This PowerPoint 2007 template produces a 36”x48” Yun Fei and … · 2020-01-02 · This...
Transcript of This PowerPoint 2007 template produces a 36”x48” Yun Fei and … · 2020-01-02 · This...
QUICK TIPS
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QUICK DESIGN GUIDE (--THIS SECTION DOES NOT PRINT--)
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Fast Multi-image-based Photon Tracing with Grid-based Gathering
We developed a real-time solution for approximate global
illumination, where the temporal cost in complex scenes is
dramatically reduced. Our approach initially traces photon-rays
with multiple cube-maps, and then gathers the irradiance of
photons using uniform grids filled with low-order spherical
harmonics. Numerous global illumination effects can be rendered
efficiently in our framework.
ABSTRACT
Problem Formation
Improved Multi-image-based Ray-tracing
Limitations for Future Works
References
[1] Yao, C., Wang, B., Chan, B., Yong, J., and Paul, J.-C. Multi-
image based photon tracing for interactive global illumination of
dynamic scenes. Comput. Graph. Forum 29, 4 (2010), 1315—1324.
[2] Szirmay-Kalos, L., Aszodi, B., Lazanyi, I., and Premecz, M.
Approximate ray-tracing on the gpu with distance impostors.
Comput. Graph. Forum 24, 3 (2005), 695—704.
[3] Kajiya, J.T. The rendering equation, In Proceedings of the
SIGGRAPH ‘86, pp. 143—150.
[4] Sloan, P.-P. Stupid spherical harmonics (sh) tricks. In
Lectures of the GDC '08 (2008), pp. 1—41.
[5] Kaplanyan, A., and Dachsbacher, C. Cascaded light
propagation volumes for real-time indirect illumination.
In Proceedings of the I3D '10 (2010), pp. 99—107.
Ray-tracing and light-gathering are the two key steps in two-pass
rendering algorithms, such as photon mapping, etc. Recent method
focusing on multi-image-based photon mapping [1] works well in
simple scenes, but has serious limitations in complex scenes due to
three reasons: a) they intersect a photon-ray iteratively with
distance imposters (cube maps), where, however, the initialization
can be far from accurate, which leads the iterative refinement to
be failed (Figure 1); b) they intersect a photon-ray with all the
distance imposters in the scene, which is costly and unnecessary; c)
the method for radiance estimation called splatting, is not
efficient when there are large amount of photons, since splatting
millions of photons will need the rasterization of billions of pixels.
School of Software, Tsinghua University, P. R. China
Yun Fei and Bin Wang
Introduction
We propose an effective solution focusing on ray-tracing and
intensity-estimating in complex scenes. Our first contribution is a
heuristic ray-tracing scheme that initializes in a more reasonable
way, providing a reliable beginning for the later refinement;
afterwards only one or two cube-maps are used by each photon-ray,
which increases the efficiency of ray-cube-map intersection over
an order of magnitude. Our second contribution is an approximate
grid-based light-gathering technique for all-frequency effects.
Each photon is represented with a spherical harmonics (SH) vector,
which is later stored into two types of uniform grids. One grid
called light-gathering volume, or LGV, is a 3D volume used to
gather smoothed light such as diffuse lighting, and the other one,
called screen-space LGV (SSLGV), is a screen-space grid used to
gather more detailed light such as caustics.
To solve the failure case in the existing algorithm and to improve
the efficiency, we propose a new solution, based on two
observations that: 1) the intersection point is only strongly
related to the ambient objects near to the photon-ray, and 2) the
existing methods failed since their initialization is not reliable.
We detailed our method in two stages:
1) use a cascaded partition scheme to find an intersection close to
be accurate, used as the initialized point (Figure 2). In this step,
the cube-map closest to the photon-ray origin is chosen as the
distance imposter. We then subdivide the 3D plane (the yellow
region) into several intervals. Then we minimize an energy across
these intervals. Then we check whether the energy changing
between the energy in a previous loop to the current one is
sufficiently small. If it is not, we uniformly subdivide the newly
computed 3D fan-shape again (the blue region, for example) and
minimize the energies; otherwise, we exit the loop.
2) From the initialized point we find an exact solution following
the work proposed by Szirmay-Kalos et al.[2], using the cube-map
closest to the initial testing point.
The Energy Function:
To compute the energy function, we firstly fetch two distance
imposters from the cube-map, in the directions of the two
boundaries, denoted as 𝑝𝑖 and 𝑝𝑖+1. Then we individually compute
functions 𝑓 𝑝𝑖 and 𝑓 𝑝𝑖+1 (defined below), and add them up as
the energy function.
𝑓 𝑝 is defined as the difference volume (Figure 3) estimated
between a testing point 𝑝 and the correct intersection. It is
designed based on the two key observations below:
1) the distance from the position of a photon 𝑡 to a point on the
distance impostor 𝑝 should be as close as to the length of its
projection on the ray direction, specifically:
𝑑 𝑝 = 𝑝 − 𝑡 − 𝑝 − 𝑡 , 𝑟 ≈ 0
2) both of the terms, 𝑝 − 𝑡 and 𝑝 − 𝑡 , 𝑟 , should be small.
To fulfill theses two conditions, we compute the volume of a
triangle frame around 𝑝 − 𝑡 and its projection on 𝑟 .
𝑓 𝑥 = 𝑝 − 𝑡 − 𝑝 − 𝑡 , 𝑟 2
𝑝 − 𝑡 + 𝑝 − 𝑡 , 𝑟 , 𝑝 − 𝑡 , 𝑟 > 0
&∞, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Light Gathering Volume
In this section, we introduce our novel strategy for photon
gathering. Our approach can be detailed into three phases: 1)
photon injection, 2) light-gathering, and 3) scene illumination
(Figure 4).
Screen-space Light Gathering Volume
High frequency details such as caustics need higher order of SH-
vectors. When using a lattice filled with SH-approximation in low-
order, the resolution of the grid has to be increased. This
increasing can be unacceptable for high frequency details under
both spatial and temporal considerations. Fortunately, the high-
resolution computation is much less costly to be taken in screen-
space. Therefore, we propose a 2D grid to assist the light-
gathering process (Figure 5).
Injection: Photons are transformed into eye-space and filtered,
according to whether they are caustics photons or not. Then they
are injected into a 2D texture in the manner similar to LGV.
Gathering: For each pixel in the eye-space, the SH-approximation
is extracted from its 4-neighbored pixels and is projected to the
directions to the centroid pixel. The direction is computed using
world space coordinate recorded in the previously rendered
position buffer.
Illumination: After several times of iteration, the SSLGV-texture is
rendered with projection that estimates the intensity along the
surface normal.
Our method shares some artifacts that are pervasive in existing
lattice-based methods, specifically temporal discontinuity and
light bleeding. Besides, the rendering quality of some flattened
“middle”—frequency caustics is still very photon-dependent where
tracing billions of photons is still unavailable in real-time.
Therefore some techniques for importance sampling may be
introduced into our pipeline in the future.
The Light Gathering Volume (LGV) is a 3D texture covering the
entire scene. After ray-traced, photons are injected into the LGV
via two stages: 1) we transform the position that a photon-ray
intersects with objects into the coordinate of texel in the 3D
texture, and 2) we accumulate the SH-approximation of intensity
into the texel. Each texel stores the SH-approximations of the
radiance contributed by injected photons. For each photon 𝑗, the
radiance 𝐿𝑗 is calculated with the following formula (which can be
derived from the Kajiya’s rendering equation [3]):
𝐿𝑗 =𝐴𝐶0
2
4𝑁Φ𝑝 Θ𝑗 , 𝑛
+𝑓𝑟(𝑥)
𝐴: the total area of the scene; 𝑁: the amount of photons cast; 𝐶0:
a variant bandwidth factor [1]; Θ𝑗: the normalized incident
direction of the photon. Φ𝑝: the power of the photon injected;
𝑓𝑟(𝑥): the BRDF around point 𝑥; 𝑛: the normal of surface hit by the
photon.
The radiance 𝐿𝑗 is approximated by spherical harmonics (SH)
vectors [4]. Multiple SH-vectors each of which corresponds to one
photon are accumulated with additive blending. After injection,
the radiance in each texel can represent the local illumination
around the position of the texel (in world space). Then for each
texel, we gather intensity from its six neighborhoods adjacent to it
following Kaplanyan’s light propagation framework [5].
Figure 1: the photon ray 𝑟 is intersected with the
distance imposter. With an
unreliable initialization
point 𝐴 chosen, the wrong
result 𝐵&would be generated
by existing approaches. Even
with two cube maps used
(two blue points), the
correct result is still
unapproachable.
Figure 2: We divide the fan
shape area (yellow)
supported by the center-
photon vector and the ray
direction into several
intervals, and find a
position with the minimum
energy as a “reliable initial
testing point” (point 𝐼 in the
figure), then we refine this
point to the correct result.
Figure 4: The photon injection, light gathering and reprojection,
the figure is adapted from [4].
Figure 3: The difference
volume showed with
trans-lucent blue boxes.
When the 𝑝 − 𝑡 gets
smaller, 𝑓 𝑥 is
determined by
𝑝 − 𝑡 − 𝑝 − 𝑡 , 𝑟 2,
which is the thickness
of the triangle frame.
Figure 5: During the photon
injection, the light contributed
by each photon is accumulated
in the axis perpendicular to the
clipping plane. During gathering,
SH-approximations in the yellow
cells (pixels) are accumulated
into the current grey cell (pixel),
and the one in the red cell
(pixel) is declined for its
distance to the current pixel is
larger than some given radius.
Figure 6: Without pre-computation, our technique renders
dynamic global illumination effects in a complex scene in real-
time on a GTX480).
Figure 7: Comparisons of the results. Our result is comparable to
the referenced results rendered in two hours with V-Ray, as well
as the result rendered in 24 minutes with PBRT.
Contact: E-mail: [email protected], [email protected]
a) 56Hz b) 22Hz
c) 19Hz 38Hz