ERRATA for Digital Geometry,
first printing

Ordered by date of discovery. Also available in order of appearance in the text.
Last updated 28 November 13. Do not forget to reload this page to get the most current version.
Send additional errors and comments to: Reinhard Klette

Page 24, line 8 from bottom.
Change || R^+ into \R^+ (i.e., set of positive real numbers).
Reported 08 August 04.
First detected occurrence of the systematic error that all references with numbers 640 to 737 need to be increased by 1:
Page 33, line 8.
Change 702 to 703.
Reported 10 August 04.
Page 226, line 4.
Delete hbox.
Reported 12 August 04.
Page 459, line 14.
Delete !.
Reported 12 August 04.
Page 75, line 10 from bottom.
Change of the Association into of the Southpacific Chapter of the Association.
Reported 12 August 04 by Dr. Radu Nicolescu (Auckland).
Page 232, line 10.
delete tesub.
Reported 18 August 04.
Page 235, line 5.
delete tesub.
Reported 18 August 04.
Systematic error: all references in the book with numbers 640 to 737 need to be increased by 1. The first occurrence in the book:
Page 1, line 4 from bottom.
Change 640 to 641.
Reported 06 October 04.
Page 507, first line in algorithm b).
Change (a) alternates into (a) [which keeps the test of condition (2)] alternates.
Page 507, fourth line in algorithm b).
Change 0. An into 0, provided that the following is not true: (x,y+1)=(x+1,y+1)=(x+1,y)=1 and (x-1,y)=(x,y-1)=(x+2,y+1)=(x+1,y+2)=0. An
Reported 23 October 04 by Prof. T. Yung Kong (New York City).
Page 508, Proposition 16.3.
Change remains A_j-simple into remains simple both in b8) and in b4).
Also note that condition c) is only required for sets of mutually adjacent 1s that are 8-components; if c) is true then condition b4) is vacuous.
Reported 23 October 04 by Prof. T. Yung Kong (New York City).
Page 531, Proposition 16.11.
Change remains A_j-simple into remains simple in b).
Also note that condition c) is only required for 26-components of 1s; if c) is true then condition b) is vacuous.
Reported 23 October 04 by Prof. T. Yung Kong (New York City).
Page 652
line 16: change open set, 188 into open set, 166
Reported 16 November 04 by Prof. Vladimir Kovalevsky (Berlin).
Page 569
line 1: change 120 into 121,
line 2: change 136 into 137,
line 3: change 217 into 222,
line 4: change 192 into 197,
line 5: change 193 into 198,
line 6: change 214 into 220,
line 7: change 450-452 into 457-459,
line 8: change 419-420 into 427-428,
line 9: change 158-160 into 161-163,
line 10: change 12-13 into 12 and M1-M5 into M1-M3,
line 14: change 188 into 193,
line 15: change 18 into 17-18.
Reported 16 November 04 by Prof. Akira Nakamura (Hiroshima).
Page xvi, lines 3 and 4 from bottom.
Delete both lines (subsections are not listed in Contents).
Reported 17 November 04.
Page 61, line 1 from bottom.
Change 4 into 2.
Reported 17 November 04.
Page 588, line 15.
Change Theorems on Abstract Graphs into theorems on abstract graphs.
Reported 17 November 04.
Page 625, line 2 from bottom.
Change C. Ronse, H.J.A.M. into C. Ronse and H.J.A.M..
Reported 17 November 04.
Page 312, Theorem 9.3.
Change are periodic into are eventually periodic.
Reported 4 December 04.
Page 314, line 8 from bottom.
Change N^2 into \N^2 (i.e., set of all natural numbers).
Reported 4 December 04.
Page 347, line 11 from bottom.
Change r^{-1.5} into h^{-1.5}.
Reported 4 December 04.
Page 361, Table 10.1.
Swap References with 3D extensions (for example, [203] reports on a 3D extension for 8ss).
Reported 4 December 04.
Page 63, line 1 in Algorithm 2.3.
Change y=y_q into y=y_p.
Reported 11 January 05.
Page 650, line 13 from bottom.
Change labelling, 53 into labeling, 51.
Reported 11 January 05.
Page 433, line 7 from bottom.
the following is true should be in normal font, not Italics.
Reported 15 January 05.
Page 12, line 7 from bottom.
Change \epsilon into \varepsilon (identical symbol as used twice in the following line).
Reported 3 February 05.
Page 26, Definition 1.4.
Change [1001] into [1000].
Reported 3 February 05.
Page 110, Figure 3.13.
The squareroot symbol did not print out properly. It should be b/\sqrt{2} and b/\sqrt{2}-1.
Reported 10 February 05.
Page 112, lines 8 and 9.
Delete the sentence On the other hand,... medial axis.
Reported 10 February 05.
Page 131, line 20 from bottom.
Change Section 4.2.2 into end of Section 4.1.4.
Reported 11 February 05.
Page 279, line 14 (second line of formula).
Change k=1 into k=2.
Reported 11 February 05.
Page 146, line 6 from bottom.
Change \alpha_1 into \alpha_2.
Reported 16 February 05.
Page 161, Figure 5.2.
The node on the right has label 2.
Reported 16 February 05.
Page 186, line 18 from bottom.
Change \G that into \F that (i.e., the 4-path is in the frontier grid).
Reported 16 February 05.
Page 187, Figure 5.26.
The label (x,y) in step ``down'' should be at the lower (terminal) node.
Reported 16 February 05.
Page 335, line 9.
Change p_N:=q_P:=p, q_N:=p_P:=q into p_N:=p_P:=p, q_N:=q_P:=q
Reported 16 February 05.
Page 81, header of 3.1.4.
Change Valued into valued
Reported 26 February 05.
Page 566, line 18 from bottom.
Change m \le n into 0 \le m \le n
Reported 26 February 05.
Page 175, Equation (5.3).
Change a_{ij} into a_{ij}=
Reported 14 March 05.
Page 225, top row in Figure 6.27.
Change b into \beta (six times)
Reported 14 March 05.
Page 225, line 4.
Change 0s into 0
Reported 14 March 05.
Page 397, line 13.
Delete array!
Reported 24 March 05.
Page 399, lines 8 and 9.
Change twice M_ into R_ (remainder maps are denoted by $R$; see bottom of page 395)
Reported 24 March 05.
Page 400, caption of Figure 11.17.
Change M_ into R_ (remainder maps are denoted by $R$; see bottom of page 395)
Reported 24 March 05.
Page 280, line 2.
Change 64 into 64 - 2, and 54 into 54 - 4
Reported 11 April 05.
Page 362, line 11 from bottom.
Change > c_{i,k_j} into > c_{j,k_j}
Reported 15 April 05.
Page 362, line 4 from bottom.
This formula fits better into its context when replacing first k by k_0, and then l by k
Reported 15 April 05.
Page 364, line 3 from bottom.
two fraction strokes are missing, between the two variables in the arguments of the tan^{-1} and cot^{-1} functions
Reported 15 April 05.
Page 366, line 13 from bottom.
Change l + 1 into l_i + 1 and delete radius of in the next line
Reported 15 April 05.
Page 378, line 17.
Change integer \nu such into integer \mu such
Reported 15 April 05.
Page 313, line 3.
Change l_{\alpha,\beta} into \gamma_{\alpha,\beta}.
Reported 2 May 05 by A/Prof. John Morris (Auckland).
Page 330, line 9.
Change T_{2,1}(k,d) AND T_{2,2}(k,d) into [ T_{2,1}(k,d) OR T_{2,2}(k,d) ]
Reported 11 May 05 by Goran Nikodijevic (Auckland).
Page 330, line 17.
Change s(k+1)=-1 IMPLIES r(k) <= n(k+1) into s(k+1)=-1 AND n(k+1)!= -1 IMPLIES r(k) <= n(k+1)
Reported 12 May 05.
Page 350, bottom line in box of Algorithm 10.1.
Change 6. Go to Step 3. into 6. i:=i+1, go to Step 3.
Reported 26 May 05.
Page 589, references [291] and [292]
Change magic-software into geometrictools
Reported 8 July 05.
Page 366, line 17 from bottom.
Change [208] into [207]
Reported 15 July 05.
Page 391, line 13.
Change I_{m+1,0}-I_{m+1,0} into I_{m+1,0}-I_{m,0}
Reported 15 July 05.
Page 583, reference [194]
Change \^{A}...CG into \"{O}CG
Reported 17 August 05.
Page 39, line 3.
Change R. In this notation into R; with {x,y} \in R short for (x,y) \in R and (y,x) \in R. In this notation
Reported 12 December 05
Page 2, Definition 1.2.
Change (cuboid) in into (cuboid) \G in
Reported 28 February 06 by Prof. Akira Nakamura (Hiroshima)
Page 17, line 16 from bottom.
Change (x_1,y_1), (x_2,y_2) into (x_1,x_2), (y_1,y_2)
Reported 28 February 06 by Prof. Akira Nakamura (Hiroshima).
Page 18, line 16 from bottom.
Change a \ne 0, and b \ne 0 into a \ne 0 or b \ne 0
Reported 28 February 06 by Prof. Akira Nakamura (Hiroshima).
Page 18, line 16 from bottom.
Change ap+bq=0 into ap+bq=o (note: o as in V8)
Reported 28 February 06 by Prof. Akira Nakamura (Hiroshima).
Page 20, line 1.
Change pixels of voxels into pixels or voxels
Reported 28 February 06 by Prof. Akira Nakamura (Hiroshima).
Page 27, line 4 from bottom.
Change \mu'_\lambda into \mu_{\lambda'}
Reported 28 February 06 by Prof. Akira Nakamura (Hiroshima).
Page 27, line 3 from bottom.
Change picture p into picture P
Reported 28 February 06 by Prof. Akira Nakamura (Hiroshima).
Page 28, line 6 from bottom.
Change 21 / \pi d into 2l / \pi d (note: small L, not 1)
Reported 28 February 06 by Prof. Akira Nakamura (Hiroshima).
Page 45, Definition 2.5.
complete should be in Italics, and iff in normal font
Reported 28 February 06 by Prof. Akira Nakamura (Hiroshima).
Page 51, Figure 2.21.
One hollow dot (at bottom left) should be filled.
Reported 28 February 06 by Prof. Akira Nakamura (Hiroshima).
Page 68, line 9 from bottom.
Change disk of unit into disk D of unit
Reported 28 February 06 by Prof. Akira Nakamura (Hiroshima).
Page 72, lines 1 and 10.
Change 2.21 into 2.20 (twice)
Reported 28 February 06 by Prof. Akira Nakamura (Hiroshima).
Page 72, lines 8 from bottom.
Change (x^2 - into (x - (twice)
Reported 28 February 06 by Prof. Akira Nakamura (Hiroshima).
Page 81, lines 9.
it should be [a], the nearest
Reported 28 February 06 by Prof. Akira Nakamura (Hiroshima).
Page 224, line 4 from bottom.
Delete hbox
Reported 14 March 06.
Page 225, top row in Figure 6.27.
Change indixes 2,2,2 of three betas on the left into indices 0,1,2
Reported 14 March 06.
Page 225, Figure 6.27.
Values for solid torus should be 1,1,0,0 (and not 1,2,0,-1)
Values for solid sphere with two handles should be 1,2,0,-1 (and not 1,4,0,-3).
Reported 14 March 06 by Fajie Li (Auckland).
Page 225, line 1.
Change \beta_1/2 into \beta_1
Reported 14 March 06 by Fajie Li (Auckland).
Page 225, lines 6-8.
Delete Note that we do not .... is the number of tunnels.
Reported 14 March 06.
Page 225, lines 10-11.
Delete (i.e., faces are not ... one-dimensional)
Reported 14 March 06.
Page 234, lines 5 and 6.
Change in line 5 at most m. For into at most m, and for
delete in line 6 it follows that,
Reported 04 April 06 by Gisela Klette (Auckland).
Page 585, line 5.
Change Das and P.P. Chakrabarti into Das, P.P. Chakrabarti, and B.M. Chatterji
Reported 12 July 07.
Page 194, line 17 from bottom.
Change A \in Z into A \in G
Reported 14 January 08 by Prof. Akira Nakamura (Hiroshima).
Page 198, third line above Theorem 6.2.
Change p \in q into p \neq q
Reported 14 January 08 by Prof. Akira Nakamura (Hiroshima).
Page 168, change caption of Figure 5.9 into the following:
Two regions (bold, unfilled circles). Left: border (bold, shaded circles) of a closed region. Right: boundary (bold, shaded circles) of an open region.
Reported 28 April 08 by Prof. James R. Thomas (Ohio).
Page 170, caption of Figure 5.12.
Change Boundary into Border
Reported 28 April 08.
Page 417, line 3.
Change Exercise 2 into Exercise 5
Reported 30 April 08.
Page 164, line 2 from bottom.
Change principal nodes of M into principal nodes of C
Reported 30 April 08 by Prof. James R. Thomas (Ohio).
Page 162, line 5 from bottom.
Change (ii) If into (ii) For a marginal c, if
Reported 3 May 08 by Prof. James R. Thomas (Ohio).
Page 166, lines 11 and 10 from bottom.
Change Any closed or open M is complete. into Any closed M is complete; if M is closed then $M^\nabla$ is complete.
Reported 7 May 08 by Prof. James R. Thomas (Ohio).
Page 321, line 4 from top.
Change (a+b)/(c+d) into (a+c)/(b+d).
Reported 10 July 12 by Dr. Partha Bhowmick (Kharagpur).
Page 431, line 8 from bottom.
Change D(p^\star,q_t,p)=R into D(q_t^\star,q_t,p)=R
Reported 28 November 13 by Olivier Lauffenburger (Ramonville St Agne).