bool IntrSphere3Sphere3x::Test (fixed fTMax,
const Vector3x& rkVelocity0, const Vector3x& rkVelocity1)
{
Vector3x kVDiff = rkVelocity1 - rkVelocity0;
fixed fA = kVDiff.SquaredLength();
Vector3x kCDiff = m_rkSphere1.Center - m_rkSphere0.Center;
fixed fC = kCDiff.SquaredLength();
fixed fRSum = m_rkSphere0.Radius + m_rkSphere1.Radius;
fixed fRSumSqr = fRSum*fRSum;
if (fA > FIXED_ZERO)
{
fixed fB = kCDiff.Dot(kVDiff);
if (fB <= FIXED_ZERO)
{
if (-fTMax*fA <= fB)
{
return fA*fC - fB*fB <= fA*fRSumSqr;
}
else
{
return fTMax*(fTMax*fA + FixedFromFloat((float)2.0)*fB) + fC <= fRSumSqr;
}
}
}
return fC <= fRSumSqr;
}
void Matrix2x::EigenDecomposition (Matrix2x& rkRot, Matrix2x& rkDiag) const
{
fixed fTrace = m_afEntry[0] + m_afEntry[3];
fixed fDiff = m_afEntry[0] - m_afEntry[3];
fixed fDiscr = Mathx::Sqrt(fDiff*fDiff +
FixedFromFloat((float)4.0)*m_afEntry[1]*m_afEntry[1]);
fixed fEVal0 = FIXED_HALF*(fTrace-fDiscr);
fixed fEVal1 = FIXED_HALF*(fTrace+fDiscr);
rkDiag.MakeDiagonal(fEVal0,fEVal1);
fixed fCos, fSin;
if (fDiff >= FIXED_ZERO)
{
fCos = m_afEntry[1];
fSin = fEVal0 - m_afEntry[0];
}
else
{
fCos = fEVal0 - m_afEntry[3];
fSin = m_afEntry[1];
}
fixed fTmp = Mathx::InvSqrt(fCos*fCos + fSin*fSin);
fCos *= fTmp;
fSin *= fTmp;
rkRot.m_afEntry[0] = fCos;
rkRot.m_afEntry[1] = -fSin;
rkRot.m_afEntry[2] = fSin;
rkRot.m_afEntry[3] = fCos;
}
Sphere3x MergeSpheres (const Sphere3x& rkSphere0,
const Sphere3x& rkSphere1)
{
Vector3x kCDiff = rkSphere1.Center - rkSphere0.Center;
fixed fLSqr = kCDiff.SquaredLength();
fixed fRDiff = rkSphere1.Radius - rkSphere0.Radius;
fixed fRDiffSqr = fRDiff*fRDiff;
if (fRDiffSqr >= fLSqr)
{
return (fRDiff >= FIXED_ZERO ? rkSphere1 : rkSphere0);
}
fixed fLength = Mathx::Sqrt(fLSqr);
Sphere3x kSphere;
if (fLength > Mathx::ZERO_TOLERANCE)
{
fixed fCoeff = (fLength + fRDiff)/(FixedFromFloat((float)2.0)*fLength);
kSphere.Center = rkSphere0.Center + fCoeff*kCDiff;
}
else
{
kSphere.Center = rkSphere0.Center;
}
kSphere.Radius = (FIXED_HALF)*(fLength + rkSphere0.Radius +
rkSphere1.Radius);
return kSphere;
}
static bool FillGlyphDimensions(HDC hDC, const TEXTMETRICW& TextMetric, CTextureStringGlyph* pGlyphs, uint32 nNumGlyphs)
{
// Setup the transform for the glyph. Just use identity.
MAT2 mat;
mat.eM11 = FixedFromFloat( 1.0f );
mat.eM12 = FixedFromFloat( 0.0f );
mat.eM21 = FixedFromFloat( 0.0f );
mat.eM22 = FixedFromFloat( 1.0f );
//determine if this is a truetype font or not
bool bTrueType = (TextMetric.tmPitchAndFamily & TMPF_TRUETYPE) != 0;
// Get the individual widths of all chars in font, indexed by character values.
GLYPHMETRICS GlyphMetrics;
memset( &GlyphMetrics, 0, sizeof( GlyphMetrics ) );
for( uint32 nCurrGlyph = 0; nCurrGlyph < nNumGlyphs; nCurrGlyph++ )
{
// Get the character for this glyph.
CTextureStringGlyph& Glyph = pGlyphs[nCurrGlyph];
if(bTrueType)
{
// Get the glyph metrics for this glyph.
if( GDI_ERROR == GetGlyphOutlineW( hDC, Glyph.m_cGlyph, GGO_METRICS, &GlyphMetrics, 0, NULL, &mat ))
{
// Use the default character on anything that has issues.
if( GDI_ERROR == GetGlyphOutlineW( hDC, TextMetric.tmDefaultChar, GGO_METRICS, &GlyphMetrics, 0, NULL, &mat ))
{
return false;
}
}
//we have the glyph outline, so we now need to convert the data from that over to the glyph data
//format
Glyph.m_nTotalWidth = GlyphMetrics.gmCellIncX;
Glyph.m_rBlackBox.Left() = GlyphMetrics.gmptGlyphOrigin.x;
Glyph.m_rBlackBox.Top() = TextMetric.tmAscent - GlyphMetrics.gmptGlyphOrigin.y;
Glyph.m_rBlackBox.Right() = Glyph.m_rBlackBox.Left() + GlyphMetrics.gmBlackBoxX + 1;
Glyph.m_rBlackBox.Bottom() = Glyph.m_rBlackBox.Top() + GlyphMetrics.gmBlackBoxY + 1;
}
else
{
//this is not a truetype font, so we have to use a different approach for getting the glyph
//sizes
INT nWidth = 0;
if(!GetCharWidth32W(hDC, Glyph.m_cGlyph, Glyph.m_cGlyph, &nWidth))
{
if(!GetCharWidth32W(hDC, TextMetric.tmDefaultChar, TextMetric.tmDefaultChar, &nWidth))
{
return false;
}
}
//setup our character from that information
Glyph.m_nTotalWidth = nWidth;
Glyph.m_rBlackBox.Left() = 0;
Glyph.m_rBlackBox.Top() = 0;
Glyph.m_rBlackBox.Right() = nWidth;
Glyph.m_rBlackBox.Bottom() = TextMetric.tmHeight;
}
}
//success
return true;
}
bool IntrSphere3Sphere3x::Find (fixed fTMax,
const Vector3x& rkVelocity0, const Vector3x& rkVelocity1)
{
Vector3x kVDiff = rkVelocity1 - rkVelocity0;
fixed fA = kVDiff.SquaredLength();
Vector3x kCDiff = m_rkSphere1.Center - m_rkSphere0.Center;
fixed fC = kCDiff.SquaredLength();
fixed fRSum = m_rkSphere0.Radius + m_rkSphere1.Radius;
fixed fRSumSqr = fRSum*fRSum;
if (fA > FIXED_ZERO)
{
fixed fB = kCDiff.Dot(kVDiff);
if (fB <= FIXED_ZERO)
{
if (-fTMax*fA <= fB
|| fTMax*(fTMax*fA + FixedFromFloat((float)2.0)*fB) + fC <= fRSumSqr )
{
fixed fCDiff = fC - fRSumSqr;
fixed fDiscr = fB*fB - fA*fCDiff;
if (fDiscr >= FIXED_ZERO)
{
if (fCDiff <= FIXED_ZERO)
{
// The spheres are initially intersecting. Estimate a
// point of contact by using the midpoint of the line
// segment connecting the sphere centers.
m_fContactTime = FIXED_ZERO;
m_kContactPoint = (FIXED_HALF)*(m_rkSphere0.Center +
m_rkSphere1.Center);
}
else
{
// The first time of contact is in [0,fTMax].
m_fContactTime = -(fB + Mathx::Sqrt(fDiscr))/fA;
if (m_fContactTime < FIXED_ZERO)
{
m_fContactTime = FIXED_ZERO;
}
else if (m_fContactTime > fTMax)
{
m_fContactTime = fTMax;
}
Vector3x kNewCDiff = kCDiff +
m_fContactTime*kVDiff;
m_kContactPoint = m_rkSphere0.Center +
m_fContactTime*rkVelocity0 +
(m_rkSphere0.Radius/fRSum)*kNewCDiff;
}
return true;
}
}
return false;
}
}
if (fC <= fRSumSqr)
{
// The spheres are initially intersecting. Estimate a point of
// contact by using the midpoint of the line segment connecting the
// sphere centers.
m_fContactTime = FIXED_ZERO;
m_kContactPoint = (FIXED_HALF)*(m_rkSphere0.Center +
m_rkSphere1.Center);
return true;
}
return false;
}
