some marginal gains + added documentation

5 files changed, 509 insertions, 294 deletions

diff --git a/include/astra/FanFlatBeamLineKernelProjector2D.inl b/include/astra/FanFlatBeamLineKernelProjector2D.inl
index 1676cb1..23438fb 100644
--- a/include/astra/FanFlatBeamLineKernelProjector2D.inl
+++ b/include/astra/FanFlatBeamLineKernelProjector2D.inl
@@ -25,9 +25,7 @@ along with the ASTRA Toolbox. If not, see <http://www.gnu.org/licenses/>.
 -----------------------------------------------------------------------
 $Id$
 */
-
-
-using namespace astra;
+#define policy_weight(p,rayindex,volindex,weight) if (p.pixelPrior(volindex)) { p.addWeight(rayindex, volindex, weight); p.pixelPosterior(volindex); }
 
 template <typename Policy>
 void CFanFlatBeamLineKernelProjector2D::project(Policy& p)
@@ -55,12 +53,6 @@ void CFanFlatBeamLineKernelProjector2D::projectSingleRay(int _iProjection, int _
 template <typename Policy>
 void CFanFlatBeamLineKernelProjector2D::projectBlock_internal(int _iProjFrom, int _iProjTo, int _iDetFrom, int _iDetTo, Policy& p)
 {
-	// variables
-	float32 detX, detY, S, T, I, x, y, c, r, update_c, update_r, offset;
-	float32 lengthPerRow, lengthPerCol, inv_pixelLengthX, inv_pixelLengthY, invTminSTimesLengthPerRow, invTminSTimesLengthPerCol;
-	int iVolumeIndex, iRayIndex, row, col, iAngle, iDetector, colCount, rowCount, detCount;
-	const SFanProjection * proj = 0;
-
 	// get vector geometry
 	const CFanFlatVecProjectionGeometry2D* pVecProjectionGeometry;
 	if (dynamic_cast<CFanFlatProjectionGeometry2D*>(m_pProjectionGeometry)) {
@@ -70,16 +62,26 @@ void CFanFlatBeamLineKernelProjector2D::projectBlock_internal(int _iProjFrom, in
 	}
 
 	// precomputations
-	inv_pixelLengthX = 1.0f / m_pVolumeGeometry->getPixelLengthX();
-	inv_pixelLengthY = 1.0f / m_pVolumeGeometry->getPixelLengthY();
-	colCount = m_pVolumeGeometry->getGridColCount();
-	rowCount = m_pVolumeGeometry->getGridRowCount();
-	detCount = pVecProjectionGeometry->getDetectorCount();
+	const float32 pixelLengthX = m_pVolumeGeometry->getPixelLengthX();
+	const float32 pixelLengthY = m_pVolumeGeometry->getPixelLengthY();
+	const float32 inv_pixelLengthX = 1.0f / pixelLengthX;
+	const float32 inv_pixelLengthY = 1.0f / pixelLengthY;
+	const int colCount = m_pVolumeGeometry->getGridColCount();
+	const int rowCount = m_pVolumeGeometry->getGridRowCount();
+	const int detCount = pVecProjectionGeometry->getDetectorCount();
+	const float32 Ex = m_pVolumeGeometry->getWindowMinY() + pixelLengthX*0.5f;
+	const float32 Ey = m_pVolumeGeometry->getWindowMaxY() - pixelLengthY*0.5f;
 
 	// loop angles
-	for (iAngle = _iProjFrom; iAngle < _iProjTo; ++iAngle) {
+	#pragma omp parallel for
+	for (int iAngle = _iProjFrom; iAngle < _iProjTo; ++iAngle) {
+
+		// variables
+		float32 Dx, Dy, Rx, Ry, S, T, weight, c, r, deltac, deltar, offset, RxOverRy, RyOverRx;
+		float32 lengthPerRow, lengthPerCol, invTminSTimesLengthPerRow, invTminSTimesLengthPerCol;
+		int iVolumeIndex, iRayIndex, row, col, iDetector;
 
-		proj = &pVecProjectionGeometry->getProjectionVectors()[iAngle];
+		const SFanProjection * proj = &pVecProjectionGeometry->getProjectionVectors()[iAngle];
 
 		// loop detectors
 		for (iDetector = _iDetFrom; iDetector < _iDetTo; ++iDetector) {
@@ -89,156 +91,116 @@ void CFanFlatBeamLineKernelProjector2D::projectBlock_internal(int _iProjFrom, in
 			// POLICY: RAY PRIOR
 			if (!p.rayPrior(iRayIndex)) continue;
 	
-			detX = proj->fDetSX + (iDetector+0.5f) * proj->fDetUX;
-			detY = proj->fDetSY + (iDetector+0.5f) * proj->fDetUY;
+			Dx = proj->fDetSX + (iDetector+0.5f) * proj->fDetUX;
+			Dy = proj->fDetSY + (iDetector+0.5f) * proj->fDetUY;
 
-			float32 fRayX = proj->fSrcX - detX;
-			float32 fRayY = proj->fSrcY - detY;
+			Rx = proj->fSrcX - Dx;
+			Ry = proj->fSrcY - Dy;
 
-			bool vertical = fabs(fRayX) < fabs(fRayY);
+			bool vertical = fabs(Rx) < fabs(Ry);
 			if (vertical) {
-				lengthPerRow = m_pVolumeGeometry->getPixelLengthX() * sqrt(fRayY*fRayY + fRayX*fRayX) / abs(fRayY);
-				update_c = -m_pVolumeGeometry->getPixelLengthY() * (fRayX/fRayY) * inv_pixelLengthX;
-				S = 0.5f - 0.5f*fabs(fRayX/fRayY);
-				T = 0.5f + 0.5f*fabs(fRayX/fRayY);
+				RxOverRy = Rx/Ry;
+				lengthPerRow = pixelLengthX * sqrt(Rx*Rx + Ry*Ry) / abs(Ry);
+				deltac = -pixelLengthY * RxOverRy * inv_pixelLengthX;
+				S = 0.5f - 0.5f*fabs(RxOverRy);
+				T = 0.5f + 0.5f*fabs(RxOverRy);
 				invTminSTimesLengthPerRow = lengthPerRow / (T - S);
 			} else {
-				lengthPerCol = m_pVolumeGeometry->getPixelLengthY() * sqrt(fRayY*fRayY + fRayX*fRayX) / abs(fRayX);
-				update_r = -m_pVolumeGeometry->getPixelLengthX() * (fRayY/fRayX) * inv_pixelLengthY;
-				S = 0.5f - 0.5f*fabs(fRayY/fRayX);
-				T = 0.5f + 0.5f*fabs(fRayY/fRayX);
+				RyOverRx = Ry/Rx;
+				lengthPerCol = pixelLengthY * sqrt(Rx*Rx + Ry*Ry) / abs(Rx);
+				deltar = -pixelLengthX * RyOverRx * inv_pixelLengthY;
+				S = 0.5f - 0.5f*fabs(RyOverRx);
+				T = 0.5f + 0.5f*fabs(RyOverRx);
 				invTminSTimesLengthPerCol = lengthPerCol / (T - S);
 			}
 
+			bool isin = false;
+
 			// vertically
 			if (vertical) {
 
-				// calculate x for row 0
-				x = detX + (fRayX/fRayY)*(m_pVolumeGeometry->pixelRowToCenterY(0)-detY);
-				c = (x - m_pVolumeGeometry->getWindowMinX()) * inv_pixelLengthX - 0.5f;
+				// calculate c for row 0
+				c = (Dx + (Ey - Dy)*RxOverRy - Ex) * inv_pixelLengthX;
 
 				// for each row
-				for (row = 0; row < rowCount; ++row, c += update_c) {
+				for (row = 0; row < rowCount; ++row, c += deltac) {
 
 					col = int(c+0.5f);
+					if (col <= 0 || col >= colCount-1) { if (!isin) continue; else break; }
 					offset = c - float32(col);
 
-					if (col <= 0 || col >= colCount-1) continue;
-
 					// left
 					if (offset < -S) {
-						I = (offset + T) * invTminSTimesLengthPerRow;
+						weight = (offset + T) * invTminSTimesLengthPerRow;
 
 						iVolumeIndex = row * colCount + col - 1;
-						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, lengthPerRow-I);
-							p.pixelPosterior(iVolumeIndex);
-						}
+						policy_weight(p, iRayIndex, iVolumeIndex, lengthPerRow-weight)
 
 						iVolumeIndex++;
-						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, I);
-							p.pixelPosterior(iVolumeIndex);
-						}
+						policy_weight(p, iRayIndex, iVolumeIndex, weight)
 					}
 
 					// right
 					else if (S < offset) {
-						I = (offset - S) * invTminSTimesLengthPerRow;
+						weight = (offset - S) * invTminSTimesLengthPerRow;
 
 						iVolumeIndex = row * colCount + col;
-						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, lengthPerRow-I);
-							p.pixelPosterior(iVolumeIndex);
-						}
+						policy_weight(p, iRayIndex, iVolumeIndex, lengthPerRow-weight)
 
 						iVolumeIndex++;
-						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, I);
-							p.pixelPosterior(iVolumeIndex);
-						}
+						policy_weight(p, iRayIndex, iVolumeIndex, weight)
 					}
 
 					// centre
 					else {
 						iVolumeIndex = row * colCount + col;
-						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, lengthPerRow);
-							p.pixelPosterior(iVolumeIndex);
-						}
+						policy_weight(p, iRayIndex, iVolumeIndex, lengthPerRow)
 					}
-		
+					isin = true;
 				}
 			}
 
 			// horizontally
 			else {
 
-				// calculate y for col 0
-				y = detY + (fRayY/fRayX)*(m_pVolumeGeometry->pixelColToCenterX(0)-detX);
-				r = (m_pVolumeGeometry->getWindowMaxY() - y) * inv_pixelLengthY - 0.5f;
+				// calculate r for col 0
+				r = -(Dy + (Ex - Dx)*RyOverRx - Ey) * inv_pixelLengthY;
 
 				// for each col
-				for (col = 0; col < colCount; ++col, r += update_r) {
+				for (col = 0; col < colCount; ++col, r += deltar) {
 
 					int row = int(r+0.5f);
+					if (row <= 0 || row >= rowCount-1) { if (!isin) continue; else break; }
 					offset = r - float32(row);
 
-					if (row <= 0 || row >= rowCount-1) continue;
-
 					// up
 					if (offset < -S) {
-						I = (offset + T) * invTminSTimesLengthPerCol;
+						weight = (offset + T) * invTminSTimesLengthPerCol;
 
 						iVolumeIndex = (row-1) * colCount + col;
-						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, lengthPerCol-I);
-							p.pixelPosterior(iVolumeIndex);
-						}
+						policy_weight(p, iRayIndex, iVolumeIndex, lengthPerCol-weight)
 
 						iVolumeIndex += colCount;
-						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, I);
-							p.pixelPosterior(iVolumeIndex);
-						}
+						policy_weight(p, iRayIndex, iVolumeIndex, weight)
 					}
 
 					// down
 					else if (S < offset) {
-						I = (offset - S) * invTminSTimesLengthPerCol;
+						weight = (offset - S) * invTminSTimesLengthPerCol;
 
 						iVolumeIndex = row * colCount + col;
-						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, lengthPerCol-I);
-							p.pixelPosterior(iVolumeIndex);
-						}
+						policy_weight(p, iRayIndex, iVolumeIndex, lengthPerCol-weight)
 
 						iVolumeIndex += colCount;
-						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, I);
-							p.pixelPosterior(iVolumeIndex);
-						}
+						policy_weight(p, iRayIndex, iVolumeIndex, weight)
 					}
 
 					// centre
 					else {
 						iVolumeIndex = row * colCount + col;
-						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, lengthPerCol);
-							p.pixelPosterior(iVolumeIndex);
-						}
+						policy_weight(p, iRayIndex, iVolumeIndex, lengthPerCol)
 					}
-
+					isin = true;
 				}
 			}
 	
diff --git a/include/astra/ParallelBeamBlobKernelProjector2D.inl b/include/astra/ParallelBeamBlobKernelProjector2D.inl
index 1945cdd..c2aa193 100644
--- a/include/astra/ParallelBeamBlobKernelProjector2D.inl
+++ b/include/astra/ParallelBeamBlobKernelProjector2D.inl
@@ -50,6 +50,63 @@ void CParallelBeamBlobKernelProjector2D::projectSingleRay(int _iProjection, int
 
 //----------------------------------------------------------------------------------------
 // PROJECT BLOCK - vector projection geometry
+// 
+// Kernel limitations: isotropic pixels (PixelLengthX == PixelLengthY)
+//
+// For each angle/detector pair:
+// 
+// Let D=(Dx,Dy) denote the centre of the detector (point) in volume coordinates, and
+// let R=(Rx,Ry) denote the direction of the ray (vector).
+// 
+// For mainly vertical rays (|Rx|<=|Ry|), 
+// let E=(Ex,Ey) denote the centre of the most upper left pixel:
+//    E = (WindowMinX +  PixelLengthX/2, WindowMaxY - PixelLengthY/2),
+// and let F=(Fx,Fy) denote a vector to the next pixel 
+//    F = (PixelLengthX, 0)
+// 
+// The intersection of the ray (D+aR) with the centre line of the upper row of pixels (E+bF) is
+//    { Dx + a*Rx = Ex + b*Fx
+//    { Dy + a*Ry = Ey + b*Fy
+// Solving for (a,b) results in:
+//    a = (Ey + b*Fy - Dy)/Ry
+//      = (Ey - Dy)/Ry
+//    b = (Dx + a*Rx - Ex)/Fx
+//      = (Dx + (Ey - Dy)*Rx/Ry - Ex)/Fx
+//
+// Define c as the x-value of the intersection of the ray with the upper row in pixel coordinates. 
+//    c = b 
+//
+// The intersection of the ray (D+aR) with the centre line of the second row of pixels (E'+bF) with
+//    E'=(WindowMinX + PixelLengthX/2, WindowMaxY - 3*PixelLengthY/2)
+// expressed in x-value pixel coordinates is
+//    c' = (Dx + (Ey' - Dy)*Rx/Ry - Ex)/Fx.
+// And thus:
+//    deltac = c' - c = (Dx + (Ey' - Dy)*Rx/Ry - Ex)/Fx - (Dx + (Ey - Dy)*Rx/Ry - Ex)/Fx
+//                    = [(Ey' - Dy)*Rx/Ry - (Ey - Dy)*Rx/Ry]/Fx
+//                    = [Ey' - Ey]*(Rx/Ry)/Fx
+//                    = [Ey' - Ey]*(Rx/Ry)/Fx
+//                    = -PixelLengthY*(Rx/Ry)/Fx.
+// 
+// Given c on a certain row, its pixel directly on its left (col), and the distance (offset) to it, can be found: 
+//    col = floor(c)
+//    offset = c - col
+//
+// The index of this pixel is
+//    volumeIndex = row * colCount + col
+//
+//
+// Mainly horizontal rays (|Rx|<=|Ry|) are handled in a similar fashion:
+//
+//    E = (WindowMinX +  PixelLengthX/2, WindowMaxY - PixelLengthY/2),
+//    F = (0, -PixelLengthX)
+//
+//    a = (Ex + b*Fx - Dx)/Rx = (Ex - Dx)/Rx
+//    b = (Dy + a*Ry - Ey)/Fy = (Dy + (Ex - Dx)*Ry/Rx - Ey)/Fy
+//    r = b
+//    deltar = PixelLengthX*(Ry/Rx)/Fy.
+//    row = floor(r+1/2)
+//    offset = r - row
+//
 template <typename Policy>
 void CParallelBeamBlobKernelProjector2D::projectBlock_internal(int _iProjFrom, int _iProjTo, int _iDetFrom, int _iDetTo, Policy& p)
 {
@@ -62,6 +119,8 @@ void CParallelBeamBlobKernelProjector2D::projectBlock_internal(int _iProjFrom, i
 	}
 
 	// precomputations
+	const float32 pixelLengthX = m_pVolumeGeometry->getPixelLengthX();
+	const float32 pixelLengthY = m_pVolumeGeometry->getPixelLengthY();	
 	const float32 inv_pixelLengthX = 1.0f / m_pVolumeGeometry->getPixelLengthX();
 	const float32 inv_pixelLengthY = 1.0f / m_pVolumeGeometry->getPixelLengthY();
 	const int colCount = m_pVolumeGeometry->getGridColCount();
@@ -73,7 +132,7 @@ void CParallelBeamBlobKernelProjector2D::projectBlock_internal(int _iProjFrom, i
 	for (int iAngle = _iProjFrom; iAngle < _iProjTo; ++iAngle) {
 
 		// variables
-		float32 detX, detY, x, y, c, r, update_c, update_r, offset, invBlobExtent, weight, d;
+		float32 Dx, Dy, Ex, Ey, c, r, deltac, deltar, offset, invBlobExtent, RxOverRy, RyOverRx;
 		int iVolumeIndex, iRayIndex, row, col, iDetector;
 		int col_left, col_right, row_top, row_bottom, index;
 
@@ -81,15 +140,18 @@ void CParallelBeamBlobKernelProjector2D::projectBlock_internal(int _iProjFrom, i
 
 		bool vertical = fabs(proj->fRayX) < fabs(proj->fRayY);
 		if (vertical) {
-			update_c = -m_pVolumeGeometry->getPixelLengthY() * (proj->fRayX/proj->fRayY) * inv_pixelLengthX;
-			float32 normR = sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX);
-			invBlobExtent = m_pVolumeGeometry->getPixelLengthY() / abs(m_fBlobSize * normR / proj->fRayY);
+			RxOverRy = proj->fRayX/proj->fRayY;
+			deltac = -m_pVolumeGeometry->getPixelLengthY() * (proj->fRayX/proj->fRayY) * inv_pixelLengthX;
+			invBlobExtent = m_pVolumeGeometry->getPixelLengthY() / abs(m_fBlobSize * sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX) / proj->fRayY);
 		} else {
-			update_r = -m_pVolumeGeometry->getPixelLengthX() * (proj->fRayY/proj->fRayX) * inv_pixelLengthY;
-			float32 normR = sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX);
-			invBlobExtent = m_pVolumeGeometry->getPixelLengthX() / abs(m_fBlobSize * normR / proj->fRayX);
+			RyOverRx = proj->fRayY/proj->fRayX;
+			deltar = -m_pVolumeGeometry->getPixelLengthX() * (proj->fRayY/proj->fRayX) * inv_pixelLengthY;
+			invBlobExtent = m_pVolumeGeometry->getPixelLengthX() / abs(m_fBlobSize * sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX) / proj->fRayX);
 		}
 
+		Ex = m_pVolumeGeometry->getWindowMinY() + pixelLengthX*0.5f;
+		Ey = m_pVolumeGeometry->getWindowMaxY() - pixelLengthY*0.5f;
+
 		// loop detectors
 		for (iDetector = _iDetFrom; iDetector < _iDetTo; ++iDetector) {
 			
@@ -98,18 +160,17 @@ void CParallelBeamBlobKernelProjector2D::projectBlock_internal(int _iProjFrom, i
 			// POLICY: RAY PRIOR
 			if (!p.rayPrior(iRayIndex)) continue;
 	
-			detX = proj->fDetSX + (iDetector+0.5f) * proj->fDetUX;
-			detY = proj->fDetSY + (iDetector+0.5f) * proj->fDetUY;
+			Dx = proj->fDetSX + (iDetector+0.5f) * proj->fDetUX;
+			Dy = proj->fDetSY + (iDetector+0.5f) * proj->fDetUY;
 
 			// vertically
 			if (vertical) {
 
-				// calculate x for row 0
-				x = detX + (proj->fRayX/proj->fRayY)*(m_pVolumeGeometry->pixelRowToCenterY(0)-detY);
-				c = (x - m_pVolumeGeometry->getWindowMinX()) * inv_pixelLengthX - 0.5f;
+				// calculate c for row 0
+				c = (Dx + (Ey - Dy)*RxOverRy - Ex) * inv_pixelLengthX;
 
-				// for each row
-				for (row = 0; row < rowCount; ++row, c += update_c) {
+				// loop rows
+				for (row = 0; row < rowCount; ++row, c += deltac) {
 
 					col_left = int(c - 0.5f - m_fBlobSize);
 					col_right = int(c + 0.5f + m_fBlobSize);
@@ -117,17 +178,15 @@ void CParallelBeamBlobKernelProjector2D::projectBlock_internal(int _iProjFrom, i
 					if (col_left < 0) col_left = 0; 
 					if (col_right > colCount-1) col_right = colCount-1; 
 
-					// for each column
+					// loop columns
 					for (col = col_left; col <= col_right; ++col) {
 
-						offset = abs(c - float32(col)) * invBlobExtent;
-						index = (int)(offset*m_iBlobSampleCount+0.5f);
-						weight = m_pfBlobValues[min(index,m_iBlobSampleCount-1)];
-				
 						iVolumeIndex = row * colCount + col;
 						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
 						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, weight);
+							offset = abs(c - float32(col)) * invBlobExtent;
+							index = (int)(offset*m_iBlobSampleCount+0.5f);
+							p.addWeight(iRayIndex, iVolumeIndex, m_pfBlobValues[min(index,m_iBlobSampleCount-1)]);
 							p.pixelPosterior(iVolumeIndex);
 						}
 					}
@@ -137,12 +196,11 @@ void CParallelBeamBlobKernelProjector2D::projectBlock_internal(int _iProjFrom, i
 			// horizontally
 			else {
 
-				// calculate y for col 0
-				y = detY + (proj->fRayY/proj->fRayX)*(m_pVolumeGeometry->pixelColToCenterX(0)-detX);
-				r = (m_pVolumeGeometry->getWindowMaxY() - y) * inv_pixelLengthY - 0.5f;
+				// calculate r for col 0
+				r = -(Dy + (Ex - Dx)*RyOverRx - Ey) * inv_pixelLengthY;
 
-				// for each col
-				for (col = 0; col < colCount; ++col, r += update_r) {
+				// loop columns
+				for (col = 0; col < colCount; ++col, r += deltar) {
 
 					row_top = int(r - 0.5f - m_fBlobSize);
 					row_bottom = int(r + 0.5f + m_fBlobSize);
@@ -150,21 +208,18 @@ void CParallelBeamBlobKernelProjector2D::projectBlock_internal(int _iProjFrom, i
 					if (row_top < 0) row_top = 0; 
 					if (row_bottom > rowCount-1) row_bottom = rowCount-1; 
 
-					// for each column
+					// loop rows
 					for (row = row_top; row <= row_bottom; ++row) {
 
-						offset = abs(r - float32(row)) * invBlobExtent;
-						index = (int)(offset*m_iBlobSampleCount+0.5f);
-						weight = m_pfBlobValues[min(index,m_iBlobSampleCount-1)];
-				
 						iVolumeIndex = row * colCount + col;
 						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
 						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, weight);
+							offset = abs(r - float32(row)) * invBlobExtent;
+							index = (int)(offset*m_iBlobSampleCount+0.5f);
+							p.addWeight(iRayIndex, iVolumeIndex, m_pfBlobValues[min(index,m_iBlobSampleCount-1)]);
 							p.pixelPosterior(iVolumeIndex);
 						}
 					}
-
 				}
 			}
 	
diff --git a/include/astra/ParallelBeamLineKernelProjector2D.inl b/include/astra/ParallelBeamLineKernelProjector2D.inl
index 9c58d60..199cfd7 100644
--- a/include/astra/ParallelBeamLineKernelProjector2D.inl
+++ b/include/astra/ParallelBeamLineKernelProjector2D.inl
@@ -25,6 +25,7 @@ along with the ASTRA Toolbox. If not, see <http://www.gnu.org/licenses/>.
 -----------------------------------------------------------------------
 $Id$
 */
+#define policy_weight(p,rayindex,volindex,weight) if (p.pixelPrior(volindex)) { p.addWeight(rayindex, volindex, weight); p.pixelPosterior(volindex); }
 
 template <typename Policy>
 void CParallelBeamLineKernelProjector2D::project(Policy& p)
@@ -48,10 +49,95 @@ void CParallelBeamLineKernelProjector2D::projectSingleRay(int _iProjection, int
 }
 
 
-
-
 //----------------------------------------------------------------------------------------
 // PROJECT BLOCK - vector projection geometry
+// 
+// Kernel limitations: isotropic pixels (PixelLengthX == PixelLengthY)
+//
+// For each angle/detector pair:
+// 
+// Let D=(Dx,Dy) denote the centre of the detector (point) in volume coordinates, and
+// let R=(Rx,Ry) denote the direction of the ray (vector).
+// 
+// For mainly vertical rays (|Rx|<=|Ry|), 
+// let E=(Ex,Ey) denote the centre of the most upper left pixel:
+//    E = (WindowMinX +  PixelLengthX/2, WindowMaxY - PixelLengthY/2),
+// and let F=(Fx,Fy) denote a vector to the next pixel 
+//    F = (PixelLengthX, 0)
+// 
+// The intersection of the ray (D+aR) with the centre line of the upper row of pixels (E+bF) is
+//    { Dx + a*Rx = Ex + b*Fx
+//    { Dy + a*Ry = Ey + b*Fy
+// Solving for (a,b) results in:
+//    a = (Ey + b*Fy - Dy)/Ry
+//      = (Ey - Dy)/Ry
+//    b = (Dx + a*Rx - Ex)/Fx
+//      = (Dx + (Ey - Dy)*Rx/Ry - Ex)/Fx
+//
+// Define c as the x-value of the intersection of the ray with the upper row in pixel coordinates. 
+//    c = b 
+//
+// The intersection of the ray (D+aR) with the centre line of the second row of pixels (E'+bF) with
+//    E'=(WindowMinX + PixelLengthX/2, WindowMaxY - 3*PixelLengthY/2)
+// expressed in x-value pixel coordinates is
+//    c' = (Dx + (Ey' - Dy)*Rx/Ry - Ex)/Fx.
+// And thus:
+//    deltac = c' - c = (Dx + (Ey' - Dy)*Rx/Ry - Ex)/Fx - (Dx + (Ey - Dy)*Rx/Ry - Ex)/Fx
+//                    = [(Ey' - Dy)*Rx/Ry - (Ey - Dy)*Rx/Ry]/Fx
+//                    = [Ey' - Ey]*(Rx/Ry)/Fx
+//                    = [Ey' - Ey]*(Rx/Ry)/Fx
+//                    = -PixelLengthY*(Rx/Ry)/Fx.
+// 
+// Given c on a certain row, its closest pixel (col), and the distance (offset) to it, can be found: 
+//    col = floor(c+1/2)
+//    offset = c - col
+//
+// The index of this pixel is
+//    volumeIndex = row * colCount + col
+//
+// The projection kernel is defined by
+//
+//         _____       LengthPerRow
+//       /|  |  |\
+//      / |  |  | \
+//   __/  |  |  |  \__ 0
+//    -T -S  0  S  T
+//
+// with S = 1/2 - 1/2*|Rx/Ry|, T = 1/2 + 1/2*|Rx/Ry|, and LengthPerRow = pixelLengthX * sqrt(Rx^2+Ry^2) / |Ry|
+//
+// And thus
+//                            { (offset+T)/(T-S) * LengthPerRow    if  -T <= offset < S
+//    W_(rayIndex,volIndex) = { LengthPerRow                       if  -S <= offset <= S
+//                            { (offset-S)/(T-S) * LengthPerRow    if   S < offset <= T
+//
+// If -T <= offset < S, the weight for the pixel directly to the left is
+//    W_(rayIndex,volIndex-1) = LengthPerRow - (offset+T)/(T-S) * LengthPerRow,
+// and if S < offset <= T, the weight for the pixel directly to the right is
+//    W_(rayIndex,volIndex+1) = LengthPerRow - (offset-S)/(T-S) * LengthPerRow.
+//
+//
+// Mainly horizontal rays (|Rx|<=|Ry|) are handled in a similar fashion:
+//
+//    E = (WindowMinX +  PixelLengthX/2, WindowMaxY - PixelLengthY/2),
+//    F = (0, -PixelLengthX)
+//
+//    a = (Ex + b*Fx - Dx)/Rx = (Ex - Dx)/Rx
+//    b = (Dy + a*Ry - Ey)/Fy = (Dy + (Ex - Dx)*Ry/Rx - Ey)/Fy
+//    r = b
+//    deltar = PixelLengthX*(Ry/Rx)/Fy.
+//    row = floor(r+1/2)
+//    offset = r - row
+//    S = 1/2 - 1/2*|Ry/Rx|
+//    T = 1/2 + 1/2*|Ry/Rx|
+//    LengthPerCol = pixelLengthY * sqrt(Rx^2+Ry^2) / |Rx|
+//
+//                            { (offset+T)/(T-S) * LengthPerCol    if  -T <= offset < S
+//    W_(rayIndex,volIndex) = { LengthPerCol                       if  -S <= offset <= S
+//                            { (offset-S)/(T-S) * LengthPerCol    if   S < offset <= T
+//
+//    W_(rayIndex,volIndex-colcount) = LengthPerCol - (offset+T)/(T-S) * LengthPerCol
+//    W_(rayIndex,volIndex+colcount) = LengthPerCol - (offset-S)/(T-S) * LengthPerCol
+//
 template <typename Policy>
 void CParallelBeamLineKernelProjector2D::projectBlock_internal(int _iProjFrom, int _iProjTo, int _iDetFrom, int _iDetTo, Policy& p)
 {
@@ -64,8 +150,10 @@ void CParallelBeamLineKernelProjector2D::projectBlock_internal(int _iProjFrom, i
 	}
 
 	// precomputations
-	const float32 inv_pixelLengthX = 1.0f / m_pVolumeGeometry->getPixelLengthX();
-	const float32 inv_pixelLengthY = 1.0f / m_pVolumeGeometry->getPixelLengthY();
+	const float32 pixelLengthX = m_pVolumeGeometry->getPixelLengthX();
+	const float32 pixelLengthY = m_pVolumeGeometry->getPixelLengthY();
+	const float32 inv_pixelLengthX = 1.0f / pixelLengthX;
+	const float32 inv_pixelLengthY = 1.0f / pixelLengthY;
 	const int colCount = m_pVolumeGeometry->getGridColCount();
 	const int rowCount = m_pVolumeGeometry->getGridRowCount();
 	const int detCount = pVecProjectionGeometry->getDetectorCount();
@@ -75,87 +163,92 @@ void CParallelBeamLineKernelProjector2D::projectBlock_internal(int _iProjFrom, i
 	for (int iAngle = _iProjFrom; iAngle < _iProjTo; ++iAngle) {
 
 		// variables
-		float32 detX, detY, S, T, I, x, y, c, r, update_c, update_r, offset;
-		float32 lengthPerRow, lengthPerCol, invTminSTimesLengthPerRow, invTminSTimesLengthPerCol;
+		float32 Dx, Dy, Ex, Ey, S, T, weight, c, r, deltac, deltar, offset;
+		float32 RxOverRy, RyOverRx, lengthPerRow, lengthPerCol, invTminSTimesLengthPerRow, invTminSTimesLengthPerCol;
 		int iVolumeIndex, iRayIndex, row, col, iDetector;
 
 		const SParProjection * proj = &pVecProjectionGeometry->getProjectionVectors()[iAngle];
 
 		bool vertical = fabs(proj->fRayX) < fabs(proj->fRayY);
 		if (vertical) {
-			lengthPerRow = m_pVolumeGeometry->getPixelLengthX() * sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX) / abs(proj->fRayY);
-			update_c = -m_pVolumeGeometry->getPixelLengthY() * (proj->fRayX/proj->fRayY) * inv_pixelLengthX;
-			S = 0.5f - 0.5f*fabs(proj->fRayX/proj->fRayY);
-			T = 0.5f + 0.5f*fabs(proj->fRayX/proj->fRayY);
+			RxOverRy = proj->fRayX/proj->fRayY;
+			lengthPerRow = pixelLengthX * sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX) / abs(proj->fRayY);
+			deltac = -pixelLengthY * RxOverRy * inv_pixelLengthX;
+			S = 0.5f - 0.5f*fabs(RxOverRy);
+			T = 0.5f + 0.5f*fabs(RxOverRy);
 			invTminSTimesLengthPerRow = lengthPerRow / (T - S);
 		} else {
-			lengthPerCol = m_pVolumeGeometry->getPixelLengthY() * sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX) / abs(proj->fRayX);
-			update_r = -m_pVolumeGeometry->getPixelLengthX() * (proj->fRayY/proj->fRayX) * inv_pixelLengthY;
-			S = 0.5f - 0.5f*fabs(proj->fRayY/proj->fRayX);
-			T = 0.5f + 0.5f*fabs(proj->fRayY/proj->fRayX);
+			RyOverRx = proj->fRayY/proj->fRayX;
+			lengthPerCol = pixelLengthY * sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX) / abs(proj->fRayX);
+			deltar = -pixelLengthX * RyOverRx * inv_pixelLengthY;
+			S = 0.5f - 0.5f*fabs(RyOverRx);
+			T = 0.5f + 0.5f*fabs(RyOverRx);
 			invTminSTimesLengthPerCol = lengthPerCol / (T - S);
 		}
 
+		Ex = m_pVolumeGeometry->getWindowMinY() + pixelLengthX*0.5f;
+		Ey = m_pVolumeGeometry->getWindowMaxY() - pixelLengthY*0.5f;
+
 		// loop detectors
-		for (iDetector = _iDetFrom; iDetector < _iDetTo; ++iDetector) {
-			
+		for (int iDetector = _iDetFrom; iDetector < _iDetTo; ++iDetector) {
+
 			iRayIndex = iAngle * m_pProjectionGeometry->getDetectorCount() + iDetector;
 
 			// POLICY: RAY PRIOR
 			if (!p.rayPrior(iRayIndex)) continue;
-	
-			detX = proj->fDetSX + (iDetector+0.5f) * proj->fDetUX;
-			detY = proj->fDetSY + (iDetector+0.5f) * proj->fDetUY;
 
+			Dx = proj->fDetSX + (iDetector+0.5f) * proj->fDetUX;
+			Dy = proj->fDetSY + (iDetector+0.5f) * proj->fDetUY;
+
+			bool isin = false;
+			
 			// vertically
 			if (vertical) {
 
-				// calculate x for row 0
-				x = detX + (proj->fRayX/proj->fRayY)*(m_pVolumeGeometry->pixelRowToCenterY(0)-detY);
-				c = (x - m_pVolumeGeometry->getWindowMinX()) * inv_pixelLengthX - 0.5f;
+				// calculate c for row 0
+				c = (Dx + (Ey - Dy)*RxOverRy - Ex) * inv_pixelLengthX;
 
-				// for each row
-				for (row = 0; row < rowCount; ++row, c += update_c) {
+				// loop rows
+				for (row = 0; row < rowCount; ++row, c += deltac) {
 
 					col = int(c+0.5f);
+					if (col <= 0 || col >= colCount-1) { if (!isin) continue; else break; }
 					offset = c - float32(col);
 
-					if (col <= 0 || col >= colCount-1) continue;
-
 					// left
 					if (offset < -S) {
-						I = (offset + T) * invTminSTimesLengthPerRow;
+						weight = (offset + T) * invTminSTimesLengthPerRow;
 
 						iVolumeIndex = row * colCount + col - 1;
 						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
 						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, lengthPerRow-I);
+							p.addWeight(iRayIndex, iVolumeIndex, lengthPerRow-weight);
 							p.pixelPosterior(iVolumeIndex);
 						}
 
 						iVolumeIndex++;
 						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
 						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, I);
+							p.addWeight(iRayIndex, iVolumeIndex, weight);
 							p.pixelPosterior(iVolumeIndex);
 						}
 					}
 
 					// right
 					else if (S < offset) {
-						I = (offset - S) * invTminSTimesLengthPerRow;
+						weight = (offset - S) * invTminSTimesLengthPerRow;
 
 						iVolumeIndex = row * colCount + col;
 						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
 						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, lengthPerRow-I);
+							p.addWeight(iRayIndex, iVolumeIndex, lengthPerRow-weight);
 							p.pixelPosterior(iVolumeIndex);
 						}
 
 						iVolumeIndex++;
 						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
 						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, I);
+							p.addWeight(iRayIndex, iVolumeIndex, weight);
 							p.pixelPosterior(iVolumeIndex);
 						}
 					}
@@ -169,73 +262,51 @@ void CParallelBeamLineKernelProjector2D::projectBlock_internal(int _iProjFrom, i
 							p.pixelPosterior(iVolumeIndex);
 						}
 					}
-		
+					isin = true;
 				}
 			}
 
 			// horizontally
 			else {
 
-				// calculate y for col 0
-				y = detY + (proj->fRayY/proj->fRayX)*(m_pVolumeGeometry->pixelColToCenterX(0)-detX);
-				r = (m_pVolumeGeometry->getWindowMaxY() - y) * inv_pixelLengthY - 0.5f;
+				// calculate r for col 0
+				r = -(Dy + (Ex - Dx)*RyOverRx - Ey) * inv_pixelLengthY;
 
-				// for each col
-				for (col = 0; col < colCount; ++col, r += update_r) {
+				// loop columns
+				for (col = 0; col < colCount; ++col, r += deltar) {
 
-					int row = int(r+0.5f);
+					row = int(r+0.5f);
+					if (row <= 0 || row >= rowCount-1) { if (!isin) continue; else break; }
 					offset = r - float32(row);
 
-					if (row <= 0 || row >= rowCount-1) continue;
-
 					// up
 					if (offset < -S) {
-						I = (offset + T) * invTminSTimesLengthPerCol;
+						weight = (offset + T) * invTminSTimesLengthPerCol;
 
 						iVolumeIndex = (row-1) * colCount + col;
-						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, lengthPerCol-I);
-							p.pixelPosterior(iVolumeIndex);
-						}
+						policy_weight(p, iRayIndex, iVolumeIndex, lengthPerCol-weight)
 
 						iVolumeIndex += colCount;
-						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, I);
-							p.pixelPosterior(iVolumeIndex);
-						}
+						policy_weight(p, iRayIndex, iVolumeIndex, weight)
 					}
 
 					// down
 					else if (S < offset) {
-						I = (offset - S) * invTminSTimesLengthPerCol;
+						weight = (offset - S) * invTminSTimesLengthPerCol;
 
 						iVolumeIndex = row * colCount + col;
-						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, lengthPerCol-I);
-							p.pixelPosterior(iVolumeIndex);
-						}
+						policy_weight(p, iRayIndex, iVolumeIndex, lengthPerCol-weight)
 
 						iVolumeIndex += colCount;
-						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, I);
-							p.pixelPosterior(iVolumeIndex);
-						}
+						policy_weight(p, iRayIndex, iVolumeIndex, weight)
 					}
 
 					// centre
 					else {
 						iVolumeIndex = row * colCount + col;
-						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-						if (p.pixelPrior(iVolumeIndex)) {
-							p.addWeight(iRayIndex, iVolumeIndex, lengthPerCol);
-							p.pixelPosterior(iVolumeIndex);
-						}
+						policy_weight(p, iRayIndex, iVolumeIndex, lengthPerCol)
 					}
-
+					isin = true;
 				}
 			}
 	
diff --git a/include/astra/ParallelBeamLinearKernelProjector2D.inl b/include/astra/ParallelBeamLinearKernelProjector2D.inl
index 79b82d4..ecbdeb3 100644
--- a/include/astra/ParallelBeamLinearKernelProjector2D.inl
+++ b/include/astra/ParallelBeamLinearKernelProjector2D.inl
@@ -25,6 +25,7 @@ along with the ASTRA Toolbox. If not, see <http://www.gnu.org/licenses/>.
 -----------------------------------------------------------------------
 $Id$
 */
+#define policy_weight(p,rayindex,volindex,weight) if (p.pixelPrior(volindex)) { p.addWeight(rayindex, volindex, weight); p.pixelPosterior(volindex); }
 
 template <typename Policy>
 void CParallelBeamLinearKernelProjector2D::project(Policy& p)
@@ -51,6 +52,79 @@ void CParallelBeamLinearKernelProjector2D::projectSingleRay(int _iProjection, in
 
 //----------------------------------------------------------------------------------------
 // PROJECT BLOCK - vector projection geometry
+// 
+// Kernel limitations: isotropic pixels (PixelLengthX == PixelLengthY)
+//
+// For each angle/detector pair:
+// 
+// Let D=(Dx,Dy) denote the centre of the detector (point) in volume coordinates, and
+// let R=(Rx,Ry) denote the direction of the ray (vector).
+// 
+// For mainly vertical rays (|Rx|<=|Ry|), 
+// let E=(Ex,Ey) denote the centre of the most upper left pixel:
+//    E = (WindowMinX +  PixelLengthX/2, WindowMaxY - PixelLengthY/2),
+// and let F=(Fx,Fy) denote a vector to the next pixel 
+//    F = (PixelLengthX, 0)
+// 
+// The intersection of the ray (D+aR) with the centre line of the upper row of pixels (E+bF) is
+//    { Dx + a*Rx = Ex + b*Fx
+//    { Dy + a*Ry = Ey + b*Fy
+// Solving for (a,b) results in:
+//    a = (Ey + b*Fy - Dy)/Ry
+//      = (Ey - Dy)/Ry
+//    b = (Dx + a*Rx - Ex)/Fx
+//      = (Dx + (Ey - Dy)*Rx/Ry - Ex)/Fx
+//
+// Define c as the x-value of the intersection of the ray with the upper row in pixel coordinates. 
+//    c = b 
+//
+// The intersection of the ray (D+aR) with the centre line of the second row of pixels (E'+bF) with
+//    E'=(WindowMinX + PixelLengthX/2, WindowMaxY - 3*PixelLengthY/2)
+// expressed in x-value pixel coordinates is
+//    c' = (Dx + (Ey' - Dy)*Rx/Ry - Ex)/Fx.
+// And thus:
+//    deltac = c' - c = (Dx + (Ey' - Dy)*Rx/Ry - Ex)/Fx - (Dx + (Ey - Dy)*Rx/Ry - Ex)/Fx
+//                    = [(Ey' - Dy)*Rx/Ry - (Ey - Dy)*Rx/Ry]/Fx
+//                    = [Ey' - Ey]*(Rx/Ry)/Fx
+//                    = [Ey' - Ey]*(Rx/Ry)/Fx
+//                    = -PixelLengthY*(Rx/Ry)/Fx.
+// 
+// Given c on a certain row, its pixel directly on its left (col), and the distance (offset) to it, can be found: 
+//    col = floor(c)
+//    offset = c - col
+//
+// The index of this pixel is
+//    volumeIndex = row * colCount + col
+//
+// The projection kernel is defined by
+//
+//                LengthPerRow
+//       /|\
+//      / | \
+//   __/  |  \__ 0
+//     p0 p1 p2
+//
+// And thus
+//    W_(rayIndex,volIndex) = (1 - offset) * lengthPerRow
+//    W_(rayIndex,volIndex+1) = offset * lengthPerRow
+//
+//
+// Mainly horizontal rays (|Rx|<=|Ry|) are handled in a similar fashion:
+//
+//    E = (WindowMinX +  PixelLengthX/2, WindowMaxY - PixelLengthY/2),
+//    F = (0, -PixelLengthX)
+//
+//    a = (Ex + b*Fx - Dx)/Rx = (Ex - Dx)/Rx
+//    b = (Dy + a*Ry - Ey)/Fy = (Dy + (Ex - Dx)*Ry/Rx - Ey)/Fy
+//    r = b
+//    deltar = PixelLengthX*(Ry/Rx)/Fy.
+//    row = floor(r+1/2)
+//    offset = r - row
+//    LengthPerCol = pixelLengthY * sqrt(Rx^2+Ry^2) / |Rx|
+//
+//    W_(rayIndex,volIndex) = (1 - offset) * lengthPerCol
+//    W_(rayIndex,volIndex+colcount) = offset * lengthPerCol
+//
 template <typename Policy>
 void CParallelBeamLinearKernelProjector2D::projectBlock_internal(int _iProjFrom, int _iProjTo, int _iDetFrom, int _iDetTo, Policy& p)
 {
@@ -63,8 +137,10 @@ void CParallelBeamLinearKernelProjector2D::projectBlock_internal(int _iProjFrom,
 	}
 
 	// precomputations
-	const float32 inv_pixelLengthX = 1.0f / m_pVolumeGeometry->getPixelLengthX();
-	const float32 inv_pixelLengthY = 1.0f / m_pVolumeGeometry->getPixelLengthY();
+	const float32 pixelLengthX = m_pVolumeGeometry->getPixelLengthX();
+	const float32 pixelLengthY = m_pVolumeGeometry->getPixelLengthY();
+	const float32 inv_pixelLengthX = 1.0f / pixelLengthX;
+	const float32 inv_pixelLengthY = 1.0f / pixelLengthY;
 	const int colCount = m_pVolumeGeometry->getGridColCount();
 	const int rowCount = m_pVolumeGeometry->getGridRowCount();
 	const int detCount = pVecProjectionGeometry->getDetectorCount();
@@ -74,21 +150,26 @@ void CParallelBeamLinearKernelProjector2D::projectBlock_internal(int _iProjFrom,
 	for (int iAngle = _iProjFrom; iAngle < _iProjTo; ++iAngle) {
 
 		// variables
-		float32 detX, detY, x, y, c, r, update_c, update_r, offset;
-		float32 lengthPerRow, lengthPerCol;
+		float32 Dx, Dy, Ex, Ey, x, y, c, r, deltac, deltar, offset;
+		float32 RxOverRy, RyOverRx, lengthPerRow, lengthPerCol;
 		int iVolumeIndex, iRayIndex, row, col, iDetector;
 
 		const SParProjection * proj = &pVecProjectionGeometry->getProjectionVectors()[iAngle];
 
 		bool vertical = fabs(proj->fRayX) < fabs(proj->fRayY);
 		if (vertical) {
+			RxOverRy = proj->fRayX/proj->fRayY;
 			lengthPerRow = m_pVolumeGeometry->getPixelLengthX() * sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX) / abs(proj->fRayY);
-			update_c = -m_pVolumeGeometry->getPixelLengthY() * (proj->fRayX/proj->fRayY) * inv_pixelLengthX;
+			deltac = -pixelLengthY * RxOverRy * inv_pixelLengthX;
 		} else {
+			RyOverRx = proj->fRayY/proj->fRayX;
 			lengthPerCol = m_pVolumeGeometry->getPixelLengthY() * sqrt(proj->fRayY*proj->fRayY + proj->fRayX*proj->fRayX) / abs(proj->fRayX);
-			update_r = -m_pVolumeGeometry->getPixelLengthX() * (proj->fRayY/proj->fRayX) * inv_pixelLengthY;
+			deltar = -pixelLengthX * RyOverRx * inv_pixelLengthY;
 		}
 
+		Ex = m_pVolumeGeometry->getWindowMinY() + pixelLengthX*0.5f;
+		Ey = m_pVolumeGeometry->getWindowMaxY() - pixelLengthY*0.5f;
+
 		// loop detectors
 		for (iDetector = _iDetFrom; iDetector < _iDetTo; ++iDetector) {
 			
@@ -97,70 +178,54 @@ void CParallelBeamLinearKernelProjector2D::projectBlock_internal(int _iProjFrom,
 			// POLICY: RAY PRIOR
 			if (!p.rayPrior(iRayIndex)) continue;
 	
-			detX = proj->fDetSX + (iDetector+0.5f) * proj->fDetUX;
-			detY = proj->fDetSY + (iDetector+0.5f) * proj->fDetUY;
+			Dx = proj->fDetSX + (iDetector+0.5f) * proj->fDetUX;
+			Dy = proj->fDetSY + (iDetector+0.5f) * proj->fDetUY;
+
+			bool isin = false;
 
 			// vertically
 			if (vertical) {
 
-				// calculate x for row 0
-				x = detX + (proj->fRayX/proj->fRayY)*(m_pVolumeGeometry->pixelRowToCenterY(0)-detY);
-				c = (x - m_pVolumeGeometry->getWindowMinX()) * inv_pixelLengthX - 0.5f;
+				// calculate c for row 0
+				c = (Dx + (Ey - Dy)*RxOverRy - Ex) * inv_pixelLengthX;
 
-				// for each row
-				for (row = 0; row < rowCount; ++row, c += update_c) {
+				// loop rows
+				for (row = 0; row < rowCount; ++row, c += deltac) {
 
 					col = int(c);
+					if (col <= 0 || col >= colCount-1) { if (!isin) continue; else break; }
 					offset = c - float32(col);
 
-					if (col <= 0 || col >= colCount-1) continue;
-
 					iVolumeIndex = row * colCount + col;
-					// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-					if (p.pixelPrior(iVolumeIndex)) {
-						p.addWeight(iRayIndex, iVolumeIndex, (1.0f - offset) * lengthPerRow);
-						p.pixelPosterior(iVolumeIndex);
-					}
+					policy_weight(p, iRayIndex, iVolumeIndex, (1.0f - offset) * lengthPerRow)
 					
 					iVolumeIndex++;
-					// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-					if (p.pixelPrior(iVolumeIndex)) {
-						p.addWeight(iRayIndex, iVolumeIndex, offset * lengthPerRow);
-						p.pixelPosterior(iVolumeIndex);
-					}
+					policy_weight(p, iRayIndex, iVolumeIndex, offset * lengthPerRow)
 
+					isin = true;
 				}
 			}
 
 			// horizontally
 			else {
 
-				// calculate y for col 0
-				y = detY + (proj->fRayY/proj->fRayX)*(m_pVolumeGeometry->pixelColToCenterX(0)-detX);
-				r = (m_pVolumeGeometry->getWindowMaxY() - y) * inv_pixelLengthY - 0.5f;
+				// calculate r for col 0
+				r = -(Dy + (Ex - Dx)*RyOverRx - Ey) * inv_pixelLengthY;
 
-				// for each col
-				for (col = 0; col < colCount; ++col, r += update_r) {
+				// loop columns
+				for (col = 0; col < colCount; ++col, r += deltar) {
 
-					int row = int(r);
+					row = int(r);
+					if (row <= 0 || row >= rowCount-1) { if (!isin) continue; else break; }
 					offset = r - float32(row);
 
-					if (row <= 0 || row >= rowCount-1) continue;
-
 					iVolumeIndex = row * colCount + col;
-					// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-					if (p.pixelPrior(iVolumeIndex)) {
-						p.addWeight(iRayIndex, iVolumeIndex, (1.0f - offset) * lengthPerCol);
-						p.pixelPosterior(iVolumeIndex);
-					}
+					policy_weight(p, iRayIndex, iVolumeIndex, (1.0f - offset) * lengthPerCol)
 
 					iVolumeIndex += colCount;
-					// POLICY: PIXEL PRIOR + ADD + POSTERIOR
-					if (p.pixelPrior(iVolumeIndex)) {
-						p.addWeight(iRayIndex, iVolumeIndex, offset * lengthPerCol);
-						p.pixelPosterior(iVolumeIndex);
-					}
-
+					policy_weight(p, iRayIndex, iVolumeIndex, offset * lengthPerCol)
+					
+					isin = true;
 				}
 			}
 	
diff --git a/include/astra/ParallelBeamStripKernelProjector2D.inl b/include/astra/ParallelBeamStripKernelProjector2D.inl
index 85faaa3..f0203f2 100644
--- a/include/astra/ParallelBeamStripKernelProjector2D.inl
+++ b/include/astra/ParallelBeamStripKernelProjector2D.inl
@@ -49,6 +49,68 @@ void CParallelBeamStripKernelProjector2D::projectSingleRay(int _iProjection, int
 
 //----------------------------------------------------------------------------------------
 // PROJECT BLOCK
+// 
+// Kernel limitations: isotropic pixels (PixelLengthX == PixelLengthY)
+//
+// For each angle/detector pair:
+// 
+// Let DL=(DLx,DLy) denote the left of the detector (point) in volume coordinates, and
+// Let DR=(DRx,DRy) denote the right of the detector (point) in volume coordinates, and
+// let R=(Rx,Ry) denote the direction of the ray (vector).
+// 
+// For mainly vertical rays (|Rx|<=|Ry|), 
+// let E=(Ex,Ey) denote the centre of the most upper left pixel:
+//    E = (WindowMinX +  PixelLengthX/2, WindowMaxY - PixelLengthY/2),
+// and let F=(Fx,Fy) denote a vector to the next pixel 
+//    F = (PixelLengthX, 0)
+// 
+// The intersection of the left edge of the strip (DL+aR) with the centre line of the upper row of pixels (E+bF) is
+//    { DLx + a*Rx = Ex + b*Fx
+//    { DLy + a*Ry = Ey + b*Fy
+// Solving for (a,b) results in:
+//    a = (Ey + b*Fy - DLy)/Ry
+//      = (Ey - DLy)/Ry
+//    b = (DLx + a*Rx - Ex)/Fx
+//      = (DLx + (Ey - DLy)*Rx/Ry - Ex)/Fx
+//
+// Define cL as the x-value of the intersection of the left edge of the strip with the upper row in pixel coordinates. 
+//    cL = b 
+//
+// cR, the x-value of the intersection of the right edge of the strip with the upper row in pixel coordinates can be found similarly.
+//
+// The intersection of the ray (DL+aR) with the left line of the second row of pixels (E'+bF) with
+//    E'=(WindowMinX + PixelLengthX/2, WindowMaxY - 3*PixelLengthY/2)
+// expressed in x-value pixel coordinates is
+//    cL' = (DLx + (Ey' - DLy)*Rx/Ry - Ex)/Fx.
+// And thus:
+//    deltac = cL' - cL = (DLx + (Ey' - DLy)*Rx/Ry - Ex)/Fx - (DLx + (Ey - DLy)*Rx/Ry - Ex)/Fx
+//                      = [(Ey' - DLy)*Rx/Ry - (Ey - DLy)*Rx/Ry]/Fx
+//                      = [Ey' - Ey]*(Rx/Ry)/Fx
+//                      = [Ey' - Ey]*(Rx/Ry)/Fx
+//                      = -PixelLengthY*(Rx/Ry)/Fx.
+//
+// The projection weight for a certain pixel is defined by the area between two points of 
+//
+//         _____       LengthPerRow
+//       /|  |  |\
+//      / |  |  | \
+//   __/  |  |  |  \__ 0
+//    -T -S  0  S  T
+// with S = 1/2 - 1/2*|Rx/Ry|, T = 1/2 + 1/2*|Rx/Ry|, and LengthPerRow = pixelLengthX * sqrt(Rx^2+Ry^2) / |Ry|
+// 
+// For a certain row, all columns that are 'hit' by this kernel lie in the interval
+//    (col_left, col_right) = (floor(cL-1/2+S), floor(cR+3/2-S))
+//
+// The offsets for both is
+//    (offsetL, offsetR) = (cL - floor(col_left), cR - floor(col_left))
+//
+// The projection weight is found by the difference between the integrated values of the kernel
+//         offset <= -T   Kernel = 0
+//    -T < offset <= -S   Kernel = PixelArea/2*(T+offset)^2/(T-S)
+//    -S < offset <=  S   Kernel = PixelArea/2 + offset
+//     S < offset <=  T   Kernel = PixelArea - PixelArea/2*(T-offset)^2/(T-S)
+//     T <= offset:       Kernel = PixelArea
+//
 template <typename Policy>
 void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom, int _iProjTo, int _iDetFrom, int _iDetTo, Policy& p)
 {
@@ -61,9 +123,11 @@ void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom,
 	}
 
 	// precomputations
-	const float32 inv_pixelLengthX = 1.0f / m_pVolumeGeometry->getPixelLengthX();
-	const float32 inv_pixelLengthY = 1.0f / m_pVolumeGeometry->getPixelLengthY();
-	const float32 pixelArea = m_pVolumeGeometry->getPixelLengthX() * m_pVolumeGeometry->getPixelLengthY();
+	const float32 pixelLengthX = m_pVolumeGeometry->getPixelLengthX();
+	const float32 pixelLengthY = m_pVolumeGeometry->getPixelLengthY();
+	const float32 pixelArea = pixelLengthX * pixelLengthY;
+	const float32 inv_pixelLengthX = 1.0f / pixelLengthX;
+	const float32 inv_pixelLengthY = 1.0f / pixelLengthY;
 	const int colCount = m_pVolumeGeometry->getGridColCount();
 	const int rowCount = m_pVolumeGeometry->getGridRowCount();
 	const int detCount = pVecProjectionGeometry->getDetectorCount();
@@ -73,8 +137,8 @@ void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom,
 	for (int iAngle = _iProjFrom; iAngle < _iProjTo; ++iAngle) {
 
 		// variables
-		float32 detLX, detLY, detRX, detRY, S, T, update_c, update_r, offsetL, offsetR, invTminS;
-		float32 res, fRxOverRy, fRyOverRx;
+		float32 DLx, DLy, DRx, DRy, Ex, Ey, S, T, deltac, deltar, offsetL, offsetR, invTminS;
+		float32 res, RxOverRy, RyOverRx, cL, cR, rL, rR;
 		int iVolumeIndex, iRayIndex, iDetector;
 		int row, row_top, row_bottom, col, col_left, col_right;
 
@@ -82,19 +146,22 @@ void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom,
 
 		bool vertical = fabs(proj->fRayX) < fabs(proj->fRayY);
 		if (vertical) {
-			fRxOverRy = proj->fRayX/proj->fRayY;
-			update_c = -m_pVolumeGeometry->getPixelLengthY() * fRxOverRy * inv_pixelLengthX;
-			S = 0.5f - 0.5f*fabs(fRxOverRy);
-			T = 0.5f + 0.5f*fabs(fRxOverRy);
+			RxOverRy = proj->fRayX/proj->fRayY;
+			deltac = -m_pVolumeGeometry->getPixelLengthY() * RxOverRy * inv_pixelLengthX;
+			S = 0.5f - 0.5f*fabs(RxOverRy);
+			T = 0.5f + 0.5f*fabs(RxOverRy);
 			invTminS = 1.0f / (T-S);
 		} else {
-			fRyOverRx = proj->fRayY/proj->fRayX;
-			update_r = -m_pVolumeGeometry->getPixelLengthX() * fRyOverRx * inv_pixelLengthY;
-			S = 0.5f - 0.5f*fabs(fRyOverRx);
-			T = 0.5f + 0.5f*fabs(fRyOverRx);
+			RyOverRx = proj->fRayY/proj->fRayX;
+			deltar = -m_pVolumeGeometry->getPixelLengthX() * RyOverRx * inv_pixelLengthY;
+			S = 0.5f - 0.5f*fabs(RyOverRx);
+			T = 0.5f + 0.5f*fabs(RyOverRx);
 			invTminS = 1.0f / (T-S);
 		}
 
+		Ex = m_pVolumeGeometry->getWindowMinY() + pixelLengthX*0.5f;
+		Ey = m_pVolumeGeometry->getWindowMaxY() - pixelLengthY*0.5f;
+
 		// loop detectors
 		for (iDetector = _iDetFrom; iDetector < _iDetTo; ++iDetector) {
 			
@@ -103,19 +170,17 @@ void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom,
 			// POLICY: RAY PRIOR
 			if (!p.rayPrior(iRayIndex)) continue;
 	
-			detLX = proj->fDetSX + iDetector * proj->fDetUX;
-			detLY = proj->fDetSY + iDetector * proj->fDetUY;
-			detRX = detLX + proj->fDetUX;
-			detRY = detLY + proj->fDetUY;
+			DLx = proj->fDetSX + iDetector * proj->fDetUX;
+			DLy = proj->fDetSY + iDetector * proj->fDetUY;
+			DRx = DLx + proj->fDetUX;
+			DRy = DLy + proj->fDetUY;
 
 			// vertically
 			if (vertical) {
 
 				// calculate cL and cR for row 0
-				float32 xL = detLX + fRxOverRy*(m_pVolumeGeometry->pixelRowToCenterY(0)-detLY);
-				float32 cL = (xL - m_pVolumeGeometry->getWindowMinX()) * inv_pixelLengthX - 0.5f;
-				float32 xR = detRX + fRxOverRy*(m_pVolumeGeometry->pixelRowToCenterY(0)-detRY);
-				float32 cR = (xR - m_pVolumeGeometry->getWindowMinX()) * inv_pixelLengthX - 0.5f;
+				cL = (DLx + (Ey - DLy)*RxOverRy - Ex) * inv_pixelLengthX;
+				cR = (DRx + (Ey - DRy)*RxOverRy - Ex) * inv_pixelLengthX;
 
 				if (cR < cL) {
 					float32 tmp = cL;
@@ -123,8 +188,8 @@ void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom,
 					cR = tmp;
 				}
 
-				// for each row
-				for (row = 0; row < rowCount; ++row, cL += update_c, cR += update_c) {
+				// loop rows
+				for (row = 0; row < rowCount; ++row, cL += deltac, cR += deltac) {
 
 					col_left = int(cL-0.5f+S);
 					col_right = int(cR+1.5-S);
@@ -132,27 +197,27 @@ void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom,
 					if (col_left < 0) col_left = 0; 
 					if (col_right > colCount-1) col_right = colCount-1; 
 
-					offsetL = cL - float32(col_left);
-					offsetR = cR - float32(col_left);
+					float32 tmp = float32(col_left);
+					offsetL = cL - tmp;
+					offsetR = cR - tmp;
 
-					// for each column
+					// loop columns
 					for (col = col_left; col <= col_right; ++col, offsetL -= 1.0f, offsetR -= 1.0f) {
 
 						iVolumeIndex = row * colCount + col;
-
 						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
 						if (p.pixelPrior(iVolumeIndex)) {
 
 							// right ray edge
-							if (T <= offsetR) 		res = 1.0f;
-							else if (S < offsetR) 	res = 1.0f - 0.5f*(T-offsetR)*(T-offsetR)*invTminS;
-							else if (-S < offsetR) 	res = 0.5f + offsetR;
-							else if (-T < offsetR) 	res = 0.5f*(offsetR+T)*(offsetR+T)*invTminS;
-							else 					res = 0.0f;
+							if (T <= offsetR)       res = 1.0f;
+							else if (S < offsetR)   res = 1.0f - 0.5f*(T-offsetR)*(T-offsetR)*invTminS;
+							else if (-S < offsetR)  res = 0.5f + offsetR;
+							else if (-T < offsetR)  res = 0.5f*(offsetR+T)*(offsetR+T)*invTminS;
+							else                    res = 0.0f;
 
 							// left ray edge
-							if (T <= offsetL) 		res -= 1.0f;
-							else if (S < offsetL) 	res -= 1.0f - 0.5f*(T-offsetL)*(T-offsetL)*invTminS;
+							if (T <= offsetL)       res -= 1.0f;
+							else if (S < offsetL)   res -= 1.0f - 0.5f*(T-offsetL)*(T-offsetL)*invTminS;
 							else if (-S < offsetL)  res -= 0.5f + offsetL;
 							else if (-T < offsetL)  res -= 0.5f*(offsetL+T)*(offsetL+T)*invTminS;
 
@@ -167,10 +232,8 @@ void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom,
 			else {
 
 				// calculate rL and rR for row 0
-				float32 yL = detLY + fRyOverRx*(m_pVolumeGeometry->pixelColToCenterX(0)-detLX);
-				float32 rL = (m_pVolumeGeometry->getWindowMaxY() - yL) * inv_pixelLengthY - 0.5f;
-				float32 yR = detRY + fRyOverRx*(m_pVolumeGeometry->pixelColToCenterX(0)-detRX);
-				float32 rR = (m_pVolumeGeometry->getWindowMaxY() - yR) * inv_pixelLengthY - 0.5f;
+				rL = -(DLy + (Ex - DLx)*RyOverRx - Ey) * inv_pixelLengthY;
+				rR = -(DRy + (Ex - DRx)*RyOverRx - Ey) * inv_pixelLengthY;
 
 				if (rR < rL) {
 					float32 tmp = rL;
@@ -178,8 +241,8 @@ void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom,
 					rR = tmp;
 				}
 
-				// for each column
-				for (col = 0; col < colCount; ++col, rL += update_r, rR += update_r) {
+				// loop columns
+				for (col = 0; col < colCount; ++col, rL += deltar, rR += deltar) {
 
 					row_top = int(rL-0.5f+S);
 					row_bottom = int(rR+1.5-S);
@@ -187,31 +250,30 @@ void CParallelBeamStripKernelProjector2D::projectBlock_internal(int _iProjFrom,
 					if (row_top < 0) row_top = 0; 
 					if (row_bottom > rowCount-1) row_bottom = rowCount-1; 
 
-					offsetL = rL - float32(row_top);
-					offsetR = rR - float32(row_top);
+					float32 tmp = float32(row_top);
+					offsetL = rL - tmp;
+					offsetR = rR - tmp;
 
-					// for each row
+					// loop rows
 					for (row = row_top; row <= row_bottom; ++row, offsetL -= 1.0f, offsetR -= 1.0f) {
 
 						iVolumeIndex = row * colCount + col;
-
 						// POLICY: PIXEL PRIOR + ADD + POSTERIOR
 						if (p.pixelPrior(iVolumeIndex)) {
 
 							// right ray edge
-							if (T <= offsetR) 		res = 1.0f;
-							else if (S < offsetR) 	res = 1.0f - 0.5f*(T-offsetR)*(T-offsetR)*invTminS;
-							else if (-S < offsetR) 	res = 0.5f + offsetR;
-							else if (-T < offsetR) 	res = 0.5f*(offsetR+T)*(offsetR+T)*invTminS;
-							else 					res = 0.0f;
+							if (T <= offsetR)       res = 1.0f;
+							else if (S < offsetR)   res = 1.0f - 0.5f*(T-offsetR)*(T-offsetR)*invTminS;
+							else if (-S < offsetR)  res = 0.5f + offsetR;
+							else if (-T < offsetR)  res = 0.5f*(offsetR+T)*(offsetR+T)*invTminS;
+							else                    res = 0.0f;
 
 							// left ray edge
-							if (T <= offsetL) 		res -= 1.0f;
-							else if (S < offsetL) 	res -= 1.0f - 0.5f*(T-offsetL)*(T-offsetL)*invTminS;
+							if (T <= offsetL)       res -= 1.0f;
+							else if (S < offsetL)   res -= 1.0f - 0.5f*(T-offsetL)*(T-offsetL)*invTminS;
 							else if (-S < offsetL)  res -= 0.5f + offsetL;
 							else if (-T < offsetL)  res -= 0.5f*(offsetL+T)*(offsetL+T)*invTminS;
 
-
 							p.addWeight(iRayIndex, iVolumeIndex, pixelArea*res);
 							p.pixelPosterior(iVolumeIndex);
 						}