A Lightweight Photon Tracing Method for Visualising Caustics

Adrian De Barro, Keith Bugeja, Sandro Spina, Mark Magro and Kevin Napoli

CGVG, Department of Computer Science, Faculty of ICT, University of Malta, Msida, Malta

Keywords:

Realtime Caustics, Caustics, Photon Tracing.

Abstract:

In this paper we present a biased lightweight photon tracing method for the visualisation of caustics. The

caustics volume bounds reﬂective and transmissive media and regulates the propagation of photons within

these media. The volume uses partitioning and reﬁnement to control tracing accuracy; this is modulated at

runtime using a level-of-detail approach to improve performance without visible loss to accuracy. The system

schedules traced photons for projections via a controllable number of face projectors tied to the volume.

A straightforward splatting algorithm was implemented for this paper; however, more advanced splatting

algorithms may be employed for improved visual quality.

1 INTRODUCTION

Caustics are an optical phenomenon where an emit-

ted envelope of light rays is refracted or reﬂected by

a curved surface onto another. Caustics contribute

greatly to lighting in real life and are thus highly

sought after where photorealistic rendering is con-

cerned such as visualisation of cultural heritage sites

and artefacts. In general, the generation of caus-

tics is computationally expensive; in particular, un-

biased methods used in ofﬂine rendering are slow to

converge, especially in complex scenes with a large

number of reﬂective and transmissive surfaces. As

such, biased methods, typically derivative or vari-

ants of photon mapping (Jensen, 1996), are employed

to reduce rendering times. In realtime and interac-

tive settings, a general solution for rendering caus-

tics still eludes us for anything but powerful work-

stations equipped with ray-tracing hardware acceler-

ation. In this paper we present a lightweight photon

tracing method for visualising caustics; speciﬁcally,

we take inspiration from scene creation workﬂows

in game development (Doghramachi, 2020), where

realistic illumination at interactive rates is achieved

through careful placement of light probes. Thus, we

introduce the caustics volume, a tight-ﬁtting prism

around geometry of interest for which realtime caus-

tics visualisation is desired. Our solution does not re-

quire specialised hardware accelerated ray tracing nor

any ray tracing primitives; moreover, it runs mostly

on the GPU. It does not make use of tree-based pho-

ton maps but photons are stored in a linear buffer.

The output can be adapted to any splatting algorithm

(Dachsbacher and Stamminger, 2006), (Sriwasansak

et al., 2018) and is not limited to the reference one

used in this paper.

Furthermore, our method is a perfect ﬁt for dis-

tributed rendering algorithms such as (Crassin et al.,

2015), (Bugeja et al., 2019) and (Magro et al., 2020),

where photon tracing can be computed at the server

end and its results streamed to a client, which then

proceeds to visualise caustics using adequate splatting

and ﬁltering.

The contributions of this work are a lightweight

photon tracing algorithm:

• that runs mostly on the GPU;

• that does not require ray tracing hardware accel-

eration; and

• is scalable in terms of performance.

2 RELATED WORK

In principle, faithful simulation of caustic phenom-

ena has been accomplished through the use of var-

ious rendering techniques that rely on Monte Carlo

sampling to solve the rendering equation. Single pass

techniques, such as path tracing (Kajiya, 1986) are

not able to converge on high frequency caustic effects.

In fact, effective caustic generation algorithms em-

ploy two passes (Arvo et al., 1986). Photon mapping

(Jensen, 1996) and bidirectional path tracing (Lafor-

tune and Willems, 1998) are two examples of tech-

188

De Barro, A., Bugeja, K., Spina, S., Magro, M. and Napoli, K.

A Lightweight Photon Tracing Method for Visualising Caustics.

DOI: 10.5220/0010833900003124

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

188-195

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

niques that are able to render high frequency caustic

patterns correctly. Although capable of converging

faster than single pass methods they are still not good

enough for realtime applications.

Traditional photon tracing relies on tracing pho-

tons through the scene, where refracted and reﬂected

photons aggregate to form caustic patterns. Photon

tracing relies on some form of ray tracing procedure

to traverse the scene. Once the photons reach the ﬁ-

nal intersection, different strategies exist to visualise

caustics. Screen-space techniques rely on photon

splatting to visualise the caustic formations. Trian-

gle caustics (Umenhoffer, 2008) still employ the use

of photons to calculate light propagation in the scene.

However, rather than splatting photon intersections,

photons are triangulated and drawn. Beam-tracing

(Liktor and Dachsbacher, 2011) is an extension of

triangle caustics, which also incorporates volumet-

ric caustics. Voxel-based caustic techniques, such as

Eikonal rendering (Ihrke et al., 2007) make use of

wavefronts to propagate light along arbitrary direc-

tions. The technique is capable of producing complex

refraction characteristics. However, when dynamic

scenes are concerned, light updates require approxi-

mately 5 to 10 seconds to calculate the new caustic

patterns. Unlike GPU-based photon mapping meth-

ods, the use of expensive ray/geometry intersection

techniques are not required. Progressive photon map-

ping techniques (Evangelou et al., 2020) (Jarosz et al.,

2011) deliver interactive global illumination and caus-

tic formulations. Given enough time, the solver will

converge to a solution. However, this usually varies

with the complexity of the refractive geometry. More-

over, until convergence the solution would contain

sampling error which is perceived as gritty noise.

Recent advancements in ray tracing support at

a hardware level and increased GPU computational

power have provided an opportunity for the integra-

tion of techniques such as photon mapping for real-

time purposes (Adam Marrs and Wald, 2021), (Haines

and Akenine-Moller, 2019). However, these tech-

niques are limited to hardware that supports ray trac-

ing, and as such are not applicable for most portable

devices.

3 METHOD

An overview of the proposed photon tracing algo-

rithm is shown in Algorithm 1. As presented in the

pseudocode, the algorithm requires the attributes for

the deﬁnition of the volume within the scene, which

have been previously deﬁned. Each caustics volume

has a set of light sources that will be contributing

Table 1: Attributes of the caustics volume.

Attribute Description

source

Associated light sources

entry

Entry face

exit

Set of exit faces

culling

Set of culling faces

slabs

Volume subdivisions

pro j

Splat projectors

dims Volume dimensions

orient Volume orientation

Diffuse geometry set

Reﬂective geometry set

Transmissive geometry set

dims

G-buffer resolution

energy in the scene. Sources of lights found inside

source

will be sampled to create the photon set that

will be propagated within the volume. The amount

of propagation runs for a single volume are directly

proportional to the amount of slabs contained within

the same volume, example, a caustic volume with a

slab count S equal to three will execute the ray march-

ing procedure three times. Each ray marching pro-

cedure will only take into consideration the geometry

found within the boundaries of the current slab. Once,

ray marching has executed for each slab, photons that

have been traced and intersected the exit faces will

be ray marched against the surrounding geometry to

attempt to ﬁnd the ﬁnal intersection. The resulting in-

tersection details are collected and used by the photon

splatter for visualisation.

3.1 Caustics Volume

The caustics volume C

is an oriented cuboid that

bounds the computation of light transport for photons

across reﬂective and transmissive surfaces. Three at-

tributes are associated with the faces of the volume:

entry, exit and culling. At a high level, photons at the

entry face are traced through the volume; depending

on its exit point from the volume, a photon may either

be culled or scheduled for rendering. In particular,

photons that exit the volume through a face tagged

with the culling attribute are terminated. Conversely,

photons that exit through a face tagged with the exit

attribute are marked for later rendering via splatting.

Caustics volumes have a number of attributes; these

are shown in Table 1.

3.2 Tracing Photons

The input to the algorithm is a set of photons P

and a caustics volume C

; P

represents the incoming

radiant ﬂux at the entry faces F

entry

of volume C

. C

A Lightweight Photon Tracing Method for Visualising Caustics

189

Algorithm 1: Overview of caustics volume propagation

method, symbols described in Table 1.

Input: Caustics volume C

with associated attributes

(see Table 1), G

all

= {G

, G

} and S is the set of

slabs in C

Output: A set of photons P

used as input to a caustics

splatting method.

Initialise P

through sampling of associated light

sources L

source

Set all photons in P

to a non-terminating state.

for all S

∈ S do

Generate G

f ar

and G

near

using probe camera of S

for all p

whose state is non-terminating do

= RayMarch(p

, G

near

)

if intersection with G

all

then

= RayMarch(p

, G

f ar

)

if intersection with geometry set then

= Propagate p

over boundaries F

exit

and F

culling

Update state for p

depending on intersec-

tion data

end if

end for

← contributive photons propagated over F

exit

is equally subdivided into N

slabs

slabs, where each

slab is axis-aligned with the entry faces. For each

slab S

, the photons P

are traced and their interactions

recorded. To model the interactions of the individ-

ual photons with the geometry contained within slab

, two geometry buffers are generated, G

near

, which

records geometry that is closest to the entry face of

the slab and G

f ar

, which records geometry farthest

from the entry face of the same slab. Given, G

f ar

and

near

, ∀p ∈ P

: p

is the result of p interacting with the

space described by G

near

. In particular, ray marching

is used to detect whether p would eventually intersect

any geometry along its trajectory. If an intersection

is recorded, the surface material is then considered;

a diffuse interaction means that p has terminated its

path. An opaque specularly reﬂective surface gener-

ates a new reﬂection direction for p

; the photon is

also marked as contributive, which means that any vi-

sualisation of caustics will include this photon.

Transmissive surface interactions are only consid-

ered after a number of validation checks; for instance,

if the photon is currently inside a dielectric medium,

only medium exit interactions are considered. Con-

versely, if the medium of the photon is air, then only

medium entry interactions are considered. Provided

the interaction is accepted, transmissive surfaces also

generate a new direction by refracting p, which is

marked as contributive also. For thin objects (or thin

spaces between objects), a second interaction is con-

sidered when transmissive materials are encountered;

in particular, a photon that has switched medium is

marched within the space described by G

f ar

using

the newly refracted direction from the previous in-

teraction. Any intersection is once again recorded

and a new direction and position are computed for

p. The photon is also marked as contributive. By

now, the state of a photon p

will have been updated

with its new position and direction; furthermore, at-

tributes such as contributive or terminated might have

been added to it. Terminated photons do not undergo

any additional processing in the remaining slabs. Pho-

tons that have not been terminated are propagated to

the exit face of the current slab S

; this slab is also

co-planar with the entry face of the next slab, S

i+1

Here, photons that exit the slab through the sides and

not the exit face will be assigned to a side projector,

depending if they had already been tagged as con-

tributive. This process is repeated for all slabs in the

caustics volume, following which, photons which are

tagged as contributive are selected for the splatting

process. These photons are projected onto surround-

ing diffuse geometry by using their current positions

and directions and ray marching over a newly gener-

ated geometry-buffer oriented at the exit face.

Slabs provide a tradeoff for ray marching through

complex geometry. When used in low counts they

allow us to provide a plausible approximation of the

expected results. An arbitrary number of slabs can

be deﬁned for any caustic volume, however, for S of

size n the technique would require n + 1 ray marching

passes. The ray marching procedure we are currently

applying requires the far and near g-buffer details, and

without adding multiple slabs we can only guarantee a

rough approximation for the geometry that is found in

the volume. Speciﬁcally, refractions that occur with

the closest and the furthest geometry. Figure 1 illus-

trates the ray marching procedure for a single slab.

Since we are only making use of a single slab and the

ray marching procedure only knows about the furthest

aways and nearest geometry, we are losing geometry

information about the box and the sphere. The intro-

duction of more slabs, as depicted in Figure 2, would

improve the approximative nature of the ray marching

procedure.

3.3 Ray Marching in Slabs

Ray marching in a slab starts at its entry face, which is

parallel to the caustics volume’s own entry face. The

direction of a photon is used to march a ray in texture

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

190

Figure 1: Top row shows three stages of propagating photons over G

near

column), G

f ar

column), and resulting

photon paths (3

column). The second row show the same scene with a refractive box added under the sphere. Note how the

f ar

buffer changes to account for the box and how the resulting photon paths are similar to those in the previous row.

Figure 2: Right: Three slab conﬁguration for an arbitrary

bounding volume, the green and red lines highlight what

geometry is stored in G

near

and G

f ar

respectively. Left: ray

marching procedure within a single slab.

space; a depth test is carried out against G

near

to de-

tect intersections along the trajectory of the photon. If

the test fails, traversal continues until the photon in-

tersects the boundary of the slab. If a photon arrives

at the boundary that subdivides the caustics volume,

it is carried forward to the adjacent slab. If the bound-

ary intersected by the photon is also the boundary of

the caustics volume, then, depending on the assigned

attribute, the photon may be either terminated (colli-

sion with a culling face) or scheduled for rendering

(collision with an exit face).

Now we will consider what happens when the in-

tersection test with the G

near

depth buffer succeeds

and the surface is transmissive: although the photon

may be at a media interface, the test is not conclusive.

The photon might be passing behind the object with-

out going through it. To make the test more robust,

Table 2: Photon attributes.

Attribute Description

rad

Energy

pos

Position

dir

Direction

nrm

Surface normal

len

Current path length

grid

Density grid tile index

med

Photon medium

a further depth test is carried out against G

f ar

; if the

photon position is between the depth values sourced

from G

near

and G

f ar

, then we assume it is at a media

interface. The next thing to ascertain is whether the

photon is going from air to dielectric medium or vice-

versa. The photon attribute P

med

(see Table 2) is used

to tell whether a photon is inside a dielectric medium

or outside. Thus, if P

med

is false, and the surface nor-

mal at the interface lies in the opposite hemisphere

as the photon direction, we assume the photon is at

an air-dielectric medium interface and is entering the

denser medium. Conversely, if P

med

is true, the pho-

ton is inside the denser medium (inside a transmissive

object); if the surface normal at the interface lies in

the same hemisphere as the photon direction, then we

assume the photon is exiting the denser medium.

In both cases, if the surface normal tests fail, the

interface is ignored and the photon is assumed to re-

main in the original medium, air when P

med

is false

A Lightweight Photon Tracing Method for Visualising Caustics

191

and the dielectric when P

med

is true.If an intersection

is recorded, the photon trajectory is amended to ac-

count for a change in medium or a reﬂection, when

the surface material is either transmissive or specu-

larly reﬂective. When a diffuse surface is encountered

at an intersection, the photon path is terminated; the

photon is then scheduled for rendering if it had been

earlier tagged as contributive. To account for trans-

missive objects that are entirely contained within a

single slab, ray marching switches to testing exclu-

sively against G

f ar

after the ﬁrst recorded intersec-

tion. When all photons have been marched through

the slab, those with recorded intersections are propa-

gated to the boundaries of the slab.

3.4 Photon Splatting

The photon tracing process moves to the last step

when all input photons have reached either an exit or

a culling face. The former are scheduled for render-

ing via projectors, which are assigned to each of the

faces in F

exit

; any photon that exits the volume at one

of these faces is associated with the respective pro-

jector. In a sense, we emulate the generation process

of a cube-map, in a similar fashion to that applied by

(Ganestam and Doggett, 2015). For each projector,

a g-buffer is generated, capturing the scene from the

respective side of the caustics volume. Each photon

in the projector is marched to ﬁnd the closest point of

intersection in the g-buffer; the position and surface

normal at the point of intersection are recorded and

used for photon density estimation and later, splatting.

For density estimation, the g-buffer is split into a grid

of square tiles. This is naive at best, and interested

readers are directed to more accurate techniques pro-

vided in (Mara et al., 2013). Each contributive photon

that has intersected the scene geometry, will be repre-

sented as splats. Splats are represented by quads with

a circular texture. However, the quad is not uniform

but adjusted according to the ray length and density

estimate. Orthogonal basis for each quad are con-

structed, namely from the surface normal at the inter-

section, the projection of the intersection direction at

the plane deﬁned by the surface normal and the third

vector is the cross products of the previous two vec-

tors as detailed in (Haines and Akenine-Moller, 2019)

and (Adam Marrs and Wald, 2021). Finally, once all

photons have been rendered as oriented quads in a dif-

ferent frame-buffer, a Gaussian kernel is applied to

smoothen the result.

Photons are distributed evenly over the F

entry

sur-

face of the caustics volume and seeded with the cur-

rent direction of the light that is associated with the

volume. If there is more than one light, the pho-

ton pool is divided equally between all the contribut-

ing lights. Other sampling techniques can be utilised

(Shirley and Morley, 2003).

3.5 Optimisations

Algorithmic optimisations have been introduced to

improve the performance of the technique. Volumes

that are close to the camera are prioritised, by keeping

the slab count to the explicit number speciﬁed by the

user. However, if the volume is further away from the

camera, we make use of level-of-detail to reduce the

amount of slabs for the given volume. In case the vol-

ume is out of the camera frustum, we do not render

the photons for the respective volume.

Differential updates were introduced to the caus-

tics volume; as the volume is split into distinct slabs,

we only need to update any of the slabs in which a

change has occurred. As such, if we have 5 slabs

and a change occurred in the 5

slab, we would only

require to update slab 5 and the projectors. If light-

related updates occur in the scene, this optimisation

is not applicable and the whole propagation cycle is

executed.

4 RESULTS

Results address runtime performance and scalabil-

ity for different execution parameters. Speciﬁcally,

we show how the method scales for different pho-

ton counts, polygon counts and geometry buffer sizes.

Furthermore, we compare, qualitatively, results ren-

dered using our method in the Unity game engine to

renders using Blender. The system has been tested on

ﬁves different scenes, which consist of transmissive or

reﬂective objects inside a Cornell Box variants; these

have been labelled as diamond (2K polygons), ring

(2.9K polygons), glass-ball (4K polygons), Suzanne

(97K polygons) and ﬂoating blocks (47.6K polygons).

Experiment Setup. For all performance tests, the fol-

lowing g-buffer resolutions (G

dims

) were used: 100 ×

100, 200 × 200 and 500 × 500 pixels. The higher

dims

, the more accurate the output is expected to be.

The tests were run using the following input photon

counts (

): 10K, 20K and 50K. A higher number

of input photons is expected to generate more deﬁned

caustics formations and patterns at the cost of runtime

performance. The number of partitions of the caus-

tics volume (N

slabs

) was varied between 1 and 3 slabs.

The number of slabs is expected to guide the level

of reﬁnement of the algorithm; a higher number of

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

192

slabs means that the interactions of photons and com-

plex geometry may be better captured and modelled,

whereas a lower number of slabs yields a coarser rep-

resentation of the actual interactions. A steep cost is

associated with an increased number of slabs as each

traversal requires expensive state copies from GPU to

CPU, for photons to be ﬁltered and passed on to the

next slab or projector(s).

Table 3: Timings for the ofﬂine renders.

Scene Ref Sample Time

Count mins

diamond A 2000 5:41

ring B 2000 9:56

glass-ball C 2000 5:20

Suzanne D 2000 6:41

ﬂoating Blocks E 2000 6:21

Table 4: Timing and performance results for one-slab caus-

tics volume.

Scene S

Proj

(ms) (ms)

A 48 47

B 54 44

C 22 18

D 72 62

E 54 50

A 53 52

B 64 45

C 56 52

D 93 69

E 58 54

A 53 52

B 64 45

C 56 52

D 93 69

E 58 54

Performance. Tables 4, 5 and 6 show the perfor-

mance results for the ﬁve scenes, and highlight the

cost of projection passes for the respective photon

paths. Costs are expressed in ms. Each table con-

tains three different sets of results that vary according

to G

dims

(g-buffer size) and P

(photon count) and the

following combinations were used: 100

and 10K,

200

and 20K and ﬁnally 500

and 50K. Optimisa-

tions (see 3.5) were disabled for these tests. A full up-

date of the caustics volume was enforced on each and

every change in the lighting or scene geometry. As

expected, an increase in quality settings (higher G

dims

slabs

and

) result in a decrease in runtime perfor-

mance, directly impacting the average frame rate of

the main rendering pipeline. For simple scene conﬁg-

Table 5: Timing and performance results for two-slab caus-

tics volume.

Sc. S

Proj

(ms) (ms) (ms)

A 44 46 43

B 49 49 52

C 47 52 72

D 82 63 72

E 77 56 67

A 53 50 48

B 52 67 40

C 60 50 50

D 92 78 71

E 84 72 68

A 56 62 58

B 61 104 47

C 62 59 70

D 141 113 117

E 130 100 105

Table 6: Timing and performance results for three-slab

caustics volume.

Sc. S

Proj

(ms) (ms) (ms) (ms)

A 48 46 46 49

B 37 41 42 43

C 20 17 20 14

D 64 53 46 58

E 65 56 57 65

A 52 60 51 44

B 49 72 49 50

C 49 71 49 47

D 78 69 66 60

E 81 69 68 71

A 75 62 63 63

B 58 107 58 54

C 92 76 74 73

D 124 103 92 95

E 141 106 104 102

urations (ring, glass ball and diamond) with low poly-

gon counts, a single slab was enough to visualise the

caustics pattern. Increasing the slab count for these

scenes did not increase the quality of the pattern, but

was rather detrimental in that performance was im-

pacted at the cost of no visible beneﬁt.

Image Comparison. The quality of rendered caus-

tics was compared to reference images of the same

scenes generated using Blender (see Figure 3). These

images were path-traced; speciﬁcally, LuxCore was

used to ensure high quality caustics in the output. The

best quality settings were used to generate images us-

ing out method: g-buffer resolution was set to 500

A Lightweight Photon Tracing Method for Visualising Caustics

193

Figure 3: Top row: Test scenes rendered using Blender and LuxCore. Bottom row: Test scenes rendered using our implemen-

tation in Unity3D.

× 500, the photon count to 50K and the caustics vol-

ume partitioned into three slabs. The ofﬂine rendering

times for the reference images are shown in Table 3.

There are noticeable differences between the caustics

in the reference images and those generated using our

method; nevertheless, images generated by the latter

were rendered in a fraction of the time taken to render

the references. In our method, a naive photon splat-

ting algorithm was used with a simple density estima-

tion (3.4); replacing this with state of the art methods

could yield a better caustics visualisation.

Discussion. Fast interactive rendering of dynamic

caustics is still a holy grail in real time rendering.

Hardware accelerated ray tracing has pushed the en-

velope further and brought us closer to a solution;

nevertheless, this excludes a plethora of devices, par-

ticularly portable devices and platforms without the

latest GPU hardware advancements. The presented

method does not require any ray tracing hardware; in-

stead, it employs screen-space ray marching to com-

pute photon traversal through the volume. The par-

titioning of the caustics volume into slabs serves a

twofold goal: the amortisation of computation over a

number of frames and geometry reﬁnement. Further-

more, only slabs affected by dynamic scene changes

are considered during updates. A progressive ap-

proach was also presented, where a fraction of the

total number of photons is traversed per update, up

to some maximum count, to preserve frame rates in

weak and low-end devices. The image comparison

shows that although some caustics formations are cor-

rectly captured by our method, it is still an approxi-

mation that has correctness and numerical limitations.

Caustics visualised on the sides walls of the Cornell

box in LuxCore rendered scenes could not be visu-

alised with the caustics volume due to the light sam-

pling method utilised.

5 CONCLUSION

In this paper we have proposed a lightweight method

for photon tracing aimed at visualising caustics. The

results show that the method is promising notwith-

standing the clear room for optimisation in our im-

plementation.

The approximative nature of the method is such

that certain paths cannot be modelled; for instance,

back reﬂections, or light paths that are reﬂected back

in the general direction of the light source, cannot

be accurately modelled. To do so, further render-

ing passes would be required, potentially impacting

performance. This limitation also affects a transpar-

ent medium that is embedded within another trans-

parent medium; for each slab, it is assumed that at

most two media interfaces exist. Updates to slabs in

the caustics volume are ordered. Therefore, in a full

update, n slabs require n + 1 iterations; when the it-

erations are amortised over a number of frames, the

resulting caustics appear to be trailing behind updates

to light sources or geometry that triggered the up-

date. Optical Flow (Horn and Schunck, 1981) could

be employed to predict the general direction of mo-

tion and extrapolate the pattern, thus reducing the ap-

parent lag. Furthermore, pipelined parallelism could

be introduced, to compute slabs from different itera-

tions concurrently, similar to how instructions are ex-

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

194

ecuted in a RISC CPU pipeline. This would also re-

quire substantial improvement to the current photon

tracing implementation. Plausibility does not entail

correctness: implementing photon tracing using ray

tracing, hardware accelerated also, would enable us

to measure the accuracy of the solution and quantify

the ﬁdelity of the resulting caustics formations.An in-

teresting avenue to explore is the light transport be-

tween different caustics volumes in the scene; at the

moment, these volumes are independent of one an-

other. Furthermore, integration into distributed ren-

dering pipelines is another avenue worth exploring,

especially in the context of VR rendering systems,

which would greatly beneﬁt from the added realism

provided by caustics.Finally, the current implemen-

tation would greatly beneﬁt from optimisation, to fur-

ther minimise frame rates and make it suitable for ren-

dering on low-end devices.

ACKNOWLEDGMENTS

This work was supported by the Notarial Archives of

Malta.

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