# caustic object construction based on multiple caustic patterns

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Caustic Object Construction Based on Multiple Caustic Patterns

Budianto Tandianus, Henry Johan, Hock Soon Seah

School of Computer EngineeringgameLAB

Nanyang Technological University

CONTENTIntroductionRelated WorkBasic IdeaImproving the Reconstructed CausticsGeometry ConstructionResultsApplicationsConclusions and Future Work

INTRODUCTIONWhat is caustics ?Light sourceFrom bottom plateGlasses/reflector(Caustic Object)Caustics

CAUSTICS IN COMPUTER GRAPHICSTypically simulated in CG by using Photon Mapping (Jensen 1996, Graphics Interface)Kruger et al. 2006 Eurographics Symp. on RenderingJensen 1996Graphics InterfaceWyman 2008i3DSpencer and Jones 2009Computer Graphics ForumHu et al. 2010i3DTandianus et al. 2010ICEC

CAUSTICS IN COMPUTER GRAPHICSThe previous slide shows forward problem of caustics in computer graphics :Input : caustic object, light source, and diffuse surfaceOutput : caustic pattern

But how about inverse caustics problem ?Input : caustic pattern, light source, and diffuse surfaceOutput : caustic object

Reflective caustics in an optical setPatow et al. 2004, International Journal of Shape ModellingPatow et al. 2007, Computer & GraphicsMas et al. 2009, Computer Graphics ForumReflector is represented as grid of vertices or cellsIs validated using computer simulationRELATED WORKOptical setTarget and reconstructedcaustics

Generate smooth B-Spline surface (Finckh et al 2010, European Conference on Computer Vision)Optimize the control points until they can reconstruct the caustic patternsAnother similar work by Anson et. Al. 2008, CEIG 2008Surface is represented as a NURBS and caustic pattern shape is assumed to be circularIs validated using computer simulation

RELATED WORK

Generate a small patch that can have certain BRDF or caustic pattern (Weyrich et al. 2009, Transactions on Graphics)The patch is subdivided into a regular grid of cellsRELATED WORKTarget and reconstructed caustic patternsReal-life validation

Refractive caustics on a larger scale (Papas et al. 2011, Computer Graphics Forum) Improvement of their previous work (Weyrich et al. 2009, Transactions on Graphics)RELATED WORK

The most recent work, focusing on modularity (Yue et al. 2012, Computer Graphics Forum)Compute optimal combination of caustic object cells with predefined refraction directionsRELATED WORKAssembling caustic object from pieces of predefined caustic object cellsGenerated caustic pattern by using assembled caustic object

All these work can generate caustic objects producing interesting caustic patterns

However, they only consider a single caustic patternHow about if multiple caustic patterns ?RELATED WORK

Multiple caustic patterns with each caustic pattern is formed at a locationIs validated using mental rayOUR WORK

Input : multiple caustic patterns, directional light source, and planar diffuse surface (caustic receiver)Output : caustic objectBASIC IDEAOur scene configuration

Many caustic object cell orientation possibilities that might satisfy the input caustic patternsPROBLEM FORMULATIONPossible combinationTwo caustic patterns input,compute refraction directions

Represent each caustic pattern as a 2D probabilistic mass function (pmf)For each caustic object cell, to determine its refracted orientation, compute the joint pmf and select the refraction direction based on the joint pmf :OUR SOLUTIONNumber of causticpatterns in the scene

Joint pmf :

Example : OUR SOLUTIONNumber of causticpatterns in the scene

PROBLEMOnly a single caustic patternWith multiple caustic patterns

However, some sets of caustic patterns cannot be reconstructed wellDue to differences of the input caustic patternsCause some joint pmf to be zero (e.g. topmost caustic cell in the first caustic pattern of below figure)PROBLEM

Solutions :Adjust positions and sizes of the caustic regionsAdjust shapes of the caustic regions

Use Simulated Annealing

Optimize the cost (based on L-2 distance)IMPROVING THE RECONSTRUCTED CAUSTICS

Iteratively translate the caustic regions in 3D spaceIn x (blue arrows in the left figure below) directionIn y (red arrows in the left figure below) directionIn z (pink arrows in the left figure below) direction, i.e. distance between the caustic pattern and the caustic objectScale the caustic regions (green arrows in the right figure below)

ADJUSTING POSITIONS AND SIZESTranslating the caustic regionsScaling the caustic regions

Extend each caustic region such that missing caustic cells of other caustic patterns can be reconstructed

ADJUSTING SHAPES OF THE CAUSTIC REGIONSTo solve this, thesecond caustic regionis extendedThe green caustic cell cannot be reconstructed since all possiblelight paths passing through it hits emptypart in the second caustic pattern

At the same time, we also allow some light to miss some of the caustic patternsIn the example figure below, Light #4 hits the first caustic pattern and misses the rest of caustic patternsADJUSTING SHAPES OF THE CAUSTIC REGIONS

OPTIMIZATION RESULTSWithout optimizationCost : 4.45 x 10-1

OPTIMIZATION RESULTSFirst optimizationCost : 4.08 x 10-1

OPTIMIZATION RESULTSSecond optimizationCost : 2.64 x 10-1

Assume the z coordinate of each caustic object cell center is the sameFor each caustic object cell, from its refracted light direction, we can compute its normal, and in turn compute the coordinates of its four cornersClose the vertical gaps between caustic object cells

GEOMETRY CONSTRUCTION

Specifications of PCs used in our experiments :Intel i7 920 2.67 GHz (CPU) with NVIDIA GeForce GTX 285 (GPU)Intel i7 880 3.07 GHz (CPU) with NVIDIA GeForce GT 330 (GPU)

RESULTS

RESULTSFruitsfour caustic patternscomputational time : 7.7 hours

RESULTSFour barsfour caustic patternscomputational time : 15.7 hours

RESULTSRotating starnine caustic patternscomputational time : 27.6 hours

ArtsValidation testsInformation encodingAPPLICATIONS

VIDEO

Click to play

Compute a caustic object that can generate a set of caustic patternsOur two-step optimization processes can alleviate the missing caustic problemsResults are validated using mental rayCONCLUSIONS

Manufacture the real caustic object for further validationNeed to devise an algorithm to smoothen the caustic object cells such that it is easy to manufacture

Dynamic lightStatic caustic object and caustic receiverDifferent caustic pattern for every light position or directionFUTURE WORK

THE END

CAUSTICS IN COMPUTER GRAPHICS

Extend each caustic region such that caustic cells of other caustic regions can be reconstructedHowever, adjusting too much will cause the caustic region to change too muchDetermine the maximum adjustment, by projecting the missing caustic cells and then iteratively compute good adjustment amountADJUSTING SHAPES OF THE CAUSTIC REGIONS

At the same time, also allow some light to miss some of the caustic patternsIn the projection computation (previous slide) also count how many of projections that miss other caustic patternsAllow too much light to miss other caustic patterns will cause those caustic patterns to be too darkAlso iteratively compute good amount of light to miss the caustic patternsADJUSTING SHAPES OF THE CAUSTIC REGIONS

*Good afternoon everyone and thank you for attending the presentation. My name is Budianto Tandianus and Im going to present our work with the title Caustic Object Construction based on Multiple Caustic PatternsThis is the brief outline of my presentation. I will start with some introduction of our work and related work. Afterward, I will explain our work consisting of the our basic idea and also our proposed technique to improve the caustics, and finally how to compute the geometry. Afterward, I will show some results and possible applications. I will end this presentation with the conclusion and future work.*Before I start, let me give a brief introduction about caustics effects. What is caustics ? In a scene in a real life such as this photo, when we have a light source illuminating a glasses object, we see a bright patterns. And the patterns are called caustic patterns. As shown in this photo, the green light source from the bottom illuminates a bunch of glasses object, and we see the caustic patterns on the white wall.*Definitely, there are already some works in computer graphics than simulate the caustics effects. In most of the works, they use a photon mapping and its related techniques to generate caustic patterns.*In the examples I show in the previous slides, we compute the caustic pattern given the caustic object, light source and diffuse surface. We call this forward problem.But, how about inverse problem ? That is we have the caustic pattern, light source, and diffuse surface, and we need to compute the geometry of a caustic object such that it can produce the caustic patterns similar to the input caustic pattern ?*There are few related work in inverse caustic problem. For example, in this work they compute a reflector in a lighting set such that it can generate caustic pattern similar to the input caustic pattern.*In this work, they parameterize the caustic object surface as an implicit surface such as B-Spline and NURBS*This is one of the recent one, and they also compute a reflector, albeit in a much smaller scale.*And this is one of the most recent work. They generate a larger size caustic object that can produce an input caustic pattern.*And this is o

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