Encoding Normal Vectors using Optimized Spherical Coordinates J. - - PowerPoint PPT Presentation

▶
encoding normal vectors using optimized spherical
SMART_READER_LITE
LIVE PREVIEW

Encoding Normal Vectors using Optimized Spherical Coordinates J. - - PowerPoint PPT Presentation

Jan 18, 2023 155 likes •565 views

Encoding Normal Vectors using Optimized Spherical Coordinates J. Smith, G. Petrova, S. Schaefer Texas A&M University Motivation Motivation Motivation Motivation Normal Vectors On floating-point normal vectors [Meyer et al. 2010]

slide-1
SLIDE 1

Encoding Normal Vectors using Optimized Spherical Coordinates

  • J. Smith, G. Petrova, S. Schaefer

Texas A&M University

slide-2
SLIDE 2

Motivation

slide-3
SLIDE 3

Motivation

slide-4
SLIDE 4

Motivation

slide-5
SLIDE 5

Motivation

slide-6
SLIDE 6

Normal Vectors

  • On floating-point normal vectors [Meyer et al. 2010]

– 96 bit vectors redundant – Only 51 bits are sufficient to represent floating point accuracy

  • Is floating point necessary?

– Bound error – Robust – Efficient encode / Decode

slide-7
SLIDE 7

Point Distribution

slide-8
SLIDE 8

Point Distribution

slide-9
SLIDE 9

Point Distribution

slide-10
SLIDE 10

Point Distribution

slide-11
SLIDE 11

Related Work

[Botsch et al. 2002] [Taubin et al. 1998]

slide-12
SLIDE 12

Related Work

[Oliveira and Buxton 2006] [Griffith et al. 2007]

slide-13
SLIDE 13

Related Work

[Deering 1995] [Górski et al. 2004]

slide-14
SLIDE 14

Related Work

[Meyer et al. 2010]

slide-15
SLIDE 15

Contributions

  • User Specified Maximal Bounded Error
  • Variable Bit Encoding
  • Constant Time Encode and Decode

– Independent of accuracy

  • Differential Encoding Method

– Usable with other methods

slide-16
SLIDE 16

Spherical Coordinates

slide-17
SLIDE 17

Spherical Coordinates

slide-18
SLIDE 18

Rectangular Domain

slide-19
SLIDE 19

Solve for Minimum Nθ(j)

slide-20
SLIDE 20

Choose Nφ

ε = 4ο Nφ= 23

slide-21
SLIDE 21

Choose Nφ

ε = 4ο Nφ= 34

slide-22
SLIDE 22

Choose Nφ

ε = 4ο Nφ= 81

slide-23
SLIDE 23

Minimize Encoding Points

slide-24
SLIDE 24

Uniform Encoding Points

# of symbols = 2112

slide-25
SLIDE 25

Optimized Encoding Points

# of symbols = 1334

slide-26
SLIDE 26

Regions on the Sphere

slide-27
SLIDE 27

Variable Bit Encoding

3 bits 6 bits

slide-28
SLIDE 28

Moving Frame

slide-29
SLIDE 29

Moving Frame

slide-30
SLIDE 30

Moving Frame

slide-31
SLIDE 31

Moving Frame

slide-32
SLIDE 32

Moving Frame

slide-33
SLIDE 33

Moving Frame

slide-34
SLIDE 34

Arithmetic Encoder

  • Adaptive Arithmetic Coding [F. Wheeler 1996]

– Source code at http://www.cipr.rpi.edu/˜wheeler/ac

8 bits 10 bits 3 bits

slide-35
SLIDE 35

Arithmetic Encoder - Phi

100000 200000 300000 400000 500000 600000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

slide-36
SLIDE 36

Arithmetic Encoder - Phi

100000 200000 300000 400000 500000 600000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

3 4 5 5 5 6 6 6 6

slide-37
SLIDE 37

No Moving Frame

slide-38
SLIDE 38

Moving Frame

slide-39
SLIDE 39

Timings

20 40 60 80 100 120 Ours ONV Sphere1 Octa HealPix Sextant Encode 1.2 Decode 1.2 Encode .0045 Decode .0045

slide-40
SLIDE 40

Conclusions

  • Encoding method that produces the smallest

file sizes for a given maximum error

  • Constant time encoding and decoding
  • Differential encoding frame to improve

encoding techniques

  • Variable Bit Encoding