StdMeshMatrix Class Reference

#include <StdMeshMath.h>

Public Member Functions
float &	operator() (int i, int j)
float	operator() (int i, int j) const
float	Determinant () const
StdMeshTransformation	Decompose () const
const float *	data () const

Static Public Member Functions
static StdMeshMatrix	Zero ()
static StdMeshMatrix	Identity ()
static StdMeshMatrix	Inverse (const StdMeshMatrix &mat)
static StdMeshMatrix	Translate (float dx, float dy, float dz)
static StdMeshMatrix	Scale (float sx, float sy, float sz)
static StdMeshMatrix	Rotate (float angle, float rx, float ry, float rz)
static StdMeshMatrix	Transform (const StdMeshTransformation &transform)
static StdMeshMatrix	TransformInverse (const StdMeshTransformation &transform)
static StdMeshMatrix	LookAt (const StdMeshVector &eye, const StdMeshVector &center, const StdMeshVector &up)

Static Public Attributes
static const int	NColumns = 4
static const int	NRows = 3

Detailed Description

Definition at line 89 of file StdMeshMath.h.

Member Function Documentation

data()

const float* StdMeshMatrix::data ( ) const

inline

Definition at line 111 of file StdMeshMath.h.

{ return &a[0][0]; }

Referenced by C4ShaderCall::SetUniformMatrix3x4().

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Decompose()

StdMeshTransformation StdMeshMatrix::Decompose

(

)

const

Definition at line 442 of file StdMeshMath.cpp.

{
    // Extract the scale part of the matrix
    const float sx = sqrt(a[0][0]*a[0][0] + a[1][0]*a[1][0] + a[2][0]*a[2][0]);
    const float sy = sqrt(a[0][1]*a[0][1] + a[1][1]*a[1][1] + a[2][1]*a[2][1]);
    const float sz = sqrt(a[0][2]*a[0][2] + a[1][2]*a[1][2] + a[2][2]*a[2][2]);
 
    // What remains is the rotation part
    // TODO: This can be optimized by not doing the full matrix multiplication
    StdMeshMatrix rot = Scale(1.0f/sx, 1.0f/sy, 1.0f/sz) * *this;
 
    // Note that this does not work for skew matrices -- we cannot
    // represent skews in StdMeshTransformation
    const float cos_angle = 0.5f * (rot.a[0][0] + rot.a[1][1] + rot.a[2][2] - 1.0f);
 
    const float rdx = rot.a[2][1] - rot.a[1][2];
    const float rdy = rot.a[0][2] - rot.a[2][0];
    const float rdz = rot.a[1][0] - rot.a[0][1];
    const float det = sqrt(rdx*rdx + rdy*rdy + rdz*rdz);
 
    const float rx = (rot.a[2][1] - rot.a[1][2]) / det;
    const float ry = (rot.a[0][2] - rot.a[2][0]) / det;
    const float rz = (rot.a[1][0] - rot.a[0][1]) / det;
 
    StdMeshTransformation trans;
    trans.scale.x = sx;
    trans.scale.y = sy;
    trans.scale.z = sz;
    trans.rotate = StdMeshQuaternion::AngleAxis(acos(cos_angle), StdMeshVector::Translate(rx, ry, rz));
    trans.translate.x = a[0][3];
    trans.translate.y = a[1][3];
    trans.translate.z = a[2][3];
 
    return trans;
}

References a, StdMeshQuaternion::AngleAxis(), StdMeshTransformation::rotate, StdMeshTransformation::scale, Scale(), StdMeshVector::Translate(), StdMeshTransformation::translate, StdMeshVector::x, StdMeshVector::y, and StdMeshVector::z.

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Determinant()

float StdMeshMatrix::Determinant

(

)

const

Definition at line 358 of file StdMeshMath.cpp.

{
    return a[0][0]*a[1][1]*a[2][2] + a[0][1]*a[1][2]*a[2][0] + a[0][2]*a[1][0]*a[2][1]
           - a[0][0]*a[1][2]*a[2][1] - a[0][1]*a[1][0]*a[2][2] - a[0][2]*a[1][1]*a[2][0];
}

Referenced by Inverse(), and CStdGL::PerformMesh().

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Identity()

StdMeshMatrix StdMeshMatrix::Identity ( )

static

Definition at line 183 of file StdMeshMath.cpp.

{
    StdMeshMatrix m;
    m.a[0][0] = 1.0f; m.a[0][1] = 0.0f; m.a[0][2] = 0.0f; m.a[0][3] = 0.0f;
    m.a[1][0] = 0.0f; m.a[1][1] = 1.0f; m.a[1][2] = 0.0f; m.a[1][3] = 0.0f;
    m.a[2][0] = 0.0f; m.a[2][1] = 0.0f; m.a[2][2] = 1.0f; m.a[2][3] = 0.0f;
    return m;
}

Referenced by C4Object::DrawFaceImpl(), StdSubMeshInstance::LoadFacesForCompletion(), CStdGL::PerformMesh(), C4Draw::RenderMesh(), StdMeshInstance::ReorderFaces(), StdMeshUpdate::Update(), and StdMeshInstance::UpdateBoneTransforms().

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Inverse()

StdMeshMatrix StdMeshMatrix::Inverse ( const StdMeshMatrix &  mat )

static

Definition at line 192 of file StdMeshMath.cpp.

{
    StdMeshMatrix m;
 
    const float det = mat.Determinant();
    assert(det != 0.0f);
 
    m.a[0][0] = (mat.a[1][1]*mat.a[2][2] - mat.a[1][2]*mat.a[2][1]) / det;
    m.a[1][0] = (mat.a[1][2]*mat.a[2][0] - mat.a[1][0]*mat.a[2][2]) / det;
    m.a[2][0] = (mat.a[1][0]*mat.a[2][1] - mat.a[1][1]*mat.a[2][0]) / det;
 
    m.a[0][1] = (mat.a[0][2]*mat.a[2][1] - mat.a[0][1]*mat.a[2][2]) / det;
    m.a[1][1] = (mat.a[0][0]*mat.a[2][2] - mat.a[0][2]*mat.a[2][0]) / det;
    m.a[2][1] = (mat.a[0][1]*mat.a[2][0] - mat.a[0][0]*mat.a[2][1]) / det;
 
    m.a[0][2] = (mat.a[0][1]*mat.a[1][2] - mat.a[0][2]*mat.a[1][1]) / det;
    m.a[1][2] = (mat.a[0][2]*mat.a[1][0] - mat.a[0][0]*mat.a[1][2]) / det;
    m.a[2][2] = (mat.a[0][0]*mat.a[1][1] - mat.a[0][1]*mat.a[1][0]) / det;
 
    m.a[0][3] = (mat.a[0][1]*mat.a[1][3]*mat.a[2][2]
                 +  mat.a[0][2]*mat.a[1][1]*mat.a[2][3]
                 +  mat.a[0][3]*mat.a[1][2]*mat.a[2][1]
                 -  mat.a[0][1]*mat.a[1][2]*mat.a[2][3]
                 -  mat.a[0][2]*mat.a[1][3]*mat.a[2][1]
                 -  mat.a[0][3]*mat.a[1][1]*mat.a[2][2]) / det;
 
    m.a[1][3] = (mat.a[0][0]*mat.a[1][2]*mat.a[2][3]
                 +  mat.a[0][2]*mat.a[1][3]*mat.a[2][0]
                 +  mat.a[0][3]*mat.a[1][0]*mat.a[2][2]
                 -  mat.a[0][0]*mat.a[1][3]*mat.a[2][2]
                 -  mat.a[0][2]*mat.a[1][0]*mat.a[2][3]
                 -  mat.a[0][3]*mat.a[1][2]*mat.a[2][0]) / det;
 
    m.a[2][3] = (mat.a[0][0]*mat.a[1][3]*mat.a[2][1]
                 +  mat.a[0][1]*mat.a[1][0]*mat.a[2][3]
                 +  mat.a[0][3]*mat.a[1][1]*mat.a[2][0]
                 -  mat.a[0][0]*mat.a[1][1]*mat.a[2][3]
                 -  mat.a[0][1]*mat.a[1][3]*mat.a[2][0]
                 -  mat.a[0][3]*mat.a[1][0]*mat.a[2][1]) / det;
 
    return m;
}

References Determinant().

Referenced by CStdGL::SetupMultiBlt(), and StdMeshInstance::UpdateBoneTransforms().

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LookAt()

StdMeshMatrix StdMeshMatrix::LookAt ( const StdMeshVector &  eye, const StdMeshVector &  center, const StdMeshVector &  up  )

static

Definition at line 340 of file StdMeshMath.cpp.

{
    // See http://stackoverflow.com/questions/349050/calculating-a-lookat-matrix
    StdMeshVector z = eye - center;
    z.Normalize();
 
    StdMeshVector x = StdMeshVector::Cross(up, z);
    x.Normalize();
 
    StdMeshVector y = StdMeshVector::Cross(z, x);
 
    StdMeshMatrix m;
    m.a[0][0] = x.x; m.a[0][1] = x.y; m.a[0][2] = x.z; m.a[0][3] = -x.x*eye.x - x.y*eye.y - x.z*eye.z;
    m.a[1][0] = y.x; m.a[1][1] = y.y; m.a[1][2] = y.z; m.a[1][3] = -y.x*eye.x - y.y*eye.y - y.z*eye.z;
    m.a[2][0] = z.x; m.a[2][1] = z.y; m.a[2][2] = z.z; m.a[2][3] = -z.x*eye.x - z.y*eye.y - z.z*eye.z;
    return m;
}

References StdMeshVector::Cross(), StdMeshVector::Normalize(), StdMeshVector::x, StdMeshVector::y, z, and StdMeshVector::z.

Referenced by CStdGL::PerformMesh().

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operator()() [1/2]

float& StdMeshMatrix::operator() ( int  i, int  j  )

inline

Definition at line 105 of file StdMeshMath.h.

{ return a[i][j]; }

operator()() [2/2]

float StdMeshMatrix::operator() ( int  i, int  j  ) const

inline

Definition at line 106 of file StdMeshMath.h.

{ return a[i][j]; }

Rotate()

StdMeshMatrix StdMeshMatrix::Rotate ( float  angle, float  rx, float  ry, float  rz  )

static

Definition at line 253 of file StdMeshMath.cpp.

{
    StdMeshMatrix m;
 
    // We do normalize the rx,ry,rz vector here: This is only required for
    // precalculations anyway, thus not time-critical.
    float abs = sqrt(rx*rx+ry*ry+rz*rz);
    rx/=abs; ry/=abs; rz/=abs;
    float c = cos(angle), s = sin(angle);
 
    m.a[0][0] = rx*rx*(1-c)+c;    m.a[0][1] = rx*ry*(1-c)-rz*s; m.a[0][2] = rx*rz*(1-c)+ry*s; m.a[0][3] = 0.0f;
    m.a[1][0] = ry*rx*(1-c)+rz*s; m.a[1][1] = ry*ry*(1-c)+c;    m.a[1][2] = ry*rz*(1-c)-rx*s; m.a[1][3] = 0.0f;
    m.a[2][0] = rz*rx*(1-c)-ry*s; m.a[2][1] = ry*rz*(1-c)+rx*s; m.a[2][2] = rz*rz*(1-c)+c;    m.a[2][3] = 0.0f;
    return m;
}

References s.

Referenced by C4Object::DrawFaceImpl().

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Scale()

StdMeshMatrix StdMeshMatrix::Scale ( float  sx, float  sy, float  sz  )

static

Definition at line 244 of file StdMeshMath.cpp.

{
    StdMeshMatrix m;
    m.a[0][0] = sx;   m.a[0][1] = 0.0f; m.a[0][2] = 0.0f; m.a[0][3] = 0.0f;
    m.a[1][0] = 0.0f; m.a[1][1] = sy;   m.a[1][2] = 0.0f; m.a[1][3] = 0.0f;
    m.a[2][0] = 0.0f; m.a[2][1] = 0.0f; m.a[2][2] = sz;   m.a[2][3] = 0.0f;
    return m;
}

Referenced by Decompose(), C4Object::DrawFaceImpl(), CStdGL::PerformMesh(), and OgreToClonk::TransformScaleVector().

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Transform()

StdMeshMatrix StdMeshMatrix::Transform ( const StdMeshTransformation &  transform )

static

Definition at line 269 of file StdMeshMath.cpp.

{
    StdMeshMatrix m;
 
    float tx = 2*transform.rotate.x;
    float ty = 2*transform.rotate.y;
    float tz = 2*transform.rotate.z;
    float twx = tx*transform.rotate.w;
    float twy = ty*transform.rotate.w;
    float twz = tz*transform.rotate.w;
    float txx = tx*transform.rotate.x;
    float txy = ty*transform.rotate.x;
    float txz = tz*transform.rotate.x;
    float tyy = ty*transform.rotate.y;
    float tyz = tz*transform.rotate.y;
    float tzz = tz*transform.rotate.z;
 
    m.a[0][0] = (1.0f - (tyy + tzz) ) * transform.scale.x;
    m.a[0][1] = (txy - twz)           * transform.scale.y;
    m.a[0][2] = (txz + twy)           * transform.scale.z;
    m.a[1][0] = (txy + twz)           * transform.scale.x;
    m.a[1][1] = (1.0f - (txx + tzz) ) * transform.scale.y;
    m.a[1][2] = (tyz - twx)           * transform.scale.z;
    m.a[2][0] = (txz - twy)           * transform.scale.x;
    m.a[2][1] = (tyz + twx)           * transform.scale.y;
    m.a[2][2] = (1.0f - (txx + tyy) ) * transform.scale.z;
 
    m.a[0][3] = transform.translate.x;
    m.a[1][3] = transform.translate.y;
    m.a[2][3] = transform.translate.z;
 
    return m;
}

References StdMeshTransformation::rotate, StdMeshTransformation::scale, StdMeshTransformation::translate, StdMeshQuaternion::w, StdMeshVector::x, StdMeshQuaternion::x, StdMeshVector::y, StdMeshQuaternion::y, StdMeshVector::z, and StdMeshQuaternion::z.

Referenced by StdMeshInstance::UpdateBoneTransforms().

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TransformInverse()

StdMeshMatrix StdMeshMatrix::TransformInverse ( const StdMeshTransformation &  transform )

static

Definition at line 303 of file StdMeshMath.cpp.

{
    StdMeshMatrix m;
 
    float tx = 2*transform.rotate.x;
    float ty = 2*transform.rotate.y;
    float tz = 2*transform.rotate.z;
    float twx = -tx*transform.rotate.w;
    float twy = -ty*transform.rotate.w;
    float twz = -tz*transform.rotate.w;
    float txx = tx*transform.rotate.x;
    float txy = ty*transform.rotate.x;
    float txz = tz*transform.rotate.x;
    float tyy = ty*transform.rotate.y;
    float tyz = tz*transform.rotate.y;
    float tzz = tz*transform.rotate.z;
 
    m.a[0][0] = (1.0f - (tyy + tzz) ) / transform.scale.x;
    m.a[0][1] = (txy - twz)           / transform.scale.x;
    m.a[0][2] = (txz + twy)           / transform.scale.x;
    m.a[1][0] = (txy + twz)           / transform.scale.y;
    m.a[1][1] = (1.0f - (txx + tzz) ) / transform.scale.y;
    m.a[1][2] = (tyz - twx)           / transform.scale.y;
    m.a[2][0] = (txz - twy)           / transform.scale.z;
    m.a[2][1] = (tyz + twx)           / transform.scale.z;
    m.a[2][2] = (1.0f - (txx + tyy) ) / transform.scale.z;
 
    // Signs do not cancel!
    StdMeshVector invtranslate = (-transform.rotate) * (-transform.translate/transform.scale);
 
    m.a[0][3] = invtranslate.x;
    m.a[1][3] = invtranslate.y;
    m.a[2][3] = invtranslate.z;
 
    return m;
}

References StdMeshTransformation::rotate, StdMeshTransformation::scale, StdMeshTransformation::translate, StdMeshQuaternion::w, StdMeshVector::x, StdMeshQuaternion::x, StdMeshVector::y, StdMeshQuaternion::y, StdMeshVector::z, and StdMeshQuaternion::z.

Translate()

StdMeshMatrix StdMeshMatrix::Translate ( float  dx, float  dy, float  dz  )

static

Definition at line 235 of file StdMeshMath.cpp.

{
    StdMeshMatrix m;
    m.a[0][0] = 1.0f; m.a[0][1] = 0.0f; m.a[0][2] = 0.0f; m.a[0][3] = dx;
    m.a[1][0] = 0.0f; m.a[1][1] = 1.0f; m.a[1][2] = 0.0f; m.a[1][3] = dy;
    m.a[2][0] = 0.0f; m.a[2][1] = 0.0f; m.a[2][2] = 1.0f; m.a[2][3] = dz;
    return m;
}

Referenced by C4Object::DrawFaceImpl().

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Zero()

StdMeshMatrix StdMeshMatrix::Zero ( )

static

Definition at line 174 of file StdMeshMath.cpp.

{
    StdMeshMatrix m;
    m.a[0][0] = 0.0f; m.a[0][1] = 0.0f; m.a[0][2] = 0.0f; m.a[0][3] = 0.0f;
    m.a[1][0] = 0.0f; m.a[1][1] = 0.0f; m.a[1][2] = 0.0f; m.a[1][3] = 0.0f;
    m.a[2][0] = 0.0f; m.a[2][1] = 0.0f; m.a[2][2] = 0.0f; m.a[2][3] = 0.0f;
    return m;
}

Member Data Documentation

NColumns

const int StdMeshMatrix::NColumns = 4

static

Definition at line 92 of file StdMeshMath.h.

NRows

const int StdMeshMatrix::NRows = 3

static

Definition at line 93 of file StdMeshMath.h.

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The documentation for this class was generated from the following files:

• StdMeshMath.h
• StdMeshMath.cpp