VolumeRendering
Numerical Integration
← Absorption | ● | Integration with OpenGL →
Single step of numerical integration:
I′=I⋅e−μ(t)⋅Δt
Numerical integration with alpha-blending:
I′=I⋅(1−alpha)
alpha=1−e−μ(t)⋅Δt
Approximation for small Δt:
alpha=1−e−μAs(t)⋅Δt
alpha=(1−e−μAΔt)s(t)
Over-Operator:
RGB′frame=AfragmentRGBfragment+(1−Afragment)RGBframe
with
RGBfragment=(0,0,0)
Afragment=1−e−μAs(t)⋅Δt
Further approximation:
Afragment=1−e−μA⋅Δt moduliert mit s(t)
Realization of numerical integration with OpenGL: Numerical integration by view-aligned slicing with slice distance Δt with over-operator and constant vertex opacity α=1−e−μAΔt, constant vertex color (0,0,0) and modulation of vertex opacity with 3D-texture lookup of s(t).
Ambient background emission (white background) is attenuated:
X-Ray Positiv:
X-Ray Negativ:
- Advantage: commutative
- Disadvantage: no depth perception
← Absorption | ● | Integration with OpenGL →