Transpose ();

  csDMatrix3 GetTranspose () const;

  inline csDMatrix3 GetInverse () const
  {
    csDMatrix3 C(
             (m22*m33 - m23*m32), -(m12*m33 - m13*m32),  (m12*m23 - m13*m22),
            -(m21*m33 - m23*m31),  (m11*m33 - m13*m31), -(m11*m23 - m13*m21),
             (m21*m32 - m22*m31), -(m11*m32 - m12*m31),  (m11*m22 - m12*m21) );
    double s = (double)1./(m11*C.m11 + m12*C.m21 + m13*C.m31);

    C *= s;

    return C;
  }

  void Invert() { *this = GetInverse (); }

  double Determinant () const;

  void Identity ();

  friend csDMatrix3 operator+ (const csDMatrix3& m1, const csDMatrix3& m2);
  friend csDMatrix3 operator- (const csDMatrix3& m1, const csDMatrix3& m2);
  friend csDMatrix3 operator* (const csDMatrix3& m1, const csDMatrix3& m2);

  inline friend csDVector3 operator* (const csDMatrix3& m, const csDVector3& v)
  {
   return csDVector3 (m.m11*v.x + m.m12*v.y + m.m13*v.z,
                     m.m21*v.x + m.m22*v.y + m.m23*v.z,
                     m.m31*v.x + m.m32*v.y + m.m33*v.z);
  }

  friend csDMatrix3 operator* (const csDMatrix3& m, double f);
  friend csDMatrix3 operator* (double f, const csDMatrix3& m);
  friend csDMatrix3 operator/ (const csDMatrix3& m, double f);
  friend bool operator== (const csDMatrix3& m1, const csDMatrix3& m2);
  friend bool operator!= (const csDMatrix3& m1, const csDMatrix3& m2);
  friend bool operator< (const csDMatrix3& m, double f);
  friend bool operator> (double f, const csDMatrix3& m);
};


class CS_CRYSTALSPACE_EXPORT csDPlane
{
public:
  csDVector3 norm;

  double DD;

  csDPlane () : norm(0,0,1), DD(0) {}

  csDPlane (const csDVector3& plane_norm, double d=0) :
  norm(plane_norm), DD(d) {}

  csDPlane (double a, double b, double c, double d=0) : norm(a,b,c), DD(d) {}

  inline csDVector3& Normal () { return norm; }
  inline const csDVector3& Normal () const { return norm; }

  inline double A () const { return norm.x; }
  inline double B () const { return norm.y; }
  inline double C () const { return norm.z; }
  inline double D () const { return DD; }

  inline double& A () { return norm.x; }
  inline double& B () { return norm.y; }
  inline double& C () { return norm.z; }
  inline double& D () { return DD; }

  inline void Set (double a, double b, double c, double d)
   { norm.x = a; norm.y = b; norm.z = c; DD = d; }

  inline double Classify (const csDVector3& pt) const { return norm*pt+DD; }

  static double Classify (double A, double B, double C, double D,
                         const csDVector3& pt)
  { return A*pt.x + B*pt.y + C*pt.z + D; }

  inline double Distance (const csDVector3& pt) const
  { return ABS (Classify (pt)); }

  void Invert () { norm = -norm;  DD = -DD; }

  void Normalize ()
  {
    double f = norm.Norm ();
    if (f) { norm /= f;  DD /= f; }
  }

};

class CS_CRYSTALSPACE_EXPORT csDMath3
{
public:
  static int WhichSide3D (const csDVector3& p,
                          const csDVector3& v1, const csDVector3& v2)
  {
    // double s = p * (v1%v2); (original expression: expanded to the below:)
    double s = p.x*(v1.y*v2.z-v1.z*v2.y) + p.y*(v1.z*v2.x-v1.x*v2.z) +
              p.z*(v1.x*v2.y-v1.y*v2.x);
    if (s < 0) return 1;
    else if (s > 0) return -1;
    else return 0;
  }

  static bool Visible (const csDVector3& p, const csDVector3& t1,
                       const csDVector3& t2, const csDVector3& t3);

  static bool Visible (const csDVector3& p, const csDPlane& pl)
  { return pl.Classify (p) <= 0; }

  static void Between (const csDVector3& v1, const csDVector3& v2,
                       csDVector3& v, double pct, double wid);

  static void SetMinMax (const csDVector3& v,
                         csDVector3& min, csDVector3& max)
  {
    if (v.x > max.x) max.x = v.x; else if (v.x < min.x ) min.x = v.x;
    if (v.y > max.y) max.y = v.y; else if (v.y < min.y ) min.y = v.y;
    if (v.z > max.z) max.z = v.z; else if (v.z < min.z ) min.z = v.z;
  }

  inline static double DoubleArea3 (const csDVector3 &a, const csDVector3 &b,
                             const csDVector3 &c)
  {
    csDVector3 v1 = b - a;
    csDVector3 v2 = c - a;
    return (v1 % v2).Norm ();
  }

  inline static void CalcNormal (csDVector3& norm,     const csDVector3& v1,
                                 const csDVector3& v2, const csDVector3& v3)
  {
    norm = (v1-v2)%(v1-v3);
  }

  static void CalcNormal (csDVector3& norm,
                          const csDVector3& v, const csDVector3& u)
  { norm = u%v; /* NOT v%u - vertexes are defined clockwise */ }

  static void CalcPlane (const csDVector3& v1, const csDVector3& v2,
         const csDVector3& v3, csDVector3& normal, double& D)
  {
    normal = (v1-v2)%(v1-v3);
    D = - (normal * v1);
  }

  static bool PlanesEqual (const csDPlane& p1, const csDPlane& p2)
  {
    return ( ( p1.norm - p2.norm) < (double).001 ) &&
             (  ABS (p1.DD-p2.DD) < (double).001 );
  }

  static bool PlanesClose (const csDPlane& p1, const csDPlane& p2);
};

class CS_CRYSTALSPACE_EXPORT csDSquaredDist
{
public:
  static double PointPoint (const csDVector3& p1, const csDVector3& p2)
  { return dSqr (p1.x - p2.x) + dSqr (p1.y - p2.y) + dSqr (p1.z - p2.z); }

  static double PointLine (const csDVector3& p,
                          const csDVector3& l1, const csDVector3& l2);

  static double PointPlane (const csDVector3& p, const csDPlane& plane)
  { double r = plane.Classify (p);  return r * r; }

  static double PointPoly (const csDVector3& p, csDVector3 *V, int n,
                          const csDPlane& plane, double sqdist = -1);
};

class CS_CRYSTALSPACE_EXPORT csDIntersect3
{
public:
  static void Plane (
    const csDVector3& u, const csDVector3& v, // segment
    const csDVector3& normal, const csDVector3& a, // plane
    csDVector3& isect);                    // intersection point

  static bool Plane (
    const csDVector3& u, const csDVector3& v, // segment
    double A, double B, double C, double D, // plane Ax+By+Cz+D=0
    csDVector3& isect,                     // intersection point
    double& dist);                       // distance from u to isect

  static bool Plane (
    const csDVector3& u, const csDVector3& v, // segment
    const csDPlane& p,                     // plane Ax+By+Cz+D=0
    csDVector3& isect,                     // intersection point
    double& dist);                       // distance from u to isect

  static bool Planes(const csDPlane& p1, const csDPlane& p2,
                     const csDPlane& p3, csDVector3& isect);

  static double Z0Plane (
    const csDVector3& u, const csDVector3& v, // segment
    csDVector3& isect);                    // intersection point

  static double ZPlane (double zval,      // plane z = zval
    const csDVector3& u, const csDVector3& v, // segment
    csDVector3& isect);                    // intersection point

  static double XFrustum (
    double A, const csDVector3& u, const csDVector3& v, csDVector3& isect);

  static double YFrustum (
    double B, const csDVector3& u, const csDVector3& v, csDVector3& isect);
};

#endif // __CS_MATH3D_D_H__

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