real ViewEdge::getLength2D() const
{
float length = 0.0f;
ViewEdge::const_fedge_iterator itlast = fedge_iterator_last();
ViewEdge::const_fedge_iterator it = fedge_iterator_begin(), itend = fedge_iterator_end();
Vec2r seg;
do {
seg = Vec2r((*it)->orientation2d()[0], (*it)->orientation2d()[1]);
length += seg.norm();
++it;
} while ((it != itend) && (it != itlast));
return length;
}
Vec2r SVertex::ImageSpaceNormal() const
{
if (_Normals.size() == 0)
return Vec2r(0,0);
Vec3r normal = *(_Normals.begin());
Vec3r pos = _Point3D;
Vec2r imgNormal = SilhouetteGeomEngine::WorldToImage2(pos + normal) - SilhouetteGeomEngine::WorldToImage2(pos);
imgNormal.normalize();
return imgNormal;
}
/*! Calculates the trapezoidal transformation matrix \a matNT that transforms
post projection light space so that shadow map resolution in the
"foreground" is maximized.
The major steps are:
- compute the intersection of eyeFrust and lightFrust
- construct a trapezoid that contains the intersection
- determine the transformation that maps this trapezoid to the
(-1, 1) square
Returns \c true if the transform was computed, \c false otherwise (e.g. if
the intersection of eyeFrust and lightFrust is empty).
For details see "T. Martin, T.-S. Tan: Anti-aliasing and Continuity
with Trapezoidal Shadow Maps"
*/
bool TrapezoidalShadowMapEngine::calcTrapezoidalTransform(
Matrixr &matNT,
const Matrixr &matEyeToWorld,
const Matrixr &matLightFull,
const FrustumVolume &eyeFrust,
const FrustumVolume &lightFrust )
{
// obtain post proj. light space eye position
Pnt3r eyePos;
matEyeToWorld.mult (eyePos, eyePos);
matLightFull .multFull(eyePos, eyePos);
// intersect eye and light frusta, get vertices and center of intersection
std::vector<Pnt3r> intVerts;
Pnt3r intCenter;
intersectFrusta(eyeFrust, lightFrust, intVerts, intCenter);
if(intVerts.empty() == true)
return false;
// xform intCenter and intVerts to post proj. light space
matLightFull.multFull(intCenter, intCenter);
std::vector<Pnt3r>::iterator ivIt = intVerts.begin();
std::vector<Pnt3r>::iterator ivEnd = intVerts.end ();
for(; ivIt != ivEnd; ++ivIt)
matLightFull.multFull(*ivIt, *ivIt);
Pnt2r eyePos2D (eyePos [0], eyePos [1]);
Pnt2r intCenter2D(intCenter[0], intCenter[1]);
// center line, normal, direction and distance from origin
Vec2r clDir (intCenter2D - eyePos2D);
clDir.normalize();
Vec2r clNorm(-clDir[1], clDir[0]);
// distance of the center line from the origin
Real clDist = clNorm.dot(eyePos2D.subZero());
// compute top and base lines:
// - project intVerts onto the center line.
// - top line is perpendicular to center line and goes through the
// projected point closest to eyePos
// - base line is perpendicular to center line and goes through the
// projected point farthest from eyePos
Pnt2r tlBase;
Pnt2r blBase;
Real topDist = TypeTraits<Real>::getMax();
Real baseDist = TypeTraits<Real>::getMin();
std::vector<Pnt3r>::const_iterator ivCIt = intVerts.begin();
std::vector<Pnt3r>::const_iterator ivCEnd = intVerts.end ();
for(; ivCIt != ivCEnd; ++ivCIt)
{
Pnt2r ivPnt((*ivCIt)[0], (*ivCIt)[1]);
ivPnt = ivPnt - (clNorm.dot(ivPnt) - clDist) * clNorm;
Real dist = (ivPnt - eyePos2D).squareLength();
dist *= osgSgn(clDir.dot(ivPnt - eyePos2D));
if(dist < topDist)
{
topDist = dist;
tlBase = ivPnt;
}
if(dist > baseDist)
{
baseDist = dist;
blBase = ivPnt;
}
}
topDist = osgSgn(topDist ) * osgSqrt(osgAbs(topDist ));
baseDist = osgSgn(baseDist) * osgSqrt(osgAbs(baseDist));
// compute side lines:
// - choose focusPnt (everything closer to the near plane is mapped to
// 80% of the shadow map) - here we just take the point at 0.7 between
// tlBase and blBase
// - find a point (trapTip, q in the paper) on center line such that
// focusPnt is mapped the 80% line in the shadow map
// - choose lines through q that touch the convex hull of intVerts
ivCIt = intVerts.begin();
ivCEnd = intVerts.end ();
// Real centerDist = (intCenter2D - eyePos2D).length();
Real lambda = baseDist - topDist;
Real delta = 0.5f * lambda;
Real xi = -0.6f;
Real eta = ((lambda * delta) + (lambda * delta * xi)) /
(lambda - 2.f * delta - lambda * xi );
Pnt2r trapTip = tlBase - (eta * clDir);
Pnt2r focusPnt = tlBase + (delta * clDir);
// on both sides of the center line, find the point in intVerts that has
// the smallest |cosine| (largest angle) between clDir and the vector
// from trapTip to intVerts[i]
Pnt2r posPnt;
Real posCos = 1.f;
Pnt2r negPnt;
Real negCos = 1.f;
for(UInt32 i = 0; ivCIt != ivCEnd; ++ivCIt, ++i)
{
Pnt2r ivPnt((*ivCIt)[0], (*ivCIt)[1]);
Vec2r v = ivPnt - trapTip;
v.normalize();
Real currCos = osgAbs(clDir.dot(v));
if(clNorm.dot(v) >= 0.f)
{
if(currCos <= posCos)
{
posPnt = ivPnt;
posCos = currCos;
}
}
else
{
if(currCos <= negCos)
{
negPnt = ivPnt;
negCos = currCos;
}
}
}
// compute corners of trapezoid:
Pnt2r trapVerts [4];
Pnt2r extraVerts[2];
Real posTan = osgTan(osgACos(posCos));
Real negTan = osgTan(osgACos(negCos));
trapVerts[0] = blBase - ((eta + lambda) * negTan * clNorm);
trapVerts[1] = blBase + ((eta + lambda) * posTan * clNorm);
trapVerts[2] = tlBase + ( eta * posTan * clNorm);
trapVerts[3] = tlBase - ( eta * negTan * clNorm);
extraVerts[0] = focusPnt + ((eta + delta) * posTan * clNorm);
extraVerts[1] = focusPnt - ((eta + delta) * negTan * clNorm);
// == xform trapezoid to unit square ==
// M1 = R * T1 -- translate center of top line to origin and rotate
Vec2r u = 0.5f * (trapVerts[2].subZero() + trapVerts[3].subZero());
Vec2r v = trapVerts[3] - trapVerts[2];
v.normalize();
matNT.setValue( v[0], v[1], 0.f, -(u[0] * v[0] + u[1] * v[1]),
-v[1], v[0], 0.f, (u[0] * v[1] - u[1] * v[0]),
0.f, 0.f, 1.f, 0.f,
0.f, 0.f, 0.f, 1.f);
// M2 = T2 * M1 -- translate tip to origin
matNT[3][0] = - (matNT[0][0] * trapTip[0] + matNT[1][0] * trapTip[1]);
matNT[3][1] = - (matNT[0][1] * trapTip[0] + matNT[1][1] * trapTip[1]);
// M3 = H * M2 -- shear to make it symmetric wrt to the y axis
// v = M2 * u
v[0] = matNT[0][0] * u[0] + matNT[1][0] * u[1] + matNT[3][0];
v[1] = matNT[0][1] * u[0] + matNT[1][1] * u[1] + matNT[3][1];
Real a = - v[0] / v[1];
// matNT[*][0] : = mat[*][0] + a * mat[*][1]
matNT[0][0] += a * matNT[0][1];
matNT[1][0] += a * matNT[1][1];
matNT[2][0] += a * matNT[2][1];
matNT[3][0] += a * matNT[3][1];
// M4 = S1 * M3 -- scale to make sidelines orthogonal and
// top line is at y == 1
// v = 1 / (M3 * t2)
v[0] = 1.f / (matNT[0][0] * trapVerts[2][0] + matNT[1][0] * trapVerts[2][1] + matNT[3][0]);
v[1] = 1.f / (matNT[0][1] * trapVerts[2][0] + matNT[1][1] * trapVerts[2][1] + matNT[3][1]);
matNT[0][0] *= v[0]; matNT[0][1] *= v[1];
matNT[1][0] *= v[0]; matNT[1][1] *= v[1];
matNT[2][0] *= v[0]; matNT[2][1] *= v[1];
matNT[3][0] *= v[0]; matNT[3][1] *= v[1];
// M5 = N * M4 -- turn trapezoid into rectangle
matNT[0][3] = matNT[0][1];
matNT[1][3] = matNT[1][1];
matNT[2][3] = matNT[2][1];
matNT[3][3] = matNT[3][1];
matNT[3][1] += 1.f;
// M6 = T3 * M5 -- translate center to origin
// u = "M5 * t0" - only y and w coordinates
// v = "M5 * t2" - only y and w coordinates
u[0] = matNT[0][1] * trapVerts[0][0] + matNT[1][1] * trapVerts[0][1] + matNT[3][1];
u[1] = matNT[0][3] * trapVerts[0][0] + matNT[1][3] * trapVerts[0][1] + matNT[3][3];
v[0] = matNT[0][1] * trapVerts[2][0] + matNT[1][1] * trapVerts[2][1] + matNT[3][1];
v[1] = matNT[0][3] * trapVerts[2][0] + matNT[1][3] * trapVerts[2][1] + matNT[3][3];
a = - 0.5f * (u[0] / u[1] + v[0] / v[1]);
matNT[0][1] += matNT[0][3] * a;
matNT[1][1] += matNT[1][3] * a;
matNT[2][1] += matNT[2][3] * a;
matNT[3][1] += matNT[3][3] * a;
// M7 = S2 * M6 -- scale to fill -1/+1 square
// u = "M6 * t0" - only y and w coordinates
u[0] = matNT[0][1] * trapVerts[0][0] + matNT[1][1] * trapVerts[0][1] + matNT[3][1];
u[1] = matNT[0][3] * trapVerts[0][0] + matNT[1][3] * trapVerts[0][1] + matNT[3][3];
a = -u[1] / u[0];
matNT[0][1] *= a;
matNT[1][1] *= a;
matNT[2][1] *= a;
matNT[3][1] *= a;
return true;
}