Caustic Object Construction Based on Multiple Caustic Patterns

Budianto Tandianus, Henry Johan, Hock Soon Seah

School of Computer EngineeringgameLAB

Nanyang Technological University

CONTENT

• Introduction• Related Work• Basic Idea• Improving the Reconstructed Caustics• Geometry Construction• Results• Applications• Conclusions and Future Work

INTRODUCTION

• What is caustics ?

Light source

From bottom plate

Glasses/reflector

(Caustic Object)

Caustics

CAUSTICS IN COMPUTER GRAPHICS

• Typically simulated in CG by using Photon Mapping (Jensen 1996, Graphics Interface)

Kruger et al. 2006

Eurographics Symp. on Rendering

Jensen 1996

Graphics Interface

Wyman 2008

i3D

Spencer and Jones 2009

Computer Graphics Forum

Hu et al. 2010

i3D

Tandianus et al. 2010

ICEC

CAUSTICS IN COMPUTER GRAPHICS

• The previous slide shows forward problem of caustics in computer graphics :– Input : caustic object, light source, and

diffuse surface– Output : caustic pattern

• But how about inverse caustics problem ?– Input : caustic pattern, light source,

and diffuse surface– Output : caustic object

• Reflective caustics in an optical set– Patow et al. 2004, International Journal of Shape

Modelling– Patow et al. 2007, Computer & Graphics– Mas et al. 2009, Computer Graphics Forum

• Reflector is represented as grid of vertices or cells• Is validated using computer simulation

RELATED WORK

Optical set Target 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 patterns

• Another similar work by Anson et. Al. 2008, CEIG 2008– Surface is represented as a NURBS and caustic

pattern shape is assumed to be circular• Is 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 cells

RELATED WORK

Target and reconstructed caustic patterns

Real-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 directions

RELATED WORK

Assembling caustic object from

pieces of predefined caustic object cells

Generated 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 pattern– How about if multiple caustic

patterns ?

RELATED WORK

• Multiple caustic patterns with each caustic pattern is formed at a location

• Is validated using mental ray

OUR WORK

• Input : multiple caustic patterns, directional light source, and planar diffuse surface (caustic receiver)

• Output : caustic object

BASIC IDEA

Our scene configuration

• Many caustic object cell orientation possibilities that might satisfy the input caustic patterns

PROBLEM FORMULATION

Possible 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 SOLUTION

Probability of the -th caustic object cell to select direction as the refraction direction

Number of causticpatterns in the scene

pmf of the -thcaustic pattern

A mapping function computing which -th caustic pattern cell is hit by a light refracted from the -th caustic object cell to the direction

• Joint pmf :

• Example : A mapping function computing which -th caustic pattern cell is hit by a light refracted from the -th caustic object cell to the direction

OUR SOLUTION

Probability of the -th caustic object cell to select direction as the refraction direction

Number of causticpatterns in the scene

Pmf of the -thcaustic pattern

PROBLEM

Only a single caustic pattern

With multiple caustic patterns

• However, some sets of caustic patterns cannot be reconstructed well– Due to differences of the input caustic

patterns– Cause 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

regions– Adjust 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 space– In x (blue arrows in the left figure below) direction– In y (red arrows in the left figure below) direction– In z (pink arrows in the left figure below) direction, i.e.

distance between the caustic pattern and the caustic object

• Scale the caustic regions (green arrows in the right figure below)

ADJUSTING POSITIONS AND SIZES

Translating the caustic regions Scaling the caustic regions

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

ADJUSTING SHAPES OF THE CAUSTIC REGIONS

To solve this, thesecond caustic region

is extended

The green caustic cell cannot be reconstructed since all possible

light 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 patterns

• In the example figure below, Light #4 hits the first caustic pattern and misses the rest of caustic patterns

ADJUSTING SHAPES OF THE CAUSTIC REGIONS

OPTIMIZATION RESULTS

Without optimizationCost : 4.45 x 10-1

OPTIMIZATION RESULTS

First optimizationCost : 4.08 x 10-1

OPTIMIZATION RESULTS

Second optimizationCost : 2.64 x 10-1

• Assume the z coordinate of each caustic object cell center is the same

• For each caustic object cell, from its refracted light direction, we can compute its normal, and in turn compute the coordinates of its four corners

• Close 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

RESULTS

Fruitsfour caustic patterns

computational time : 7.7 hours

RESULTS

Four barsfour caustic patterns

computational time : 15.7 hours

RESULTS

Rotating starnine caustic patterns

computational time : 27.6 hours

• Arts• Validation tests• Information encoding

APPLICATIONS

VIDEO

Click to play

• Compute a caustic object that can generate a set of caustic patterns

• Our two-step optimization processes can alleviate the missing caustic problems

• Results are validated using mental ray

CONCLUSIONS

• Manufacture the real caustic object for further validation– Need to devise an algorithm to smoothen

the caustic object cells such that it is easy to manufacture

• Dynamic light– Static caustic object and caustic receiver– Different caustic pattern for every light

position or direction

FUTURE WORK

THE END

CAUSTICS IN COMPUTER GRAPHICS

• Extend each caustic region such that caustic cells of other caustic regions can be reconstructed

• However, adjusting too much will cause the caustic region to change too much

• Determine the maximum adjustment, by projecting the missing caustic cells and then iteratively compute good adjustment amount

ADJUSTING SHAPES OF THE CAUSTIC REGIONS

• At the same time, also allow some light to miss some of the caustic patterns

• In the projection computation (previous slide) also count how many of projections that miss other caustic patterns

• Allow too much light to miss other caustic patterns will cause those caustic patterns to be too dark

• Also iteratively compute good amount of light to miss the caustic patterns

ADJUSTING SHAPES OF THE CAUSTIC REGIONS