1. Efficient Simulation of Furniture Layout Taking into Account Lighting Environment Takuya Yamakawa, Yoshinori Dobashi, Tsuyoshi Yamamoto 1

2. Table of Contents  Introduction  Related Works  Proposed Method  Results  Conclusion and future plans 2

3. Introduction 3

4.  Technologies for designing every day objects  Create everyday objects that satisfy his or her particular needs  Clothing design, interior and furniture design, architecture design, etc. Apply to furniture layout. 4

5. Introduction  Furniture layout design is challenging.  Several methods have been proposed. [Merrell et al 11] [Yu et al 11] [Xu et al 02] Functional criterion Visual criterion  The lighting environment is also an important factor.  Lighting rules for a room (e.g. recommend illuminance) Suggest a furniture layout design method taking into account lighting environment. 5

6. Related Work 6

7. Related Works [Xu et al 02] [Germer et al 09] [Liu et al 15] Furniture Layout Design  For large space room [Xu et al 02]  Taking into account real-time walkthroughs [Germer et al 09]  Using crowd-sourced datasets for styles of furniture layout [Liu et al 15] 7 No method taking into account lighting environment.

8. Related Works Lighting Design [Schwarz et al 14] [Shacked et al 01] [Okabe et al 07]  Computing various lighting parameters [Shacked et al 01] No works for furniture layout under fixed lighting parameters.  Desired intensities painted by user [Okabe et al 07]  The lighting design of procedurally modeled building [Schwarz et al 14] 8

9. Proposed Method 9

10. Overview  Add a new cost function to evaluate the lighting  Fast Evaluation of illuminance function  Evaluate inter-reflection suitable for furniture arrangement simulation Lighting Design Furniture Layout Simulation [Merrell et al 11]  Based on Merrell et al method.  Minimizing a cost function  Use a Markov chain Monte Carlo sampler to suggest optimized layouts 10

11. Furniture layout simulation Merrell et al method conversation m pd (F), m cd (F), m ca (F) alignment m wa (F),m fa (F) cost functiondensity function Method - Employ a Markov chain Monte Carlo sampler to explore the function. - Use the Metropolis-Hasting algorithm. 11 Functional and visual criteria

12. Lighting Environment for Furniture Layout How to evaluate lighting for interior design Our method Room functionRecommend illuminance[lx] Studying, Reading1000 ~ 500 Eating, Cooking500 ~ 220 Playing, Gatherings220 ~ 150 General lighting150 ~ 75 Sleeping, Private room30 ~ 10 12

13. Lighting Environment for Furniture Layout A new cost function for lighting environment Room functionRecommend illuminance[lx] Playing, Gatherings220 ~ 150 light source Our method L(f) : Average illuminance [lx] reflection from wall direct light higher order reflections 13 1 (L m (f),L M (f)) : the range for the recommended illuminance

14. reflection from wall direct light higher order reflections light source Lighting Environment for Furniture Layout How to calculate illuminance L(f) Our method 14 Problem  Need fast lighting calculation for furniture layout system.  Many iterations are required.  Calculating all reflections takes too much time. Our solution  Recomposing illuminance into two terms (L d,w (f) and L amb (f))  L d,w (f) has large contribution to L(f).  Approximating inter-reflection as L amb (f) because L amb (f) has less contribution than L d,w (f).  Ignore the effects of shadows.

15. Lighting Environment for Furniture Layout How to calculate illuminance L(f) light source Our method Illuminance function reflection from wall L d,w (f) ： average illuminance due to the direct light and reflections from walls direct light higher order reflections L amb (f) ： average illuminance due to higher order reflection 15

16. Evaluation of L d,w light source reflection from wall Our method direct light Lighting Environment for Furniture Layout The view from the top furniture item f ff PfPf P s S T t u v (=A) B C D room Φ ： Luminous flux Average illuminance A : Area of the top surface 16

17. Evaluation of L d,w Our method Lighting Environment for Furniture Layout furniture item f ff PfPf P s S T t u v (=A) B C D room Average illuminance from the direct light and reflection from wall Φ ： Luminous flux A : Area of the top surface 17 Precompute L d,w for all positions P f and orientations θ f

18. Summed area table algorithm Our method Lighting Environment for Furniture Layout furniture item f ff PfPf P s S T t u v (=A) B C D room 18 zero

19. Summed area table algorithm Our method Lighting Environment for Furniture Layout furniture item f ff PfPf P s S T t u v (=A) B C D room 19

20. Summed area table algorithm Our method Lighting Environment for Furniture Layout furniture item f ff PfPf P s S T t u v (=A) B C D room 20

21. Summed area table algorithm Our method Lighting Environment for Furniture Layout furniture item f ff PfPf P s S T t u v (=A) B C D room 21

22. Summed area table algorithm Our method Lighting Environment for Furniture Layout furniture item f ff PfPf P s S T t u v (=A) B C D room 22

23. Summed area table algorithm Our method Lighting Environment for Furniture Layout furniture item f ff PfPf P s S T t u v (=A) B C D room 23

24. Evaluation of L amb light source higher order reflections Our method  Assume L amb to be a const value in a room.  Radiosity algorithm to compute the inter-reflections  Calculating inter-reflections takes too much time.  Preparing a set of example layouts. Lighting Environment for Furniture Layout 24

25. Using a set of example layouts Our method Lighting Environment for Furniture Layout 25 room Example 1 room Example 2 room Example 3 L 1 (f) : radiosity solution

26. Using a set of example layouts Our method Lighting Environment for Furniture Layout 25 room Example 1 room Example 2 room Example 3 L 2 (f) : radiosity solution

27. Using a set of example layouts Our method Lighting Environment for Furniture Layout 25 room Example 1 room Example 2 room Example 3 L 3 (f) : radiosity solution

28. Using a set of example layouts Our method Lighting Environment for Furniture Layout 25 room Example 1 room Example 2 room Example 3

29. Lighting Environment for Furniture Layout Our method Evaluation of L amb Full radiosity solution 26 Higher order inter-reflection 【 Coffee Table 】 average : 34.7 [lx] standard deviation : 3.0 [lx] 【 Dining Table 】 average : 32.8 [lx] standard deviation : 1.2 [lx]

30. Results 27

31. Computational Evaluation  CPU :Intel Core i7  Graphics API :OpenGL  Memory :8GB  Number of iterations:10,000 times  Time: 1~2 sec  Time of precomputation (summed area table):about 30 sec  Rendering : Autodesk Maya 2016 28

32. Furniture objects Recommended illuminance (L m,L M ) Dining TableCoffee Table Eating, Cooking (500 ~ 220) Playing, Gatherings (220 ~ 150) Sleeping, Private room (30 ~ 10) 29

33. Eight light sources on the ceiling 30 downlight

34. Various light placement 31 downlight

35. Example 32 brighter darker brighter darker

36. Other Examples 33

37. With and without our method With our methodWithout our method Placed under the lighting equipment Not Placed under the lighting equipment Dining TableCoffee Table 263[lx] (220~500)197[lx] (150~220) Dining TableCoffee Table 97[lx] (220~500)174[lx] (150~220) 34

38. Other Example 35 Bright spot in the centerBright spot in the right Indirect lighting

39. Average illuminance of the top surface Dining TableCoffee Table 298[lx] (220~500)153[lx](150~220) Dining TableCoffee Table 346[lx] (220~500)159[lx](150~220) Dining TableCoffee Table 244[lx] (220~500)22[lx](10~30) The illuminance on the dining and coffee tables are in the recommended range 36

40. Conclusion and future plans 37

41. Conclusion  Computing furniture layout that takes lighting conditions into account  A new cost term using the average illuminance based on the lighting design guidelines  A fast method using summed area table algorithm  Succeed in designing furniture layout that is optimal in terms of functionality, visual composition, and lighting environment. 38

42. Future plans  Consideration of natural light sources  Sunlight, skylight etc.  Computing the inter-reflections from windows  Apply to real world interior design and compare our method with the manual layouts 39

43. END 40