Master Thesis - Computer Graphics and Visualization - TU Delft

Appendix E
BDPT Algorithm
This appendix gives a more detailed description of the BiDirectional Path Tracing algorithm
discussed in section 2.7. Remember that BDPT can sample a light transport path through
one of several different bidirectional sampling strategies, including the explicit and implicit
sampling strategies from the PT algorithm. In the last appendix, we already showed how
to compute the contribution for explicit and implicit paths. In this appendix, we show how
to compute the contribution for paths sampled using one of the remaining bidirectional
sampling strategies. Using these contributions and the recursive MIS weights from section
8.2, the general layout of the BDPT algorithm is given in pseudo code.
E.1 Path contribution
f (X)
p(X) (see
The contribution of a sampled path X = x0 ···xk to the Monte Carlo estimate equals
section 2.3). Just like paths sampled through path tracing, the measurement contribution
function f (X) shares several factors with the probability p(X) for bidirectionally sampling
f (X)
paths per unit path space, which again cancel out in the Monte Carlo contribution p(X) .
Remember from section 2.7 that a path X = x0 ···xk of length k can be sampled using
either one of k + 1 sampling strategies. Furthermore, ˆps (X) is the probability of bidirectionally
sampling X by connecting the eye path x0 ···xs of length s1 with the light path
xs+1 ···xk of length t = k − s. Paths sampled using light paths of length t = 0 and t = 1 correspond
to implicit and explicit paths as sampled by a path tracer. We already showed how
common factors cancel out in the contribution of implicit and explicit paths in appendix D.
What is left are the contributions for paths sampled using any of the remaining bidirectional
sampling strategies.
For paths sampled with a zero length eye path (s = 0), all vertices except x0 are sampled
as part of the light path. After combining equations B.7, C.6 and 2.4 and canceling out the
1 Note that because x0 is also part of the eye path, an eye path of length s contains s + 1 vertices.
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