Table 6 \(\alpha _{i}^{j}\): α _i values for the j-th 1D example and for the environment map example

Example 1

Example 2

Example 3

Example 4

Example EM

\(\alpha _{1}^{1}\)

\(\alpha _{2}^{1}\)

\(\alpha _{3}^{1}\)

\(\alpha _{1}^{2}\)

\(\alpha _{2}^{2}\)

\(\alpha _{3}^{2}\)

\(\alpha _{1}^{3}\)

\(\alpha _{2}^{3}\)

\(\alpha _{3}^{3}\)

\(\alpha _{1}^{4}\)

\(\alpha _{2}^{4}\)

\(\alpha _{3}^{4}\)

α ₁

α ₂

\(\alpha = \frac {1}{n}\)

0.33

0.33

0.33

0.33

0.33

0.33

0.33

0.33

0.33

0.33

0.33

0.33

0.5

0.5

\(\alpha _{k} \propto \frac {1}{v_{k}}\) [9, 10]

0.42

0.48

0.10

0.35

0.21

0.44

0.90

0.10

0.00

0.95

0.04

0.00

0.93

0.07

\(\alpha _{k} \propto \frac {1}{c_{k} v_{k}}\) [9, 10]

0.79

0.14

0.06

0.68

0.07

0.25

0.98

0.02

0.00

0.99

0.01

0.00

0.99

0.01

α _k ∝σ_k,eq[11]

0.33

0.31

0.35

0.34

0.34

0.31

0.37

0.32

0.30

0.37

0.32

0.30

0.52

0.48

\(\alpha _{k} \propto \frac {\sigma _{k,{\text {eq}}}}{\sqrt {c_{k}}} \) [11]

0.51

0.19

0.29

0.52

0.21

0.26

0.55

0.19

0.25

0.55

0.19

0.25

0.70

0.30

\(\alpha _{k} \propto \frac {1}{m_{k}^{2}}\)

0.38

0.39

0.23

0.35

0.29

0.36

0.53

0.46

0.01

0.60

0.36

0.04

0.66

0.34

\(\alpha _{k} \propto \frac {1}{c_{k} m_{k}^{2}}\)

0.52

0.16

0.32

0.69

0.09

0.22

0.87

0.12

0.00

0.56

0.19

0.25

0.90

0.10

α _k ∝M_k,eq

0.33

0.35

0.30

0.32

0.31

0.35

0.34

0.36

0.28

0.33

0.32

0.34

0.57

0.43

\(\alpha _{k} \propto \frac {M_{k,{\text {eq}}}}{\sqrt {c_{k}}}\)

0.52

0.21

0.25

0.50

0.19

0.30

0.52

0.22

0.24

0.50

0.19

0.29

0.75

0.25