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// Geometric Tools, LLC
// Copyright (c) 1998-2014
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
//
// File Version: 5.0.1 (2010/04/14)
#include "Wm5GraphicsPCH.h"
#include "Wm5Transform.h"
using namespace Wm5;
const Transform Transform::IDENTITY;
//----------------------------------------------------------------------------
Transform::Transform ()
:
mHMatrix(false), // initialize to the identity matrix
mInvHMatrix(false), // initialize to the identity matrix
mMatrix(false), // initialize to the identity matrix
mTranslate(0.0f, 0.0f, 0.0f),
mScale(1.0f, 1.0f, 1.0f),
mIsIdentity(true),
mIsRSMatrix(true),
mIsUniformScale(true),
mInverseNeedsUpdate(false)
{
}
//----------------------------------------------------------------------------
Transform::~Transform ()
{
}
//----------------------------------------------------------------------------
void Transform::MakeIdentity ()
{
mMatrix = HMatrix::IDENTITY;
mTranslate = APoint(0.0f, 0.0f, 0.0f);
mScale = APoint(1.0f, 1.0f, 1.0f);
mIsIdentity = true;
mIsRSMatrix = true;
mIsUniformScale = true;
UpdateHMatrix();
}
//----------------------------------------------------------------------------
void Transform::MakeUnitScale ()
{
assertion(mIsRSMatrix, "Matrix is not a rotation\n");
mScale = APoint(1.0f, 1.0f, 1.0f);
mIsUniformScale = true;
UpdateHMatrix();
}
//----------------------------------------------------------------------------
void Transform::SetRotate (const HMatrix& rotate)
{
mMatrix = rotate;
mIsIdentity = false;
mIsRSMatrix = true;
UpdateHMatrix();
}
//----------------------------------------------------------------------------
void Transform::SetMatrix (const HMatrix& matrix)
{
mMatrix = matrix;
mIsIdentity = false;
mIsRSMatrix = false;
mIsUniformScale = false;
UpdateHMatrix();
}
//----------------------------------------------------------------------------
void Transform::SetTranslate (const APoint& translate)
{
mTranslate = translate;
mIsIdentity = false;
UpdateHMatrix();
}
//----------------------------------------------------------------------------
void Transform::SetScale (const APoint& scale)
{
assertion(mIsRSMatrix, "Matrix is not a rotation\n");
assertion(scale[0] != 0.0f && scale[1] != 0.0f && scale[2] != 0.0f,
"Scales must be nonzero\n");
mScale = scale;
mIsIdentity = false;
mIsUniformScale = false;
UpdateHMatrix();
}
//----------------------------------------------------------------------------
void Transform::SetUniformScale (float scale)
{
assertion(mIsRSMatrix, "Matrix is not a rotation\n");
assertion(scale != 0.0f, "Scale must be nonzero\n");
mScale = APoint(scale, scale, scale);
mIsIdentity = false;
mIsUniformScale = true;
UpdateHMatrix();
}
//----------------------------------------------------------------------------
float Transform::GetNorm () const
{
if (mIsRSMatrix)
{
float maxValue = Mathf::FAbs(mScale[0]);
if (Mathf::FAbs(mScale[1]) > maxValue)
{
maxValue = Mathf::FAbs(mScale[1]);
}
if (Mathf::FAbs(mScale[2]) > maxValue)
{
maxValue = Mathf::FAbs(mScale[2]);
}
return maxValue;
}
// A general matrix. Use the max-row-sum matrix norm. The spectral
// norm (the maximum absolute value of the eigenvalues) is smaller or
// equal to this norm. Therefore, this function returns an approximation
// to the maximum scale.
float maxRowSum =
Mathf::FAbs(mMatrix[0][0]) +
Mathf::FAbs(mMatrix[0][1]) +
Mathf::FAbs(mMatrix[0][2]);
float rowSum =
Mathf::FAbs(mMatrix[1][0]) +
Mathf::FAbs(mMatrix[1][1]) +
Mathf::FAbs(mMatrix[1][2]);
if (rowSum > maxRowSum)
{
maxRowSum = rowSum;
}
rowSum =
Mathf::FAbs(mMatrix[2][0]) +
Mathf::FAbs(mMatrix[2][1]) +
Mathf::FAbs(mMatrix[2][2]);
if (rowSum > maxRowSum)
{
maxRowSum = rowSum;
}
return maxRowSum;
}
//----------------------------------------------------------------------------
Transform Transform::operator* (const Transform& transform) const
{
if (IsIdentity())
{
return transform;
}
if (transform.IsIdentity())
{
return *this;
}
Transform product;
if (mIsRSMatrix && transform.mIsRSMatrix)
{
if (mIsUniformScale)
{
product.SetRotate(mMatrix*transform.mMatrix);
product.SetTranslate(GetUniformScale()*(
mMatrix*transform.mTranslate) + mTranslate);
if (transform.IsUniformScale())
{
product.SetUniformScale(
GetUniformScale()*transform.GetUniformScale());
}
else
{
product.SetScale(GetUniformScale()*transform.GetScale());
}
return product;
}
}
// In all remaining cases, the matrix cannot be written as R*S*X+T.
HMatrix matMA = (mIsRSMatrix ? mMatrix.TimesDiagonal(mScale) : mMatrix);
HMatrix matMB = (transform.mIsRSMatrix ?
transform.mMatrix.TimesDiagonal(transform.mScale) :
transform.mMatrix);
product.SetMatrix(matMA*matMB);
product.SetTranslate(matMA*transform.mTranslate + mTranslate);
return product;
}
//----------------------------------------------------------------------------
const HMatrix& Transform::Inverse () const
{
if (mInverseNeedsUpdate)
{
if (mIsIdentity)
{
mInvHMatrix = HMatrix::IDENTITY;
}
else
{
if (mIsRSMatrix)
{
if (mIsUniformScale)
{
float invScale = 1.0f/mScale[0];
mInvHMatrix[0][0] = invScale*mMatrix[0][0];
mInvHMatrix[0][1] = invScale*mMatrix[1][0];
mInvHMatrix[0][2] = invScale*mMatrix[2][0];
mInvHMatrix[1][0] = invScale*mMatrix[0][1];
mInvHMatrix[1][1] = invScale*mMatrix[1][1];
mInvHMatrix[1][2] = invScale*mMatrix[2][1];
mInvHMatrix[2][0] = invScale*mMatrix[0][2];
mInvHMatrix[2][1] = invScale*mMatrix[1][2];
mInvHMatrix[2][2] = invScale*mMatrix[2][2];
}
else
{
// Replace 3 reciprocals by 6 multiplies and 1 reciprocal.
float s01 = mScale[0]*mScale[1];
float s02 = mScale[0]*mScale[2];
float s12 = mScale[1]*mScale[2];
float invs012 = 1.0f/(s01*mScale[2]);
float invS0 = s12*invs012;
float invS1 = s02*invs012;
float invS2 = s01*invs012;
mInvHMatrix[0][0] = invS0*mMatrix[0][0];
mInvHMatrix[0][1] = invS0*mMatrix[1][0];
mInvHMatrix[0][2] = invS0*mMatrix[2][0];
mInvHMatrix[1][0] = invS1*mMatrix[0][1];
mInvHMatrix[1][1] = invS1*mMatrix[1][1];
mInvHMatrix[1][2] = invS1*mMatrix[2][1];
mInvHMatrix[2][0] = invS2*mMatrix[0][2];
mInvHMatrix[2][1] = invS2*mMatrix[1][2];
mInvHMatrix[2][2] = invS2*mMatrix[2][2];
}
}
else
{
Invert3x3(mHMatrix, mInvHMatrix);
}
mInvHMatrix[0][3] = -(
mInvHMatrix[0][0]*mTranslate[0] +
mInvHMatrix[0][1]*mTranslate[1] +
mInvHMatrix[0][2]*mTranslate[2]
);
mInvHMatrix[1][3] = -(
mInvHMatrix[1][0]*mTranslate[0] +
mInvHMatrix[1][1]*mTranslate[1] +
mInvHMatrix[1][2]*mTranslate[2]
);
mInvHMatrix[2][3] = -(
mInvHMatrix[2][0]*mTranslate[0] +
mInvHMatrix[2][1]*mTranslate[1] +
mInvHMatrix[2][2]*mTranslate[2]
);
// The last row of mHMatrix is always (0,0,0,1) for an affine
// transformation, so it is set once in the constructor. It is
// not necessary to reset it here.
}
mInverseNeedsUpdate = false;
}
return mInvHMatrix;
}
//----------------------------------------------------------------------------
Transform Transform::InverseTransform () const
{
if (mIsIdentity)
{
return IDENTITY;
}
Transform inverse;
APoint invTrn;
if (mIsRSMatrix)
{
HMatrix invRot = mMatrix.Transpose();
inverse.SetRotate(invRot);
if (mIsUniformScale)
{
float invScale = 1.0f/mScale[0];
inverse.SetUniformScale(invScale);
invTrn = -invScale*(invRot*mTranslate);
}
else
{
APoint invScale(1.0f/mScale[0], 1.0f/mScale[1], 1.0f/mScale[2]);
inverse.SetScale(invScale);
invTrn = invRot*mTranslate;
invTrn[0] *= -invScale[0];
invTrn[1] *= -invScale[1];
invTrn[2] *= -invScale[2];
}
}
else
{
HMatrix invMat;
Invert3x3(mMatrix, invMat);
inverse.SetMatrix(invMat);
invTrn = -(invMat*mTranslate);
}
inverse.SetTranslate(invTrn);
return inverse;
}
//----------------------------------------------------------------------------
void Transform::UpdateHMatrix ()
{
if (mIsIdentity)
{
mHMatrix = HMatrix::IDENTITY;
}
else
{
if (mIsRSMatrix)
{
mHMatrix[0][0] = mMatrix[0][0]*mScale[0];
mHMatrix[0][1] = mMatrix[0][1]*mScale[1];
mHMatrix[0][2] = mMatrix[0][2]*mScale[2];
mHMatrix[1][0] = mMatrix[1][0]*mScale[0];
mHMatrix[1][1] = mMatrix[1][1]*mScale[1];
mHMatrix[1][2] = mMatrix[1][2]*mScale[2];
mHMatrix[2][0] = mMatrix[2][0]*mScale[0];
mHMatrix[2][1] = mMatrix[2][1]*mScale[1];
mHMatrix[2][2] = mMatrix[2][2]*mScale[2];
}
else
{
mHMatrix[0][0] = mMatrix[0][0];
mHMatrix[0][1] = mMatrix[0][1];
mHMatrix[0][2] = mMatrix[0][2];
mHMatrix[1][0] = mMatrix[1][0];
mHMatrix[1][1] = mMatrix[1][1];
mHMatrix[1][2] = mMatrix[1][2];
mHMatrix[2][0] = mMatrix[2][0];
mHMatrix[2][1] = mMatrix[2][1];
mHMatrix[2][2] = mMatrix[2][2];
}
mHMatrix[0][3] = mTranslate[0];
mHMatrix[1][3] = mTranslate[1];
mHMatrix[2][3] = mTranslate[2];
// The last row of mHMatrix is always (0,0,0,1) for an affine
// transformation, so it is set once in the constructor. It is not
// necessary to reset it here.
}
mInverseNeedsUpdate = true;
}
//----------------------------------------------------------------------------
void Transform::Invert3x3 (const HMatrix& mat, HMatrix& invMat)
{
// Compute the adjoint of M (3x3).
invMat[0][0] = mat[1][1]*mat[2][2] - mat[1][2]*mat[2][1];
invMat[0][1] = mat[0][2]*mat[2][1] - mat[0][1]*mat[2][2];
invMat[0][2] = mat[0][1]*mat[1][2] - mat[0][2]*mat[1][1];
invMat[1][0] = mat[1][2]*mat[2][0] - mat[1][0]*mat[2][2];
invMat[1][1] = mat[0][0]*mat[2][2] - mat[0][2]*mat[2][0];
invMat[1][2] = mat[0][2]*mat[1][0] - mat[0][0]*mat[1][2];
invMat[2][0] = mat[1][0]*mat[2][1] - mat[1][1]*mat[2][0];
invMat[2][1] = mat[0][1]*mat[2][0] - mat[0][0]*mat[2][1];
invMat[2][2] = mat[0][0]*mat[1][1] - mat[0][1]*mat[1][0];
// Compute the reciprocal of the determinant of M.
float invDet = 1.0f/(
mat[0][0]*invMat[0][0] +
mat[0][1]*invMat[1][0] +
mat[0][2]*invMat[2][0]
);
// inverse(M) = adjoint(M)/determinant(M).
invMat[0][0] *= invDet;
invMat[0][1] *= invDet;
invMat[0][2] *= invDet;
invMat[1][0] *= invDet;
invMat[1][1] *= invDet;
invMat[1][2] *= invDet;
invMat[2][0] *= invDet;
invMat[2][1] *= invDet;
invMat[2][2] *= invDet;
}
//----------------------------------------------------------------------------
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