Geometric Folding Algorithms:
Linkages, Origami, Polyhedra

by Erik D. Demaine and Joseph O'Rourke

ERRATA

Last Update:

SUBSTANTIVE ERRATA

Chap
Page
Location
Old
New
Explanation
Corrector
Date
5
66
Eq. 5.2
l3 <= (l1-l2) + (l4+...+ln) ...
But Eq. (5.2) is just a rearrangment of Eq. (5.1), ...
l3 <= (l1-l2) + (l4+...+ln)
or (l1+l2) <= l3+...+ln...
But Eq. (5.2) is just a rearrangment of Eq. (5.1), and Eq. (5.3) follows easily from Eq. (5.1) ...
Missed a case, which easily follows.
Ryuhei Uehara
23Feb08
8
143
Line+12 of Sec. 8.2.1
Define such a chain to be convex if all of its vertices lie on the convex hull Define such a chain to be convex if all of its edges lie on the convex hull A zigzag chain could have all its vertices on the hull be not be convex in the sense we intended.
Sebsatien Collette
6 Feb 08
22
326
Sec. 22.5.2 Domes, Line+5
and at most one can have adjacent faces diverge (because divergence implies an angle greater than π, and there is only 2π total angle to G).
and at most one can have adjacent faces diverge (because divergence implies a turn angle greater than π, and there is only 2π total angle to G). The one exception, when G is a trapezoid and two turn angles are =π, is easily seen to unfold without overlap.
With G a trapezoid, P is a wedge of just four faces, and nonoverlap is straightforward.
JOR
9Aug07

NONSUBSTANTIVE ERRATA (typos, etc.)

Chap
Page
Location
Old
New
Explanation
Corrector
Date
Contents
viii; 165
Part II line
Part II: Paper Part II: Origami Part name changed
JOR
6Nov07
1
9
Line -10
when a linkage is rigid, that is, can move at all. when a linkage is rigid, that is, cannot move at all. Typo
Ryuhei Uehara
17Aug07
1
11
Line -3
It is sometime useful It is sometimes useful Typo
Ryuhei Uehara
17Aug07
2
18; 19
Line -7; Line -3
let us say that k=2n ... specifying the coordinates for point reduces this to k=2n-2. ... O( n4n-2 ... ) let us say that k=2n+2 ... specifying the coordinates for one point reduces this to k=2n. ... O( n4n+2 ... ) n links means n+1 vertices
Ryuhei Uehara
17Aug07
2
19
Box 2.1, Line +4
For a univariate polynomials For univariate polynomials Typo
Ryuhei Uehara
1Jun08
2
19
Box 2.2, Line -4
is in PSPACE (1988). is in PSPACE. ~Typo
Ryuhei Uehara
17Aug07
2
21
Line -8
327 > 1010 5014 > 1023 ~Typo
Ryuhei Uehara
17Aug07
2
23
Sec. 2.2.2, Line +3
Mis M is Printer error on spacing
Ryuhei Uehara
8Nov07
2
24
Fig. 2.3 caption, Line +3
Each ... fan ... represent Each ... fan ... represents Typo
Ryuhei Uehara
8Nov07
2
26
Line +2
must both lie at 1 if all is to fit
must both lie at s if all is to fit
Typo
Joe Malkevitch
2Oct07
3
32
Figure 3.3
Edge connecting the α angle to the β angle
Should be labeled “a
The length of this edge is referred to as a in the text
Gregory Price
10Sep07
3
32
Figure 3.3
Origin Origin should be labeled “O Described as O in the text.
Ryuhei Uehara
28Nov07
3
33
Figure 3.5
Angle α at y, angle β at b
Angle β at y, angle α at b
Opposite contraparallelogram angles are equal
Andrea Hawksley & Howard Samuels
18Sep07
3
37
Line+1 of 3.2.2.1
...locate a joint in the interior of a bar. ...locate a joint in the interior of a bar (as in Figure 3.5). Used in Fig. 3.5 before its use in Fig. 3.10.
Ryuhei Uehara
30Nov07
2
41
Box 3.2, Line +4
constancy of ab . bd constancy of ac . bd Typo
Ryuhei Uehara
1Jun08
4
45
Figure 4.3 caption
graphy
graph
Typo
Gregory Price
20Sep07
4
48
Lines-8,-6
(Badoiu et al. to appear) (Badoiu et al. 2006) Editor error
Ryuhei Uehara
13Jan08
4
48
Theorem 4.3.2
A graph is generically rigid if some subgraph is minimally generically rigid A graph is generically rigid only if some subgraph is minimally generically rigid ~Typo
Ryuhei Uehara
1Jun08
4
48
Line-2
Connelly (to appear) Connelly (2005) Editor error
Ryuhei Uehara
13Jan08
4
48
Line-2
in any dimension with vertex (d+1)-connectivity in any dimension d with vertex (d+1)-connectivity Typo
Ryuhei Uehara
13Jan08
4
51
Box 4.1, last two equations
v3x = v4x
v3x = v4x = 0

v3x = v4x ,
v3x = v4x = 0 .

Typo: punctuation
Ryuhei Uehara
13Jan08
4
52
Line+3
infinitesimally rigid infinitesimally rigid Typo: should be italicized because being defined
Ryuhei Uehara
13Jan08
4
49
Section 4.4.1, first display equation
(Lxi + xj)2 + (yi + yj)2
(Lxi + xj)2 + (yi + yj)2
Signs of y's should be opposite, like x's
Edwin Chen
18Sep07
5
62
Line+7 of 2nd para. of Sec. 5.1.1.3
(i.e, αi=0 for all internal joints) (i.e, αi=π for all internal joints) ~Typo
Ryuhei Uehara
23Feb08
5
63
Caption to Fig. 5.5
(lM=6)<(s=15) (lM=6)<(s=11) Typo
Ryuhei Uehara
23Feb08
5
63
Line+4 of Sec.5.1.1.4
l1 and l3 respectively l1 and l3 respectively Typo
Ryuhei Uehara
23Feb08
5
66
Line-2
in R3 in R3 R should be \mathbb{R}.
Ryuhei Uehara
23Feb08
5
71
Line+5 of 2nd para. of Box. 5.1
Figure 5.17(b) Figure 5.17(a) Typo
Ryuhei Uehara
23Feb08
5
73
Last line of proof of Lemma 5.3.2
, which requires v1 and v3 to reach π. , which requires v1 and v3 to reach π, respectively. Did not mean to imply that the two triangles must collapse at the same time.
Ryuhei Uehara
23Feb08
5
77
Line+2 of Step 3
where ε i = min {...} where ε i = mink {...} Clarification that min is over k.
Ryuhei Uehara
23Feb08
5
78
Last 2 paras. of proof.
Let ... [2 paragraphs] [add indenting] Should be indented to be part of Step 5.
Ryuhei Uehara
23Feb08
5
79
Line+2
on the lengths a,b,c,d of its edges: on the lengths of its edges: a,b,c,d are vertex labels, not edge lengths.
Ryuhei Uehara
23Feb08
5
79
Lines-9 to -6
The initial polygon P0 Figure 5.27(a) ... The initial polygon P0 (Figure 5.27(a)) ... Citations of the four parts of this figure should be in parentheses.
Ryuhei Uehara
23Feb08
5
82
Fig. 5.30
[circle] [C] Circle in the figure should be labeled C.
Ryuhei Uehara
23Feb08
5
84
Caption to Fig. 5.33
are shown shaded. are shown red. ~Typo.
Ryuhei Uehara
23Feb08
5
84
Caption to Fig. 5.34
A 3D polygon A 3D open chain ~Typo.
Ryuhei Uehara
23Feb08
6
87
Table 6.1 column heading
Can trees trees lock? Can trees lock? Typo.
Ryuhei Uehara
6Apr08
6
89
Line-3 of proof of Theorem 6.3.1
Unfolding of P. Unfolding of K. Typo.
Ryuhei Uehara
6Apr08
6
93
Line+8
--the set all positions --the set of all positions Typo.
Ryuhei Uehara
6Apr08
6
95
Figure 6.9 caption
Biedl et al. 1998a, Tech. Rep. Biedl et al. 1998a. ~Typo.
Ryuhei Uehara
6Apr08
6
95
Section 6.5, para. 3
the tree in Figure 6.9 is locked
the tree in Figure 6.9(a) is locked
Figure 6.9 contains several trees; this sentence refers to the first
Gregory Price
20Sep07
6
105
Line+6 of Sec. 6.7.1
because each of the components are because each of the components is Typo
Ryuhei Uehara
6Apr08
6
111
Line+8
(p. 100 and (p. 100) and Typo
Ryuhei Uehara
6Apr08
6
115
Line+1 of Sec. 6.8.5
(all chains can be straightened) (all chains can be straightened/convexified) ~Typo
Ryuhei Uehara
6Apr08
7
124
Table 7.1, 2f row
?   ?
–   –
This follows from Theorem 5 of Demaine et al (2002b), as described in the last sentence on p.125.
Stefan Langerman
21May07
7
124
Line-4
The columns of the table cover .... out to k=4. The columns of the table cover .... out to k=4-5. ~Typo
Ryuhei Uehara
1May08
7
127
Fig. 7.4, 7.5 captions
... can lock. ... can interlock. More precise terminology.
Ryuhei Uehara
1May08
7
127
Line+4
if e1 and e2 are long enough if e1 and e3 are long enough Typo
Ryuhei Uehara
1May08
7
127
Theorem 7.3.1
A triangle can interlock with a closed, flexible 4-chain
A triangle can interlock with an open, flexible 4-chain
See Figure 7.5.
Stefan Langerman
21May07
8
138-141
Sections
8.1.5
8.1.6
8.1.7
8.1.4.1
8.1.4.2
8.1.4.3
Section numbering error.
Ryuhei Uehara
5May08
8
143
Lemma 8.2.1
--i.e., angle α'i is replaced with αi ≤ α'i ≤π-- --angle α'i is replaced with αi ≤ α'i ≤π-- Drop i.e., because there is not exact equivalence: at least one angle is strictly opened, i.e., cannot have αi= α'i for all i.
Ryuhei Uehara
5May08
8
146
Line-6
Instead of proving the lemma, we describe instead the fourth Instead of proving the lemma, we describe the fourth Drop 2nd instead.
Ryuhei Uehara
5May08
9
148
Central Eq.
...C...
...C'...
Typo. Replace C by C' throughout the equation.
Ryuhei Uehara
16May08
9
149-150
Figs. 9.2 & 9.3
Fig. 9.3 ... Fig. 9.2
Fig. 9.2 ... Fig. 9.3
Interchange ordering of figures, and renumber according to citation ordering.
Ryuhei Uehara
16May08
9
149-150
Figure captions
Demaine et al. 2006
Demaine et al. 2006c
Publisher error.
Ryuhei Uehara
16May08
9
153
Line+9
there is a positive probability
there is a positive probability ρ
Clarification.
Ryuhei Uehara
16May08
9
153
Line+10
> ρ
ρ
More precise.
Ryuhei Uehara
16May08
9
153
Line+4
There is,
There is such a chain,
Clarification.
Ryuhei Uehara
16May08
9
155
Line+2
(He and A.Scheraga 1998)
(He and Scheraga 1998)
Remove "A." Publisher error.
Ryuhei Uehara
16May08
9
160
Line+12
(When two P nodes are not adjacent,
(When two P nodes are adjacent,
Drop "not"! ~Typo.
Ryuhei Uehara
16May08
10
170
Figure 10.1 caption
crane crease pattern crane mountain-valley pattern More precise description
Ryuhei Uehara
28Nov07
13
219
Figure 13.5
Rightmost figure, top, above upward arrow label false missing Typo
Ryuhei Uehara
30Nov07
13
222
Line+8
Each of these three ... per input produce Each of these three ... per input produces Typo
Ryuhei Uehara
30Nov07
17
258
Figure 17.8 (turtle) [Two vertical creases] One M crease should be a V; one V crease missing. Corrected turtle.color.pdf here. Typos
JOR
23Jan08
21
299
Section 21.1, paragraph 2, sentence 1
unfoldings, are now called “nets”
unfoldings, what are now called “nets”
Grammatical error caused by typesetter
Edwin Chen
17Oct07
21
304
Section 21.2, last paragraph
notation of curvature
notion of curvature
Typo
Edwin Chen
17Oct07
24
375
Section 21.4.0.1 numbering
24.4.0.1
24.4.1
Typo
ED
1Dec07
Biblio
452
15th entry
Graver, Servatius, Servatius, Combinatorial Rigidity
Move to become 6th entry on the page
Bibliographical item out of sorted order.
Joe Malkevitch
1Oct07
Index
468
Open Problem, 9.1
9.1: Locked Length Ratio, 154
9.2: Locked Fixed-Angle Chains, 154
9.2: Locked Length Ratio, 154
9.3: Locked Fixed-Angle Chains, 154
Two open problems are accidentally labeled 9.1
ED
10Sep07