1 converting celsius to fahrenheit c 1.8 32 + f 10 18 50
TRANSCRIPT
1
Converting Celsius to Fahrenheit
C
1.8
32
+ F
10
1850
325
9 CF
2
Converting Fahrenheit to Celsius
C
1.8
32
+ F
10
1850
325
9 CF
)32(9
5 FC
3
Addition Box
+p
qr
qpr
qrp
prq
4
Muliplication Box
p
qr
qpr
0 if qq
rp
0 if pp
rq
0 if 0 pr
0q if 0 r
5
Local Propagation is Not Enough
yx
100?
6
Barometric Measurements with Varying Confidence
0
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Confidencelevels
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Actualterrain
Barometerreadings
7
Constraint Propagation by Relaxation
Barometer readings
0123456789
10
After first iteration
0123456789
10
After fifth iteration
0123456789
10
After tenth iteration
0123456789
10
After twentieth iteration
0123456789
10
After fortieth iteration
0123456789
10
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
8
GENINFER: Genetic Reasoning
9
GENINFER Results
Nothing known about uncles and
brothers
Uncles OKnothing
known about brothers
Both uncles and brothers
OK
12.5%
2.8%
0.7%
10
Line Drawing Analysis
11
Classification of Lines
Alllines
Interiorlines
Boundarylines
Convexedges
Concaveedges
12
Line Interpretation
13
Common Junctions
L
Arrow
T
Fork
X
Peak
K
Psi
Multi
Kk
14
Possible Inputs
15
Excluded Input
16
Impossible Junctions
17
Identifying Three-Faced Junctions
18
Full/Empty: 7/1, 1/7
19
1 Full, 7 Empty (Low Views)
L R
R
T
L
RL
20
1 Full, 7 Empty (High Views)
RL
L R
21
3 Full, 5 Empty
22
Junction Dictionary
Ljunctions
Forkjunctions
Tjunctions
Arrowjunctions
Alljunctions
23
Labeling a Drawing
24
A Two-Tiered Figure
25
Starting From the Middle
26
Impossible Objects?
Not possible
27
Waltz’s Algorithm
A B
C
DE
F
A B
C
DE
F
A B
C
DE
F
A B
C
DE
F
(a) (b)
(c) (d)
28
Waltz Example
AB
CD
C
B
A
D
29
The Need for More Information
30
Shadows
31
Concave Edges
32
Extended Line Catalog
C
C
Alledges
Realedges
Interioredges
Boundaryedges
Shadowedges
Pseudoedges
Crackedges
Convexedges
Concaveedges
33
Face Catalog
Illuminated
Illuminated
Illuminated
Shadowed
Self-Shadowed
34
Effects of Constraints(Basic Lines)
VertexType
Number ofunconstrained
possible junctions
Number ofphysically
realizable junctions
Ratio(%)
L 16 6 37.5
Fork 64 5 7.8
T 64 4 6.2
Arrow 64 3 4.7
35
Effects of Constraints(Expanded Categories)
VertexType
Number ofunconstrained
possible junctions
Number ofphysically
realizable junctions
Ratio (%)
L 2.5103 80 3.2Fork 1.2105 500 4.010-1
T 1.2105 500 4.010-1
Arrow 1.2105 70 5.610-2
Psi 6.2106 300 4.810-3
K 6.2106 100 1.610-3
X 6.2106 100 1.610-3
Multi 6.2106 100 1.610-3
Peak 6.2106 10 1.610-4
Kk 3.1108 30 9.610-6
36
Example
37
Waltz in Action
1 A — 123 16 E 79 33 31 C 20 2 61 P 5 1 76 T — 123
2 A 123 76 17 D 15 14 32 B 14 2 62 O 2 1 77 T 123 4
3 B — 79 18 F — 123 33 A 20 2 63 Q — 123 78 T 4 1
4 B 79 52 19 F 123 28 34 H — 79 64 Q 123 5 79 J 4 1
5 A 76 32 20 G — 593 35 H 79 1 65 Q 5 1 80 R 4 1
6 C — 388 21 G 593 42 36 I — 123 66 L 3 1
7 C 388 78 22 G 42 18 37 I 123 2 67 K 5 2
8 B 52 34 23 F 28 11 38 J — 593 68 R — 388
9 A 32 26 24 E 33 7 39 J 593 9 69 R 388 20
10 D — 79 25 D 14 6 40 K — 79 70 R 20 4
11 D 79 15 26 F 11 2 41 K 79 7 71 J 6 4
12 C 78 20 27 G 18 1 42 J 9 8 72 K 2 1
13 B 34 14 28 E 7 1 43 L — 593 73 S — 1391
14 A 26 20 29 D 6 1 44 L 593 12 74 S 1391 5
15 E — 79 30 F 2 1 45 K 7 5 75 S 5 1
38
Time Intervals
before
A
B
A B
39
Interval Arithmetic
beforeA
beforeB C
beforeA
beforeB C
before
?
40
Constraint Propagation for Time Intervals
B
A
C D Z
b e f o r e b e f o r e b e f o r e b e f o r e
b e f o r e b e f o r eb e f o r eb e f o r e
41
Using Reference Nodes
MEETS
MORNING AFTERNOON
X
Y
DURING
MEETS
MORNING AFTERNOON
X
Y
DURING
BEFORE
BEFORE
BEFORE
BEFORE
BEFORE