Trilinear interpolation along the ray

implementation of trilinear interpolation of CT voxel intensities to render properly sub-voxel transforms
related to issue #150
it seems to work, to understan how much the performance degrades and if this should be always performed or not.

reg23Topograms/itkDTRrecon/itkgSiddonJacobsRayCastInterpolateImageFunction.hxx

@@ -139,7 +139,6 @@ gSiddonJacobsRayCastInterpolateImageFunction<TInputImage, TCoordRep>::Evaluate(c
     const OutputType minOutputValue = itk::NumericTraits<OutputType>::NonpositiveMin();
     const OutputType maxOutputValue = itk::NumericTraits<OutputType>::max();
 
-
     // If the volume was shifted, recalculate the overall inverse transform
     unsigned long int interpMTime = this->GetMTime();
     unsigned long int vTransformMTime = m_Transform->GetMTime();
@@ -156,9 +155,12 @@ gSiddonJacobsRayCastInterpolateImageFunction<TInputImage, TCoordRep>::Evaluate(c
     }
 
     PointType PointReq = point;
+    //std::cout<<"PointReq: "<<point[0] <<" "<<point[1] <<" "<<point[2] <<" "<<std::endl;
     PointReq[0] += m_PanelOffset;
 
     drrPixelWorld = m_InverseTransform->TransformPoint(PointReq);
+    //std::cout<<"drrPixelWorld: "<<drrPixelWorld[0] <<" "<<drrPixelWorld[1] <<" "<<drrPixelWorld[2] <<" "<<std::endl;
+
 
     // Get ths input pointers
     InputImageConstPointer inputPtr = this->GetInputImage();
@@ -182,6 +184,7 @@ gSiddonJacobsRayCastInterpolateImageFunction<TInputImage, TCoordRep>::Evaluate(c
     SlidingSourcePoint[2] = 0.;
 
     PointType SourceWorld = m_InverseTransform->TransformPoint(SlidingSourcePoint);
+    //std::cout<<"SourceWorld: "<<SourceWorld[0] <<" "<<SourceWorld[1] <<" "<<SourceWorld[2] <<" "<<std::endl;
 
     PointType O(3);
     O[0] = -ctPixelSpacing[0]/2.;
@@ -431,6 +434,7 @@ gSiddonJacobsRayCastInterpolateImageFunction<TInputImage, TCoordRep>::Evaluate(c
     cIndex[1] = firstIntersectionIndexDown[1];
     cIndex[2] = firstIntersectionIndexDown[2];
 
+
     while (alphaCmin < alphaMax) /* Check if the ray is still in the CT volume */
     {
         /* Store the current ray position */
@@ -458,17 +462,80 @@ gSiddonJacobsRayCastInterpolateImageFunction<TInputImage, TCoordRep>::Evaluate(c
             alphaZ = alphaZ + alphaUz;
         }
 
+
         if ((cIndex[0] >= 0) && (cIndex[0] < static_cast<IndexValueType>(sizeCT[0])) && (cIndex[1] >= 0) &&
-                (cIndex[1] < static_cast<IndexValueType>(sizeCT[1])) && (cIndex[2] >= 0) &&
+            (cIndex[1] < static_cast<IndexValueType>(sizeCT[1])) && (cIndex[2] >= 0) &&
-                (cIndex[2] < static_cast<IndexValueType>(sizeCT[2])))
+            (cIndex[2] < static_cast<IndexValueType>(sizeCT[2])))
         {
-            /* If it is a valid index, get the voxel intensity. */
+            // Calculate entry and exit points using alphaCmin and alphaCminPrev
-            value = static_cast<float>(inputPtr->GetPixel(cIndex));
+
+            PointType entryPoint;
+            entryPoint[0] = SourceWorld[0] + alphaCminPrev * rayVector[0] ;
+            entryPoint[1] = SourceWorld[1] + alphaCminPrev * rayVector[1] ;
+            entryPoint[2] = SourceWorld[2] + alphaCminPrev * rayVector[2] ;
+
+            PointType exitPoint;
+            exitPoint[0] = SourceWorld[0] + alphaCmin * rayVector[0] ;
+            exitPoint[1] = SourceWorld[1] + alphaCmin * rayVector[1] ;
+            exitPoint[2] = SourceWorld[2] + alphaCmin * rayVector[2] ;
+
+//            PointType entryPoint = SourceWorld + alphaCminPrev * rayVector;
+//            PointType exitPoint = SourceWorld + alphaCmin * rayVector;
+            PointType midpoint;
+            midpoint[0]= (entryPoint[0] + exitPoint[0]) * 0.5;
+            midpoint[1]= (entryPoint[1] + exitPoint[1]) * 0.5;
+            midpoint[2]= (entryPoint[2] + exitPoint[2]) * 0.5;
+
+//            = (entryPoint + exitPoint) * 0.5;
+
+
+            // Calculate fractional parts for interpolation at the midpoint
+            double x_frac = midpoint[0] - std::floor(midpoint[0]);
+            double y_frac = midpoint[1] - std::floor(midpoint[1]);
+            double z_frac = midpoint[2] - std::floor(midpoint[2]);
+
+            // Perform boundary checks for trilinear interpolation
+            IndexType baseIndex = cIndex;
+            bool within_bounds = (baseIndex[0] >= 0 && baseIndex[0] < sizeCT[0] - 1) &&
+                                 (baseIndex[1] >= 0 && baseIndex[1] < sizeCT[1] - 1) &&
+                                 (baseIndex[2] >= 0 && baseIndex[2] < sizeCT[2] - 1);
+
+            if (within_bounds)
+            {
+                // Fetch intensities from neighboring voxels for trilinear interpolation
+                float c000 = static_cast<float>(inputPtr->GetPixel(baseIndex));
+                baseIndex[0] += 1; float c100 = static_cast<float>(inputPtr->GetPixel(baseIndex));
+                baseIndex[1] += 1; float c110 = static_cast<float>(inputPtr->GetPixel(baseIndex));
+                baseIndex[0] -= 1; float c010 = static_cast<float>(inputPtr->GetPixel(baseIndex));
+                baseIndex[2] += 1; float c011 = static_cast<float>(inputPtr->GetPixel(baseIndex));
+                baseIndex[0] += 1; float c111 = static_cast<float>(inputPtr->GetPixel(baseIndex));
+                baseIndex[1] -= 1; float c101 = static_cast<float>(inputPtr->GetPixel(baseIndex));
+                baseIndex[0] -= 1; float c001 = static_cast<float>(inputPtr->GetPixel(baseIndex));
+
+                // Perform trilinear interpolation at the midpoint
+                float c00 = c000 * (1 - x_frac) + c100 * x_frac;
+                float c01 = c001 * (1 - x_frac) + c101 * x_frac;
+                float c10 = c010 * (1 - x_frac) + c110 * x_frac;
+                float c11 = c011 * (1 - x_frac) + c111 * x_frac;
+
+                float c0 = c00 * (1 - y_frac) + c10 * y_frac;
+                float c1 = c01 * (1 - y_frac) + c11 * y_frac;
+
+                value = c0 * (1 - z_frac) + c1 * z_frac;
+            }
+            else
+            {
+                // Fallback to nearest voxel intensity if out-of-bounds
+                value = static_cast<float>(inputPtr->GetPixel(cIndex));
+            }
+
+            // Accumulate the interpolated intensity along the ray path
             if (value > m_Threshold) /* Ignore voxels whose intensities are below the threshold. */
             {
                 d12 += (alphaCmin - alphaCminPrev) * (value - m_Threshold);
             }
         }
+
     }
 
     if (d12 < minOutputValue)