Real-time Rendering of Indirectly Visible Caustics

Pierre Moreau

and Michael Doggett

Faculty of Engineering, Lund University, Lund, Sweden

Keywords:

Real-time, Ray Tracing, Caustics Rendering.

Abstract:

Caustics are a challenging light transport phenomenon to render in real-time, and most previous approaches

have used screen-space accumulation based on the fast rasterization hardware of GPUs. This limits the posi-

tion of photon collection points to ﬁrst hit screen space locations, and leads to missing caustics that should be

visible in a mirror’s reﬂection. In this paper we propose an algorithm that can render caustics visible via spec-

ular bounces in real-time. The algorithm takes advantage of hardware-accelerated ray tracing support found in

modern GPUs. By constructing an acceleration structure around multiple bounce view ray hit points in world

space, and tracing multiple bounce light rays through the scene, we ensure caustics can be created anywhere

in the scene, not just in screen space. We analyze the performance and image quality of our approach, and

show that we can produce indirectly visible caustics at real-time rates.

1 INTRODUCTION

Caustics are a natural phenomenon created by the

concentration of light as it is reﬂected and trans-

mitted through objects. While many techniques ex-

ist to generate these lighting effects in images of

three dimensional scenes, generating them in real-

time for interactive applications is challenging. A

popular approach to achieving real-time performance

is the use of screen-space algorithms, but these algo-

rithms come with limitations, in particular not work-

ing well for scenes with reﬂective surfaces and semi-

transparent objects. For consistent viewing of ren-

dered images, lighting effects like caustics need to

remain constant. Screen-space accumulation tech-

niques can lead to inconsistent renderings with light-

ing effects switching on and off, or even missing in

mirrors, as can be seen in Figure 1 for the technique

by Kim (2019).

Caustics have always been an important feature

of rendering research and go back to early backward

ray tracing techniques (Arvo, 1986). More recent ap-

proaches have used the rasterization pipeline and off-

screen buffers for a range of techniques such as caus-

tic mapping (Hu and Qin, 2007; Shah et al., 2007;

Szirmay-Kalos et al., 2005; Wyman and Davis, 2006).

While these techniques create good approximations,

many issues remain, including sampling rates, large

https://orcid.org/0000-0003-3916-1250

https://orcid.org/0000-0002-4848-3481

numbers of photons, and potential coherency prob-

lems during animation. With the recent introduc-

tion of hardware-accelerated ray tracing, new ap-

proaches (Kim, 2019; Ouyang and Yang, 2020a; Yang

and Ouyang, 2021) take advantage of this to create

high-quality caustics, but still do not handle caustics

not directly visible.

Screen-space accumulation techniques that only

collect lighting contributions at locations that are di-

rectly visible by the current camera are always lim-

ited in terms of correctly rendering a scene. For the

case of a scene where a caustic is visible via its re-

ﬂection in a mirror, the lighting contributions would

be collected on the mirror itself. This means the pho-

tons responsible for the caustic would need to be re-

ﬂected off the diffuse surface and into one of the col-

lection locations on the mirror. This is unlikely as

the BSDF sampling will have a low chance at return-

ing a direction towards the mirror in most cases and

that direction needs to be within the tight lobe of a

rough mirror, and outright impossible in the case of

a perfectly-specular mirror. Furthermore most real-

time caustic-rendering techniques stop the light path

at the ﬁrst diffuse hit, preventing the caustic photons

from ever reaching that mirror and being accounted

for; this cut is performed for performance reasons as

caustic paths with two or more diffuse hits will have

a more subtle contribution than caustic paths with a

single diffuse hit.

This paper proposes to collect photons, on dif-

Moreau, P. and Doggett, M.

Real-time Rendering of Indirectly Visible Caustics.

DOI: 10.5220/0010777800003124

In Proceedings of the 17th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2022) - Volume 1: GRAPP, pages

39-48

ISBN: 978-989-758-555-5; ISSN: 2184-4321

(a) Reference. (b) Kim (2019), 24.7 ms. (c) Our approach, 25.6 ms.

Figure 1: This ﬁgure shows a challenging setup for real-time caustics which are only visible via a chain of specular events,

such as mirror reﬂections. As Kim (2019) accumulates photon contributions in screen space, contributions for anything seen

via this perfectly specular mirror will be collected on the mirror itself requiring them to come from one very speciﬁc direction

in order to have any impact; the caustics visible via the different mirrors are completely missing as a result. Our new approach

can handle the caustics since its accumulation is based around a world-space acceleration structure. This scene was rendered

at 1920 × 1080 with a path length of 6 segments using different algorithms; (a) uses 125k samples per pixel (spp), (b) 1 spp

and 14M light paths, and (c), our temporal approach, 1 spp and 1M light paths.

fuse surfaces, at viewing ray hit points, found using

hardware-accelerated ray tracing. At each hit point

for a light path, a Bounding Volume Hierarchy (BVH)

node is created and constructed into a BVH tree using

DirectX Raytracing. By creating a full scene BVH,

the algorithm is not limited to screen-space- or view-

frustum-based images. We then query the BVH us-

ing the algorithm by Evangelou et al. (2021). We also

use ray differentials for appropriate sizing of the BVH

nodes, and use the BVH structure as a temporal cache

for ﬁltering. Our key contribution is enabling real-

time indirect caustics, by combining view and light

rays with a custom BVH, all using ray tracing hard-

ware acceleration.

2 RELATED WORK

Tracing light rays or photons from a light source to

an opaque surface and accumulating light intensity on

a surface has been a common approach to generat-

ing caustics (Arvo, 1986; Jensen, 2001). Generating

caustics in real-time can be done by reproducing pho-

ton mapping on a GPU (McGuire and Luebke, 2009),

but these approaches are expensive and not capable of

generating highly accurate caustics.

Another method for generating caustics in real-

time is caustic maps. Caustic maps are generated by

ﬁrst making a photon buffer by emitting photons from

the light’s perspective into a two-dimensional buffer

similar to shadow maps. The photons from the pho-

ton buffer are then drawn into the caustic map, which

is projected onto the ﬁnal image. Szirmay-Kalos

et al. (2005) and Wyman and Davis (2006) improved

quality by increasing photon count and Wyman and

Nichols (2009) created a hierarchical caustic map,

that adaptively processed only the necessary parts of

the photon buffer. But caustic maps still limit the lo-

cations that photons can be captured at, and the pro-

jection of high photon counts into the caustic map

quickly becomes expensive when trying to improve

image quality.

With the advent of hardware accelerated ray trac-

ing, several new approaches to real-time rendering of

caustics have made use of this feature. Kim (2019)

uses projection volumes to direct photons towards

semi-transparent objects to create photon maps lim-

iting visible caustics to these projection volumes.

Gruen (2019) focuses on creating volumetric wa-

ter caustics in single-scattering participating media

where a water surface casts a caustic on an underlying

surface, but it does not handle refracted and then re-

ﬂected light rays. Ouyang and Yang (2020a,b); Yang

and Ouyang (2021) introduce caustic meshes for gen-

eral caustics, but their method requires two passes for

reﬂected and refracted caustics, and only caustics in

the current viewport can be seen in this case. They

further combine their technique with cascaded caustic

maps for water caustics, but are focused on the caustic

on the surface underlying the water. Wang and Zhang

(2021) only trace rays after intersecting with a semi-

transparent object, at which point it ﬁres photons into

a caustic map to layer onto the ﬁnal image. By using a

caustic map, their algorithm has similar limitations to

screen-space techniques. While all these recent meth-

ods address caustics, some are screen space limited,

and none of them address the issues of indirect caus-

tics where photons must be accumulated outside the

view frustum to correctly handle reﬂected caustics,

and caustics behind semi-transparent objects.

Evangelou et al. (2021) present a fast radius search

by mapping the problem to GPU ray traversal and

can therefore take advantage of ray tracing hardware.

In our algorithm, we utilise their approach to query

the BVH used when accumulating photons as well as

when reusing the accumulation results in later frames.

GRAPP 2022 - 17th International Conference on Computer Graphics Theory and Applications

They evaluate their algorithm by using it for pro-

gressive photon mapping (Hachisuka et al., 2008) by

building an acceleration structure around the photons

traced from the light, whereas in our algorithm we

build the acceleration structure around the camera ray

hit points, where photons are collected.

3 ALGORITHM

Unlike screen-space techniques, our approach accu-

mulates photons in a world-space caching structure

based on arbitrary points and their surroundings. The

size of that area is uniquely computed at each caching

point, enabling support for ﬁne-detail caustics.

The stages of our algorithm are shown in Figure 2.

The ﬁrst stage is a path tracer which identiﬁes the ﬁrst

diffuse hit found along each camera path where light

contributions will later be collected, similar to pro-

gressive photon mapping (Hachisuka et al., 2008). In

our algorithm we refer to these hit points as collec-

tion points. An acceleration structure is then created

around the collection points, and light paths are traced

to accumulate light intensity at each collection point.

Finally the output is resolved before being processed

using a spatiotemporal ﬁlter.

We will be using the following notation: c

refers to a collection point in frame i, C

refers to all collection points present in frame

i. A collection point has the following attributes:

p world position

τ camera sub-path throughput

r search radius

n world normal

I accumulated radiant intensity

m material ID

exitant radiance

interpolated exitant radiance

weighted contributions from previous collec-

tion points

Figure 3 shows an overview of our setup with

camera and light paths. When path tracing, the col-

lection points are selected based on the BSDF com-

ponent that was evaluated for generating the reﬂected

ray at a hit: if a diffuse component was used, then we

create a collection point at the hit point. In Figure 3,

this is the case for p

and m

but not m

as it sampled

the specular component of the mirror.

Selecting a Search Radius. As collecting from a

single point in space is infeasible in practice, we in-

stead gather from a surrounding area. We use the ra-

dius of the disk enclosing the pixel footprint in world

space for the collection points at primary hits, as a

reasonable middle ground between over-blurring and

light leakage, and too restrictive radii that would ig-

nore most light paths.

To compute the pixel footprint for collection

points at secondary hits, we use half the width of ray

cones as described by Akenine-Möller et al. (2021) as

our search radius, and take the BSDF roughness into

account as described in their Section 4. The ray cones

computation is cheaper than ray differentials (Igehy,

1999), and is necessary for texture level of detail cal-

culation.

Creating the Acceleration Structure. We use a

similar approach to Evangelou et al. (2021) for ac-

celerating radius searches. In their work they recom-

mended building the acceleration structure around the

photons rather than around the collection points, as

atomics can then be avoided for updating the accumu-

lated contributions at each collection point, as having

overlapping collection points (for example when the

same area is visible both directly and via a mirror) can

noticeably decrease performance. The overhead from

using atomics is about 5%; please see Section 3.2 for

more details.

In contrast, we build the acceleration structure

around the collection points for the following reasons:

• more predictable quality reduction when decreas-

ing the number of collection points to improve

performance, than reducing the number of pho-

tons stored;

• the light contributions accumulated at collection

points can be easily reused over multiple frames,

as presented in Section 3.1.

• building around photons forces the use of the

largest radius for each of them, which can be

costly as radii depend on location and intersected

shapes and materials;

As numerical precision errors might result in the

hit position being slightly above or below the sur-

face, we gather from a cylinder rather than from a

disk, similarly to most photon mapping methods. The

cylinder is aligned along c

.n, uses the same radius

.r, and has its height set to a tenth of c

.r. We then

compute the smallest AABB containing that cylinder

and use it as the primitive around which the accelera-

tion structure is built.

Tracing Light Sub-paths. The algorithm does not

depend on how the set of light sources and individ-

ual light sources are being sampled, so different tech-

niques can be used here such as the recent works by

Kim (2019) or by Ouyang and Yang (2020a); Yang

and Ouyang (2021).

Real-time Rendering of Indirectly Visible Caustics

Identify collection points Build collection point AS

Trace light sub-paths

Resolve

Temporal feedback loop

Adapt past accumulations to current collection points

Figure 2: An overview of the different steps of our approach, with all boxes with a green colour constituting the basic algo-

rithm, and the grey ones were either added or modiﬁed to support temporal reuse. All steps are performed in programmable

shaders, except for the rectangle with non-rounded corners, which is instead taken care of by the API.

mirror

diffuse

mirror

diffuse

frame i

frame i+1

Figure 3: An overview of our indirect-caustic algorithm. Camera paths, p, m, are traced to the ﬁrst diffuse surface intersection,

where collection points (shown as red boxes) are created and placed in a BVH. Then light paths, q, are traced via specular

intersections and collected. The path m will generate an indirect caustic in the ﬁnal image. On the right half of the image

is frame i + 1, which shows how new collection points are created when the camera rays change, but collection points from

previous frames can still be reused.

Regardless of the chosen method(s) for sampling

and tracing the light sub-paths, every time the sub-

path hits a surface we will query and selectively up-

date all collection points that contain this hit. As

we leverage a hardware accelerated BVH and ray

tracing API, this is implemented by tracing a very

short ray (Wald et al., 2019), starting from the hit,

against the acceleration structure storing our collec-

tion points. For each intersected collection point,

we ﬁrst check that the hit is actually located within

the collection cylinder and that its material identiﬁer

matches the one stored in the collection point, before

accumulating in c

.I the ﬂux carried by the photon

into radiant intensity reﬂected towards the vertex prior

to the collection point in the camera sub-path (e.g. to-

wards m

if accumulating at m

Resolving. Before presenting the results to the user,

the accumulated radiant intensity needs to be trans-

formed into radiance, and take account of the through-

put of the camera sub-path connecting a collection

point to a pixel. This is summarised in the following

equation:

= c

.τ

πc

(1)

3.1 Temporal Reuse

A beneﬁt of our approach is that we can reuse the ex-

act same accumulated radiant intensity and just mul-

tiply it by the new camera sub-path throughput when

a directly-visible caustic moves behind a transparent

object for example, as only the light sub-path contri-

bution gets accumulated. Whereas this accumulated

data would usually be discarded by ﬁlters on occlu-

sions or disocclusions, having the data stored in world

space allows us to reuse it if appropriate.

The reuse happens in two separate steps: ﬁrst we

gather contributions from all past collection points lo-

cated near current ones, and second, past and present

contributions are combined together during the re-

solve step using an exponential moving average with

α = 0.8:

= αc

+ (1−α)c

(2)

Reusing Past Accumulations. This takes place be-

tween the identiﬁcation of collection points in the cur-

rent frame and resolve. If keeping two acceleration

structures in memory is an issue, this step should be

performed before updating the collection point accel-

eration structure for the current frame.

GRAPP 2022 - 17th International Conference on Computer Graphics Theory and Applications

We query all collection points c

i−1

∈ C

i−1

con-

taining c

. p, by tracing a very short ray originating

from c

. p against the acceleration structure built dur-

ing the previous frame. For each intersected collec-

tion point c

i−1

satisfying the system of equations (4)

(similar to a bilateral ﬁlter), its interpolated radiance

i−1

weighted by a Gaussian kernel w(c

i−1

) of

width σ =

.r is accumulated into c

w(c

i−1

) = exp



−kc

. p − c

i−1

. pk

2σ



(3)











i−1

. p − c

. pk ≤ c

i−1

.n · c

.n ≥ 0.9

i−1

.m = c

(4)

3.2 Implementation Details

General Constraints. If path tracing is used by

an application, care needs to be taken to avoid

the path tracer evaluating the same paths as the

photon-based approach, or to weigh them appropri-

ately. As we simply add the results from both ap-

proaches, we prevent the path tracer from evaluating

paths containing at least one diffuse and one specu-

lar bounce as those will be handled by the photon-

based approach. Using Heckbert’s light transport no-

tation (Heckbert, 1990), this corresponds to paths of

the form ES*D(S|D)*S(S|D)*L.

In all presented results, the search radius was

capped to 5 mm as a middle ground between perfor-

mance of the light tracing stage and quality.

Performance Improvements. For the ﬁrst stage of

the pipeline, we found that storing all the data asso-

ciated to our caching approach as soon as a suitable

collection point was identiﬁed, rather than at the end

to minimise control ﬂow divergence, improved the

performance of that stage from 20 ms down to about

4 ms. This is due to not having to keep all that data

live accross the tracing of path segments.

As current APIs do not expose atomic additions

for ﬂoats, we ﬁrst implemented the contribution ac-

cumulation using atomic compare-and-swap within a

loop, resulting in a 15% overhead compared to no

atomics. By instead using ﬁxed-point values and in-

teger atomic add, the overhead was reduced to 5%.

As the accumulated values are well below 1, we only

used 4 digits for the decimal part and the remaining

28 for the fractional part.

4 RESULTS

We implemented our approach on top of

Kim’s (2019), inside the Falcor (Benty et al.,

2020) 4.3 framework using the DirectX 12 and

DirectX Raytracing API. All results were obtained

on an NVIDIA Geforce RTX 3080 with NVIDIA’s

471.96 drivers, and rendered at 1920 × 1080 with a

maximum path length of 6 segments and using 1024

light paths, unless mentioned otherwise. Spatiotem-

poral Variance-Guided Filtering (SVGF) (Schied

et al., 2017) was used to ﬁlter the computed images

before presenting them to the user.

In the following section we will be using the fol-

lowing abbreviations for methods: OurBasic which

refers to our basic algorithm described in Section 3

(i.e. without the temporal component) and integrated

with a path tracer as described in Section 3.2, and

OurTemporal which is our full algorithm (i.e. Our-

Basic plus the temporal component described in Sec-

tion 3.1).

All scenes, besides the ones shown in Figure 7,

use a similar template of a closed box whose left and

back wall and ceiling are specular, with the other parts

being diffuse. This box contains a simple emissive

mesh as the only light source, a transparent object,

and a mirror. Of these scenes, four have animations

of different types: animated camera (AC), animated

light (AL), animated geometry (AG; it is the trans-

parent sphere), and all animated (AA; it combines all

previous animations). They are all 10 seconds long

and animated at 30 fps. Unless mentioned otherwise,

the specular walls and ceiling in the animated scenes

have a roughness R of 0.08.

The Bistro Exterior and Bistro Interior scenes

used in Figure 7 were modiﬁed to limit the number

of emissive triangles by setting the emissivity to 0 for

most light sources. Additionally in Bistro Interior,

light paths were only traced from the lamps placed on

tables. To more easily showcase caustics, transparent

objects were added on the tables in Bistro Exterior

while some of the glasses were removed from Bistro

Interior to make more room on the tables. In both

scenes, the windows of the bistro were changed from

a very rough glossy surface into a specular mirror.

The source code and the videos can be found on

the project page

4.1 Performance

To evaluate the performance of our approach, we ran

it on different types of animations to see their impact.

https://ﬁleadmin.cs.lth.se/graphics/research/papers/

2022/indirectly_visible_caustics/

Real-time Rendering of Indirectly Visible Caustics

Figure 4: Measuring the total frame time taken by our basic and temporal algorithms for different types of animations. For

comparison a path tracer at equal quality would require about 175 spp and take between 2.5 and 3 seconds; this was measured

for equal

LIP-mean on AC@150 and AC@298.

Figure 5: Highlighting the performance of the main stages of the algorithm during the animation in the scene AC. The

identiﬁcation of collection points is performed during the path tracing step, and the G-buffer generation time (a constant

0.6 ms) was also included under the Path tracing step, while the resolve stage (a constant 0.4 ms) was included under the

SVGF step. 90% of the re-build time is spent on the bottom level acceleration structure. Not part of these plots, there is an

additional 0.27 ms per frame from tonemapping and other miscellaneous operations to reach the timings presented in Figure 4.

Note that accumulation reuse could be run concurrently to re-building the acceleration structure and tracing the light paths.

Looking ﬁrst at the total frame times presented

in Figure 4, we can see that the cost of our ap-

proaches remains relatively constant throughout the

light and geometry animations. Larger changes can

be observed during the camera animation and seem

to mostly correspond to changes in the number of

bounces before hitting a diffuse surface from the cam-

era. Most of that time variation comes from the pass

reusing the accumulated contributions from previous

frames with the current collection points.

Our approach can extend current path tracing-

based frameworks and as such reuse some of the com-

putations already performed there. For example the

identiﬁcation of collection points can be added to an

existing path tracer to store additional data without

having to re-trace the same rays in a separate pass.

We noted an increase in the cost of that pass from

about 3 ms to about 4 ms when doing so, for a path

tracer ignoring caustic paths. This combined cost is

presented in Figure 5, along with the cost of the other

steps.

The largest part of the cost of accumulation reuse

and light tracing comes from tracing against the col-

lection point acceleration structure and the invocation

of the intersection and any-hit shader, due to over-

lapping collection points and memory accesses to get

the needed information during the evaluation of the

shaders. For comparison, the same light tracing but

with the accumulation performed in screen space as

presented by (Kim, 2019) takes 1–1.5 ms, as opposed

to the 8.5–9 ms of our approach.

The second most expensive step is rebuilding

the acceleration structure. Rebuilding remains an

expensive operation for any real-time ray tracing-

based workﬂow, and as such reﬁtting is favoured for

most frames while rebuilding can be performed asyn-

chronously every now and then to keep the tracing

performance optimal. However the location or distri-

bution of collection points seemed to vary too much

between frames, resulting in reﬁtting degrading the

tracing performance by an order of magnitude as soon

as enabled. As the number of collection points de-

pends on the resolution of the rendering and not on the

scene, the cost of this step remained the same in the

Bistro Interior and Bistro Exterior scenes from Fig-

ure 7.

GRAPP 2022 - 17th International Conference on Computer Graphics Theory and Applications

Table 1: Average image quality measurements over 10 iterations using SVGF. OurBasic performing slightly better than

OurTemporal after ﬁltering in AL@150 can be explained by both the temporal lag and the contribution of longer paths having

a larger impact on the ﬁnal image than in the other scenes. Equal Time PT (3 spp) is about the same time as, or slightly more

expensive than, OurTemporal. The standard deviation was at or below 3.7% of the mean in all conﬁgurations, except for the

ﬁltered output in AG@10 for OurTemporal which reached 12.7% of the mean.

Scene, FrameID Measure

Equal Time PT (3 spp) OurBasic OurTemporal

Unﬁltered Filtered Unﬁltered Filtered Unﬁltered Filtered

Animated Camera, MAE 0.074 0.041 0.084 0.022 0.065 0.021

Frame 150

LIP 0.335 0.292 0.280 0.190 0.241 0.168

Animated Camera, MAE 0.162 0.063 0.150 0.036 0.111 0.028

Frame 298

LIP 0.468 0.363 0.410 0.229 0.309 0.179

Animated Light, MAE 0.117 0.084 0.116 0.037 0.088 0.045

Frame 150

LIP 0.562 0.520 0.384 0.273 0.335 0.276

Animated Light, MAE 0.077 0.034 0.097 0.029 0.073 0.025

Frame 298

LIP 0.323 0.292 0.338 0.261 0.291 0.218

Animated Geometry, MAE 0.127 0.090 0.135 0.036 0.093 0.034

Frame 10

LIP 0.465 0.406 0.364 0.204 0.266 0.173

All Animated, MAE 0.077 0.033 0.096 0.020 0.077 0.019

Frame 298

LIP 0.228 0.163 0.233 0.110 0.189 0.093

4.2 Quality

As our approach targets real-time applications with

different types of motions, we evaluated the qual-

ity at different points during animations rather than

on still images. We looked at the quality both prior

and after ﬁltering, as well as both numerical (using

mean-absolute error (MAE)) and perceptual (using

LIP (Andersson et al., 2020)) methods; all measure-

ments were performed on non-tonemapped outputs.

From Table 1 we can see that both OurBasic and

OurTemporal improve for both metrics in all but one

scene compared to the baseline. OurTemporal fur-

ther improves compared to our basic algorithm in

most scenes, for example in AC@198 the

LIP re-

sults are improved by nearly 15%) but also presents

some regressions as can be seen in AG@10 for exam-

ple (though they are within run to run variance).

There are multiple reasons for those regressions

that can be illustrated with results from Table 2. First,

when we reuse accumulated radiance from previous

frames we do not know the length of the light sub-

paths having contributed, so we can end up creating

longer paths than what was speciﬁed, as can be seen

for AG@10 in Table 2 at the top of the image where

the mirror contains a reﬂection of the caustic on the

ground, but that caustic is missing from the refer-

ence. This can be seen as an advantage, as longer

paths can be created at no additional cost. A second

one, which can be seen in the caustic in AA@298 for

OurTemporal, is ghosting artefacts due to the tempo-

ral reuse simply relying on an exponential moving av-

erage; Equal time PT and OurBasic also suffer from

some ghosting introduced by SVGF, but it is not as

noticeable. Finally, there is a conﬂict between the

two temporal reuse methods, our reuse at the collec-

tion points and the SVGF’s one: as new regions be-

come visible, our temporal reuse will end up creating

two different noise levels for a given surface (the more

converged one, which was visible for several frames,

and the newly uncovered one with very few samples)

which will be interpreted by SVGF as two different

regions making them more visually distinct.

Another important note is that SVGF relies on

motion vectors which are rarely readily available for

light patterns such as caustics or shadows, or reﬂec-

tions or refractions, all of which are found all over

these scenes. A recent approach by Zeng et al. (2021)

shows promise regarding glossy reﬂections.

Temporal stability is sometimes improved in real-

time applications by performing the ﬁltering after

tonemapping rather than before, though at the cost

of image quality. This can however result in differ-

ent samples being merged together due to no longer

appearing distinct enough to the ﬁlter, such as the

few caustic samples in the second picture of Figure 6

which were mostly blurred out. Thanks to our ap-

proach providing more samples, it can be used along

that ﬁltering trick.

Apart from the previously-mentioned ghosting in

OurTemporal, the temporal quality depends strongly

on the light sampling algorithm used and better results

could be obtained with Ouyang and Yang (2020a);

Yang and Ouyang (2021).

For temporal results, we refer the reader to our

supplemental video which contains all 4 animations

(using ﬁltering post-tonemapping and R = 0) pre-

sented in this paper, as well as additional combina-

Real-time Rendering of Indirectly Visible Caustics

Table 2: Highlighting different scenarios: AC@298 where OurTemporal improved signiﬁcantly compared to OurBasic,

AG@10 presents a regression for OurTemporal, and AA@298 with an easier to sample caustic for the path tracer. For

each scene, the ﬁrst row consists of a single frame ﬁltered with SVGF, whereas the second row has error maps generated by

LIP (Andersson et al., 2020).

Reference

OurBasic OurTemporalEqual time PT (3spp)

Animated Camera@298Animated Geometry@10All Animated@298

tions for one of the scenes. Additional videos cover-

ing all combinations can be found on the project web-

site (see Section 4).

As mentioned in the introduction, screen-space

accumulation techniques could technically still be

used to collect lighting contributions on glossy sur-

faces. We tried to use the technique by (Kim, 2019)

on such surfaces, but failed to get it to match a ref-

erence unless increasing the roughness past 0.25, at

which point caustics and objects could no longer be

distinguished or seen in the reﬂections and the mir-

rors.

5 CONCLUSION

Conclusion. In this paper we presented a new al-

gorithm for real-time rendering of detailed caustics

appearing in long specular view paths. Our method

makes use of recent hardware-accelerated ray tracing

for both view and light rays, and for BVH construc-

tion. We create a temporal cache of previous frame

light intensity to improve temporal ﬁltering. Tempo-

ral ﬁltering costs more in frame time, if not performed

asynchronously, but improves image quality in most

cases. Our results show that performance of 20–28 ms

for the box scenes, is possible with temporal ﬁltering

for scenes with reﬂective surfaces showing caustics

that are not rendered by existing screen-space accu-

GRAPP 2022 - 17th International Conference on Computer Graphics Theory and Applications

Figure 6: Unlike path tracing, our approach samples the caustics sufﬁciently that they do not disappear when ﬁltering after

tonemapping, to improve temporal stability. From left to right:

LIP error map for Equal Time PT (2 spp), Equal Time PT

(2 spp), OurTemporal,

LIP error map for OurTemporal. These can be compared to the reference image and results obtained

when ﬁltering prior to tonemapping that are found in Table 2.

Figure 7: Our approach can be applied to more complex scenes (left image: 39 ms, path length of 7 segments; centre image:

46 ms, path length of 6 segments) and scales to more intricate caustics (right image, 1 s, path length of 6 segments; 175k spp

for an equal quality path tracer). For the ﬁrst two images, the main costs are path tracing (17–19 ms), light tracing (8–11 ms),

and AS re-build (6 ms). All three images were rendered using our temporal version, and while the ﬁrst two were ﬁltered with

SVGF, the last was accumulated over multiple frames.

mulation techniques. Additionally, our approach can

be applied to complex scenes.

Future Work. The variation in collection point lo-

cations from frame to frame depending on the mate-

rial sampling goes against the assumptions made by

current BVH reﬁtting approaches, resulting in low

tracing performance. Temporal ﬁltering of caustics

remains an open issue with one of its challenges be-

ing the obtention of motion vectors for the caustics,

which would help in reducing ghosting artefacts. The

data cached by our approach could be extended to in-

clude, for example, a reservoir to use ReSTIR (Bitterli

et al., 2020) even on surfaces visible via mirror(s).

ACKNOWLEDGMENTS

We thank Jacob Munkberg for valuable insights and

discussions. Pierre Moreau was supported by Veten-

skapsrådet, and Michael Doggett is supported by EL-

LIIT and WASP. The transparent glass used in the

teaser and Figure 7 was made by Simon Wendsche

The Bistro Interior and Bistro Exterior scenes used in

Figure 7 are courtesy of Amazon Lumberyard (2017).

https://byob.carbonmade.com/

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