al_Matrix4.hpp

#ifndef INCLUDE_AL_MATRIX4_HPP
#define INCLUDE_AL_MATRIX4_HPP
 
/*  Allocore --
  Multimedia / virtual environment application class library
 
  Copyright (C) 2009. AlloSphere Research Group, Media Arts & Technology, UCSB.
  Copyright (C) 2012. The Regents of the University of California.
  All rights reserved.
 
  Redistribution and use in source and binary forms, with or without
  modification, are permitted provided that the following conditions are met:
 
    Redistributions of source code must retain the above copyright notice,
    this list of conditions and the following disclaimer.
 
    Redistributions in binary form must reproduce the above copyright
    notice, this list of conditions and the following disclaimer in the
    documentation and/or other materials provided with the distribution.
 
    Neither the name of the University of California nor the names of its
    contributors may be used to endorse or promote products derived from
    this software without specific prior written permission.
 
  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
  LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
  SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
  POSSIBILITY OF SUCH DAMAGE.
 
 
  File description:
  This is a more specialized 4x4 matrix including transformations commonly
  used in computer graphics.
 
  File author(s):
  Graham Wakefield, 2010, grrrwaaa@gmail.com
*/
 
#include "al/math/al_Constants.hpp"
#include "al/math/al_Mat.hpp"
#include "al/math/al_Quat.hpp"
#include "al/math/al_Vec.hpp"
 
namespace al {
 
template <class T>
class Matrix4;
 
typedef Matrix4<double> Matrix4d;  
typedef Matrix4<float> Matrix4f;   
 
template <typename T = double>
class Matrix4 : public Mat<4, T> {
 public:
  typedef Mat<4, T> Base;
 
  Matrix4() : Base(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1) {}
 
  /*
    The constructor will map into memory locations as follows:
 
    Matrix4(arg1, arg2, arg3, ...)
 
    arg1 ->m[0]  arg2 ->m[4]  arg3 ->m[8]    arg4 ->m[12]
    arg5 ->m[1]  arg6 ->m[5]  arg7 ->m[9]    arg8 ->m[13]
    arg9 ->m[2]  arg10->m[6]  arg11->m[10]  arg12->m[14]
    arg13->m[3]  arg14->m[7]  arg15->m[11]  arg16->m[15]
 
    Matrix4(r1c1, r1c2, r1c3, r1c4,
        r2c1, r2c2, r2c3, r2c4,
        r3c1, r3c2, r3c3, r3c4,
        r4c1, r4c2, r4c3, r4c4)
  */
  Matrix4(const T& r1c1, const T& r1c2, const T& r1c3, const T& r1c4,
          const T& r2c1, const T& r2c2, const T& r2c3, const T& r2c4,
          const T& r3c1, const T& r3c2, const T& r3c3, const T& r3c4,
          const T& r4c1, const T& r4c2, const T& r4c3, const T& r4c4)
      : Base(r1c1, r1c2, r1c3, r1c4, r2c1, r2c2, r2c3, r2c4, r3c1, r3c2, r3c3,
             r3c4, r4c1, r4c2, r4c3, r4c4) {}
 
  Matrix4(const Vec<3, T>& xaxis, const Vec<3, T>& yaxis,
          const Vec<3, T>& zaxis, const Vec<3, T>& position)
      : Base(xaxis[0], yaxis[0], zaxis[0], position[0], xaxis[1], yaxis[1],
             zaxis[1], position[1], xaxis[2], yaxis[2], zaxis[2], position[2],
             0, 0, 0, 1) {}
 
  Matrix4(const T* src) : Base(src) {}
 
  Matrix4(const Mat<4, T>& src) : Base(src) {}
 
  Quat<T> toQuat() const { return Quat<T>().fromMatrix(Base::elems()); }
 
  Matrix4& fromQuat(Quat<T>& q) {
    q.toMatrix(Base::elems());
    return *this;
  }
  Matrix4& fromQuatTransposed(Quat<T>& q) {
    q.toMatrixTransposed(Base::elems());
    return *this;
  }
 
  static Matrix4 rotate(float angle, float x, float y, float z) {
    return Matrix4::rotate(angle, Vec3d(x, y, z));
  }
 
  static Matrix4 rotate(float angle, const Vec<3, T>& v) {
    Vec<3, T> axis(v);
    axis.normalize();
 
    float c = cos(angle);
    float s = sin(angle);
 
    Matrix4 m(axis[0] * axis[0] * (1 - c) + c,
              axis[1] * axis[0] * (1 - c) + axis[2] * s,
              axis[0] * axis[2] * (1 - c) - axis[1] * s, 0,
 
              axis[0] * axis[1] * (1 - c) - axis[2] * s,
              axis[1] * axis[1] * (1 - c) + c,
              axis[1] * axis[2] * (1 - c) + axis[0] * s, 0,
 
              axis[0] * axis[2] * (1 - c) + axis[1] * s,
              axis[1] * axis[2] * (1 - c) - axis[0] * s,
              axis[2] * axis[2] * (1 - c) + c, 0,
 
              0, 0, 0, 1);
 
    return m;
  }
 
  static Matrix4 shearXY(T x, T y) {
    return Matrix4(1, 0, x, 0, 0, 1, y, 0, 0, 0, 1, 0, 0, 0, 0, 1);
  }
 
  static Matrix4 shearYZ(T y, T z) {
    return Matrix4(1, 0, 0, 0, y, 1, 0, 0, z, 0, 1, 0, 0, 0, 0, 1);
  }
 
  static Matrix4 shearZX(T z, T x) {
    return Matrix4(1, x, 0, 0, 0, 1, 0, 0, 0, z, 1, 0, 0, 0, 0, 1);
  }
 
 
  static Matrix4 perspective(T l, T r, T b, T t, T n, T f) {
    T W = r - l;
    T W2 = r + l;
    T H = t - b;
    T H2 = t + b;
    T D = f - n;
    T D2 = f + n;
    T n2 = n * 2;
    T fn2 = f * n2;
    return Matrix4(n2 / W, 0, W2 / W, 0, 0, n2 / H, H2 / H, 0, 0, 0, -D2 / D,
                   -fn2 / D, 0, 0, -1, 0);
  }
 
 
  static Matrix4 perspective(T fovy, T aspect, T near, T far) {
    double f = 1. / tan(fovy * M_DEG2RAD / 2.);
    T D = far - near;
    T D2 = far + near;
    T fn2 = far * near * 2;
    return Matrix4(f / aspect, 0, 0, 0, 0, f, 0, 0, 0, 0, -D2 / D, -fn2 / D, 0,
                   0, -1, 0);
  }
 
 
  static Matrix4 perspective(const Vec<3, T>& nearBL, const Vec<3, T>& nearBR,
                             const Vec<3, T>& nearTL, const Vec<3, T>& eye,
                             T near, T far) {
    Vec<3, T> va, vb, vc;
    Vec<3, T> vr, vu, vn;
    T l, r, b, t, d;
 
    // compute orthonormal basis for the screen
    vr = (nearBR - nearBL).normalize();  // right vector
    vu = (nearTL - nearBL).normalize();  // up vector
    cross(vn, vr, vu);  // normal(forward) vector (out from screen)
    vn.normalize();
 
    // compute vectors from eye to screen corners:
    va = nearBL - eye;
    vb = nearBR - eye;
    vc = nearTL - eye;
 
    // distance from eye to screen-plane
    // = component of va along vector vn (normal to screen)
    d = -va.dot(vn);
 
    // find extent of perpendicular projection
    T nbyd = near / d;
    l = vr.dot(va) * nbyd;
    r = vr.dot(vb) * nbyd;
    b = vu.dot(va) * nbyd;  // not vd?
    t = vu.dot(vc) * nbyd;
 
    return perspective(l, r, b, t, near, far);
  }
 
  static Matrix4 perspectiveLeft(T fovy, T aspect, T near, T far, T eyeSep,
                                 T focal) {
    return perspectiveOffAxis(fovy, aspect, near, far, -0.5 * eyeSep, focal);
  }
 
  static Matrix4 perspectiveRight(T fovy, T aspect, T near, T far, T eyeSep,
                                  T focal) {
    return perspectiveOffAxis(fovy, aspect, near, far, 0.5 * eyeSep, focal);
  }
 
  static Matrix4 perspectiveOffAxis(T fovy, T aspect, T near, T far, T xShift,
                                    T focal) {
    T top = near *
            tan(fovy * M_DEG2RAD * 0.5);  // height of view at distance = near
    T bottom = -top;
    T shift = -xShift * near / focal;
    T left = -aspect * top + shift;
    T right = aspect * top + shift;
    return perspective(left, right, bottom, top, near, far);
  }
 
 
  static Matrix4 perspectiveOffAxis(T fovy, T aspect, T near, T far, T xShift,
                                    T yShift, T focal) {
    double tanfovy = tan(fovy * M_DEG2RAD / 2.);
    T t = near * tanfovy;  // height of view at distance = near
    T b = -t;
    T l = -aspect * t;
    T r = aspect * t;
 
    T shift = -xShift * near / focal;
    l += shift;
    r += shift;
    shift = -yShift * near / focal;
    t += shift;
    b += shift;
 
    return perspective(l, r, b, t, near, far);
  }
 
  static Matrix4 unPerspective(T l, T r, T b, T t, T n, T f) {
    T W = r - l;
    T W2 = r + l;
    T H = t - b;
    T H2 = t + b;
    T D = f - n;
    T D2 = f + n;
    T n2 = n * 2;
    T fn2 = f * n2;
    return Matrix4(W / n2, 0, 0, W2 / n2, 0, H / n2, 0, H2 / n2, 0, 0, 0, -1, 0,
                   0, -D / fn2, D2 / fn2);
  }
 
 
  static Matrix4 ortho(T l, T r, T b, T t, T n, T f) {
    T W = r - l;
    T W2 = r + l;
    T H = t - b;
    T H2 = t + b;
    T D = f - n;
    T D2 = f + n;
    return Matrix4(2 / W, 0, 0, -W2 / W, 0, 2 / H, 0, -H2 / H, 0, 0, -2 / D,
                   -D2 / D, 0, 0, 0, 1);
  }
 
  static Matrix4 unOrtho(T l, T r, T b, T t, T n, T f) {
    T W = r - l;
    T W2 = r + l;
    T H = t - b;
    T H2 = t + b;
    T D = f - n;
    T D2 = f + n;
    return Matrix4(W / 2, 0, 0, W2 / 2, 0, H / 2, 0, H2 / 2, 0, 0, D / -2,
                   D2 / 2, 0, 0, 0, 1);
  }
 
 
  static Matrix4 ortho2D(T l, T r, T b, T t) {
    T W = r - l;
    T W2 = r + l;
    T H = t - b;
    T H2 = t + b;
    return Matrix4(2 / W, 0, 0, -W2 / W, 0, 2 / H, 0, -H2 / H, 0, 0, -1, 0, 0,
                   0, 0, 1);
  }
 
 
  static Matrix4 lookAt(const Vec<3, T>& ur, const Vec<3, T>& uu,
                        const Vec<3, T>& uf, const Vec<3, T>& eyePos) {
    return Matrix4(ur[0], ur[1], ur[2], -(ur.dot(eyePos)), uu[0], uu[1], uu[2],
                   -(uu.dot(eyePos)), uf[0], uf[1], uf[2], -(uf.dot(eyePos)), 0,
                   0, 0, 1);
  }
 
 
  static Matrix4 lookAt(const Vec<3, T>& eyePos, const Vec<3, T>& at,
                        const Vec<3, T>& up) {
    Vec<3, T> z = (at - eyePos).normalize();
    Vec<3, T> y = up;
    y.normalize();
    Vec<3, T> x = cross(z, up).normalize();
    return lookAt(x, y, -z, eyePos);
  }
 
  //  static Matrix4 lookAtRH(const Vec<3,T>& ux, const Vec<3,T>& uy, const
  //  Vec<3,T>& uz, const Vec<3,T>& pos) {
  //    return Matrix4(
  //             ux[0], ux[1], ux[2], -(ux.dot(pos)),
  //             uy[0], uy[1], uy[2], -(uy.dot(pos)),
  //             uz[0],uz[1],uz[2],  -(uz.dot(pos)),
  //             0, 0, 0, 1
  //             );
  //  }
  //
  //  static Matrix4 lookAtRH(const Vec<3,T>& eye, const Vec<3,T>& at, const
  //  Vec<3,T>& up) {
  //    Vec<3,T> z = (at - eye).normalize();
  //    Vec<3,T> x = cross(up, z);
  //    Vec<3,T> y = cross(z, x);
  //    return lookAt(x, y, z, eye);
  //  }
 
  static Matrix4 lookAtLeft(const Vec<3, T>& ux, const Vec<3, T>& uy,
                            const Vec<3, T>& uz, const Vec<3, T>& pos,
                            double eyeSep) {
    return lookAtOffAxis(ux, uy, uz, pos, -0.5 * eyeSep);
  }
 
  static Matrix4 lookAtRight(const Vec<3, T>& ux, const Vec<3, T>& uy,
                             const Vec<3, T>& uz, const Vec<3, T>& pos,
                             double eyeSep) {
    return lookAtOffAxis(ux, uy, uz, pos, 0.5 * eyeSep);
  }
 
  static Matrix4 lookAtOffAxis(const Vec<3, T>& ux, const Vec<3, T>& uy,
                               const Vec<3, T>& uz, const Vec<3, T>& pos,
                               double eyeShift) {
    return lookAt(ux, uy, uz, pos + (ux * -eyeShift));
  }
 
 
  Vec<4, T> transform(const Vec<4, T>& vCol) const { return *this * vCol; }
 
  Vec<4, T> transform(const Vec<3, T>& vCol) const {
    return transform(Vec<4, T>(vCol, T(1)));
  }
 
  static Matrix4 inverse(const Mat<4, T>& m) {
    Matrix4 res(m);
    invert(res);
    return res;
  }
 
  // \deprecated Use Mat::translation
  static Matrix4 translate(T x, T y, T z) {
    return translation(Vec<3, T>(x, y, z));
  }
  // \deprecated Use Mat::translation
  template <typename V>
  static Matrix4 translate(const Vec<3, V>& v) {
    return translation(v);
  }
  // \deprecated Use Mat::scaling
  static Matrix4 scale(T x, T y, T z) { return scaling(x, y, z); }
  // \deprecated Use Mat::scaling
  template <typename V>
  static Matrix4 scale(const Vec<3, V>& v) {
    return scaling(v);
  }
  // \deprecated Use Mat::scaling
  template <typename V>
  static Matrix4 scale(const V& v) {
    return scaling(v);
  }
  // \deprecated Use Mat::rotation
  static Matrix4 rotateXY(T theta) { return rotation(theta, 0, 1); }
  static Matrix4 rotateYZ(T theta) { return rotation(theta, 1, 2); }
  static Matrix4 rotateZX(T theta) { return rotation(theta, 2, 0); }
};
 
template <class T>
inline T frustumFar(const Mat<4, T>& proj) {
  return proj[14] / (proj[10] + T(1));
}
 
template <class T>
inline T frustumNear(const Mat<4, T>& proj) {
  return proj[14] / (proj[10] - T(1));
}
 
template <class T>
inline T frustumDepth(const Mat<4, T>& proj) {
  return (T(-2) * proj[14]) / (proj[10] * proj[10] - T(1));
}
 
template <class T>
inline T frustumAspect(const Mat<4, T>& proj) {
  return proj[5] / proj[0];
}
 
}  // namespace al
 
#endif /* include guard */