The designer defines a set of. Lighting Intentions (LI). LI are the objectives and constraints that designers want to achieve. 5 ...
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Contents 1. Introduction. 2. State of the Art. 3. LRR using Sparse Matrices and GPU. 4. LRR Applied to the Inverse lighting Problem. 5. Mean and Stdev as Lighting Intentions. 6. Sample-Based Radiosity Inverse Matrix. 7. Conclusions and Future Work. 2
Contents 1. Introduction. 2. State of the Art. 3. LRR using Sparse Matrices and GPU. 4. LRR Applied to the Inverse lighting Problem. 5. Mean and Stdev as Lighting Intentions. 6. Sample-Based Radiosity Inverse Matrix. 7. Conclusions and Future Work. 3
Light is a key design element
• It Influences the way we perceive and experience our environment. • It is an object to be modeled as the forms and materials. 4
The designer defines a set of Lighting Intentions (LI)
LI are the objectives and constraints that designers want to achieve. 5
Lighting Intentions (LI)
• Which surfaces should be illuminated with natural / artificial light? • Which surfaces should be in shadow? • Which are the maximum and minimum intensities allowed?
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Defining the LI: Light Map
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Inverse Lighting Problem (ILP) ILP is the problem of finding a parameter setting that meets the LI: •Position •Shape •Spectral Spectral power
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Problems in Lighting Design
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Problems in Lighting Design
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Lighting Design Defined as an Optimization Problem
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Context of the Thesis Work 1. First the geometry, second the light intentions. • This allow us to speed-up the optimization process.
2. There is not a formal language to describe lighting intentions. • Therefore, we could define easier-to-calculate LI.
3. Surfaces with diffuse reflection. • Then, we use radiosity algorithms based on finite elements. 12
Contents 1. Introduction.
2. State of the Art. 3. LRR using Sparse Matrices and GPU. 4. LRR Applied to the Inverse lighting Problem. 5. Mean and Stdev as Lighting Intentions. 6. Sample-Based Radiosity Inverse Matrix. 7. Conclusions and Future Work. 13
Radiosity
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Radiosity
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Light Coherence in Radiosity
[Baranoski et al. 1997], [Ashdown 2001], [Hasan 2007]. 16
Low-Rank Radiosity Example for a Cornell box composed by 5632 patches: Light coherence of the scene patches. VT U
RF =
UVT =
U, V are n x k , n >> k 17
Low-Rank Radiosity RF is substitute d by UV T ~ T B = ( I − YV )E ; Low-rank M :
~ ~ B = M E complexity O ( n 2 + nk 2 )
Y , V are n × k , n >> k where Y = − U ( I − V T U ) −1 based on Sherman - Morrison - Woodbury formula
(
~ B = E − Y VT E
)
has complexity O ( nk ) 18
Alternatives to Low-Rank Radiosity • [Golub and Van Loan 1996]: Truncated SVD and rank revealing QR. O(n2k).
• [Kontkanen et al. 2006]: Global Transport Operator (GTO). Accumulates the first terms of the Neumann series. Wavelets.
• [Halko et al. 2011], [Mahoney 2011]: random sampling that captures most action. O(n2log k)
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Inverse Lighting Problem • Find the emission E given the reflection values on the scene: C=B-E RF E = ( I − RF )C – – –
Problem ill-posed. The solution may contain negative emission values. C values are usually unknown.
→ Solve the ILP as an optimization problem.
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Prev.Works in Inverse Lighting Problem •
[Kawai et al. 1993]: unconstrained optimization , penalty and barrier method, hierarchical radiosity.
•
[Contensin 2002]: pseudo-inverse, iterative method.
•
[Tourre et al. 2008]: Optimization of daylight sources.
•
[Tena 1997], [Delepoulle et al. 2008]: population based methods.
•
[Castro et al. 2012]: heuristics, energy-saving goal. 21
Inverse Lighting Problem Solver Problem Definition Optimization Geom. & Mat.
Light Intentions: Global Illumination, Emitters Filters
Evaluation Radiosity solver Ch. 3
Optimization Variables
Designer Evaluation Ch. 4, 5, 6, 7
Ch. 4, 6
Ch. 4, 5, 6
Precomputation Process (Low-rank) Ch. 7 22
Contents 1. Introduction. 2. State of the Art.
3. LRR using Sparse Matrices and GPU. 4. LRR Applied to the Inverse lighting Problem. 5. Mean and Stdev as Lighting Intentions. 6. Sample-Based Radiosity Inverse Matrix. 7. Conclusions and Future Work. 23
LRR using Sparse Matrices and GPU Problem Definition Optimization Geom. & Mat.
Light Intentions: Global Illumination, Emitters Filters
Evaluation
Designer Evaluation
LRR solver
Optimization Variables
Precomputation Process (Low-rank) 24
From V matrix to an index vector ( I − RF ) ≈ ( I − UV T ) M = ( I − RF )
−1
~ ≈ ( I − YV ) = M T
From nk floating point numbers to k+1 integers. 25
B Calculation Using GPU ~ ~ T B = ( I − YV ) E = M E
(
~ T B = E−Y V E ~ B= 1 E42 X −Y 4 3 using xGEMV cuBLAS NVIDIA
,
) X42 E = V4 1 3 T
X (i )=
I ( i +1 ) −1
∑ E (s)
s=I ( i )
26
Full vs. Sparse // CPU vs. GPU
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Contents 1. Introduction. 2. State of the Art. 3. LRR using Sparse Matrices and GPU.
4. Inverse lighting Problem using LRR. 5. Mean and Stdev as Lighting Intentions. 6. Sample-Based Radiosity Inverse Matrix. 7. Conclusions and Future Work. 28
Inverse Lighting Design for Interior Buildings Integrating Natural and Artificial Sources Problem Definition Optimization Geom. & Mat.
Light Intentions: Global Illumination, Emitters Filters
Evaluation
Designer Evaluation
LRR Solver
Optimization Variables
Precomputation Process (Low-rank) 29
Optimize the use of natural and artificial light resources
30
ILP Formulated as an Optimization Problem
31
Variable Neighborhood Search Neighborhoods:
In our case, the neighborhoods are defined by the number of variables modified and the range of variation 32
Convergence tests
25,000 iterations after 50 minutes. 33
Multilevel Method
25,000 iterations after 240 seconds.
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Multiobjective Optimization Problem
1.- VNS with ϵ-constraint method (Pareto front). 2.- Two-step process: 1st maximize natural light 2nd minimize artificial light
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Pareto Front
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Application in the Design of Filters
Institute du monde Arabe (Paris) by Jean Nouvel. 37
Application in the Design of Filters
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Contents 1. Introduction. 2. State of the Art. 3. LRR using Sparse Matrices and GPU. 4. LRR Applied to the Inverse lighting Problem.
5. Mean and Stdev as Lighting Intentions. 6. Sample-Based Radiosity Inverse Matrix. 7. Conclusions and Future Work. 39
µ and σ as Lighting Intentions Problem Definition Optimization Geom. & Mat.
Light Intentions: Global Illumination, Emitters Filters
Evaluation
Designer Evaluation
µ , σ solver
Optimization Variables
Precomputation Process (Low-rank) 40
µ and σ as Lighting Intentions s : surface B(s) : radiosity in s µ(B(s)) : mean of B(s) σ(B(s)) : Stdev of B(s) ILP: min σ(B(s)) subject to µ(B(s)) > 1
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µ and σ as Lighting Intentions Intuitive Lighting Intention
µ , σ Lighting Intention
to illuminate s
max ΣB(s)
max µ(B(s))
to overshadow s
min ΣB(s)
min µ(B(s))
to homogenize s
min σ(B(s))
to contrast s
max σ(B(s))
to delimit s
Bmin ≤ B(s) ≤ Bmax
Bmin ≤ µ ± ασ ≤ Bmax (*)
(*) Based on Chebyshev’s inequality 42
Efficient Computation of µ and σ using LRR = vE Complexity O(n), memory O(n)
= a Ca E T E
Complexity O(n+e2) ≈ O(n), memory O(n + k2) n >> k >> e 43
Simplification of the Optimization solver
25000 iterations after 10 seconds, for scenes containing 25000 patches. 44
Experimental Results
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α Determination for Chebyshev-Based Constraints
120 seconds to find a solution with α determination.
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Contents 1. Introduction. 2. State of the Art. 3. LRR using Sparse Matrices and GPU. 4. LRR Applied to the Inverse lighting Problem. 5. Mean and Stdev as Lighting Intentions.
6. Sample-Based Radiosity Inverse Matrix. 7. Conclusions and Future Work. 47
A Sample-Based Method for Computing the Radiosity Inverse Matrix Problem Definition Optimization Geom. & Mat.
Light Intentions: Global Illumination, Emitters Filters
Evaluation
Designer Evaluation
Radiosity solver
Optimization Variables
Precomputation Process (Low-rank) 48
Sample-based scene (SP)
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Sample-based RF
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Sample-based RF 200 patches
50 patches
scen e
5632 patches
RF
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Three Operators used to calculate B
b a
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Use of Operators to find B
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Use of Operators to find B
where
When u = S :
LRR equation ~ B = ( I − YV T ) E V sparse matrix
When PL = L : VT could is a sparse matrix 54
Properties Used to Build the Operators 1. The set of patches P is selected randomly, with a probability weighted by the area size. 2.
F(di,j)=F(i,j)
3. .
4.
.
5.
. 55
Operators as Matrices
complexity O(n|P| + n|P|2) , n >> |P|
LRR has O(n2 + nk2) 56
Estimation of Errors •
.
•
.
•
. LTI means Length of the Tolerance Interval. 57
Experimental Results (ER): σ •
1/ √|P|
.
•
.
•
. 58
Normal Distribution
•
Lilliefors test can not reject the normal distribution hypothesis in 80% of patches at 5% significance level, when |P|=80. 59
Sponza Atrium (80k Patches)
Hemicube view.
Upper corridor.
Lower corridor.
2 minutes to calculate 60
ILP in Sponza Atrium Sample of 2000 elements 25000 iterations
30 seconds
60 seconds
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ILP in Sponza Atrium
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Museum (170k Patches)
4 minutes to calculate
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ILP in the Museum
95 seconds to solve ILP 25000 iterations
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Contents 1. Introduction. 2. State of the Art. 3. LRR using Sparse Matrices and GPU. 4. LRR Applied to the Inverse lighting Problem. 5. Mean and Stdev as Lighting Intentions. 6. Sample-Based Radiosity Inverse Matrix.
7. Conclusions and Future Work. 65
Thesis Main Results SoA
Ch. 3, 4, 5
min f(E) Bmin ≤ B ≤ Bmax
min f(E) Bmin ≤ B ≤ Bmax ~ M based on LRR,
Trans Ch. 6
Ch. 6
Ch. 7
min f(µ,σ) gmin ≤ g(µ,σ) ≤ gmax
Sample-based method to~ compute M
~ M based on LRR, VNS
VNS, multilevel, MOP Precomp: O(n2k)
O(n2 + nk2)
O(n2 + nk2)
Iteration: O(n2)
O(nk)
O(n+e2)
O(n+e2)
Memory: O(nk)
O(nk)
O(n+k2)
O(n+k2)
n >> k
n >> k >> e
The use of GPU to calculate LRR ; V as an index vector
O(nk + nk2)
n >> k >> e 66
Future Work • Hybrid strategies: computation in CPU and GPU.
• Population based metaheuristics.
• Reduction of rank of sampled based M: – Variance reduction techniques. – Truncated SVD or rank revealing QR. 67
Future Work • Openings not covered by Lambertian diffusers:
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Future Work • Flux and Flux density goals and constraints.
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Publications
70
Thanks
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