Lagrangian point of view

Eulerian point of view

t1 t2

51 26

51 26

(-1,1) (0,1) (1,1)

(1,0)

(1,-1)(0,-1)(-1,-1)

(-1,0)(0,0)

(-1,-1)(-1, 0)(-1, 1)( 0,-1)( 0, 0)( 0, 1)( 1,-1)( 1, 0)( 1, 1)

x

y

evaluatedpairs

not evaluatedpairs with cellson opposite side

Offset

h

h

neighbors

potential neighbors

no potential neighbors

world spaceparticle positions

world spacecorner offsets

world spacebillboards / triangles

clip spacebillboards

corner shared with precursor

edge shared with precursor

new corner

new edge

image plane

pixel centre

view ray

eye point

ray exit

ray entry / first sample point

step size

L

C

last sample point

current sample point

isosurface

1

2

3

refinementsample points:1 halfway L-C

2 halfway 1-C

3 halfway 1-2

world space texture space

33

3

33

3

5

5

7

5

1

1

1

1

0.6

0.6

0.6

0.6

0.43

0.52

θr = θiθi

incident ray reflection ray

surface normal

surface cut

common plane

l

n

a

θi

sin θi

cos θi

r

bθr

θi

incident ray

refraction ray

surface normal

surface cut

common plane

θt

ni

nt

l

n

-l

-n

θi

θt

sin θi

cos θi

sin θi

t

cos θt

ni

nt

a

b

sin θt

cos θi

x

y

surface

medium with low index of refractionlight (s-polarised)

refractions

reflections

medium with high index of refraction

surface

light (s-polarised)

refractions

reflections

critical angle

medium with low index of refraction

medium with high index of refraction

view ray

reflection 1

θi1n1

-n1θr1

θt1

refraction 1

refraction 2

(if possible)

isosurface

airni

waternt

-n2

n2reflection2

view ray

volume texture

(0, 0, 0)

(1, 1, 1)

entry

exit

- +x-x

+y

-y

+z

-z

1514131111109876543210

43210

slice index

instance index

particleposition

z

render target*

*: texture z

…

…