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math3d_d.h /* Copyright (C) 1998,1999,2000 by Jorrit Tyberghein Largely rewritten by Ivan Avramovic <ivan@avramovic.com> 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 "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 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; 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 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 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 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 Area3 (const csDVector3 &a, const csDVector3 &b, const csDVector3 &c) { csDVector3 v1 = b - a; csDVector3 v2 = c - a; return ((v1.y * v2.z + v1.z * v2.x + v1.x * v2.y) - (v1.y * v2.x + v1.x * v2.z + v1.z * v2.y)); } 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 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 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__ Generated for Crystal Space by doxygen 1.2.5 written by Dimitri van Heesch, ©1997-2000