The Essentials of CAGD

by Gerald Farin & Dianne Hansford

published by AK Peters, Ltd. 2000
248 pages, ISBN: 1-56881-123-3

Errata

Please email suggestions or corrections to farin@asu.edu. If you find an error, we'll give you credit by including your name/link in this Errata page!

The errata entries are ordered by page number and the date that each correction was added is given in brackets as [mo/day/yr].

Revised June 2002

  • p. 7, after eq. (1.3): the vector v is an element of the linear space R^3, not of the affine space E^3.   [10/28/01]
    B. Ehrlich


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  • p. 8, eq. (1.4): the determinant needs to be multiplied by a factor 1/2. This applies to the following equation too.   [9/10/01]
     O. Mahmood


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  • p. 10, eq. (1.9): the volume needs to be multiplied by a factor 1/6. Thus value 12 in subsequent Example really is 2.   [4/14/02]
     K. Baker


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  • p. 11, Exercise 6: the answer is 9/2, not 9.   [9/10/01]
    Found by O. Mahmood


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  • p. 21, example 2.6: the point p_6 is listed twice in the point list, once would do. Triangle 0 has only two neighbors, not three as stated in the text.   [9/10/01]
    Found by O. Mahmood


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  • p. 40, sketch 28: the factor of a2 needs to be 1/3, that of a3 needs to be 1.   [4/24/02]
    Found by Tae Seong Kim


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  • p. 46, Example 4.1: the second derivative has a factor n(n-1), which in this case is 6, not 3. Thus the factor 3, which appears, has to be replaced by a 6. The final result is correct, however.   [10/1/01]
    Found by B. Ehrlich


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  • p. 59, Sketch 33. The caption should say "cubic curve" instead of "cubic Bezier curve".   [2/13/01]
    Found by V. Zafiris


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  • p. 67, Figure 5.3. A uniform parametrization was used to generate this figure.   [4/14/02]
    Found by James Greene, Arizona State University


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  • p. 68, 3rd line from top. Replace "1+1" by "l+1". (meaning letter "l" plus number "1")   [4/4/01]
    Found by V. Zafiris


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  • p. 68, eq. 5.18:. Replace "t_P" by "t_l".   [4/4/01]
    Found by V. Zafiris


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  • p. 70, Problem 6:. The wing data may be found on the data page.   [4/14/02]
    Found by Ron Hoppe, University of Houston-Downtown


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  • p. 79, sketch 47: the caption should say: a v-partial.   [4/02]
    Found by Chris Cera


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  • p. 83, Sketch 50: One intermediate Bezier point is drawn incorrectly. There are three u-direction curve evaluations in the sketch. The "back-most" evaluation is where the error occurs. One control point from the first step of the de Casteljau algorithm has been drawn on the wrong control net segment -- it belongs just below where it is drawn.   [3/20/01]
    Found by V. Zafiris, ZafirisV@zeus.dt.uh.edu


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  • p. 85, second set of de Casteljau algorithms: the input point [0 3 3] is missing.   [3/22/01]
    Found by V. Zafiris


  • p. 88, Example 6.11, first sentence: the reference should be to Example 6.4.   [3/22/01]
    Found by V. Zafiris


  • p. 93, Exercise 3: it should say "elevate in the u-direction".   [10/5/01]
    Found by B. Ehrlich



  • p. 101, Example 7.2, the reference should be to Example 6.4.   [4/4/01]
    Found by V. Zafiris


  • p. 104, Example 7.3: The Hermite matrix entries need to be changed as follows. x_v(0,1) = [0,3,-3]^T, x_u(1,0) = [3,0,-3]^T, x_u(1,1)=[3,0,-3], x_v(1,1) = [0,3,-3]^T, x(0,1)=[0,3,0]^T, x(1,0)=[3,0,0]^T, x(1,1)=[3,3,0]^T. In the Bezier patch matrix, the entry for b_(3,3) should be [3,3,0]^T. [10/15/01]
    Found by B. Ehrlich


  • p. 108, "big" matrix: The subscript "K" should be replaced by "K-1" (five occurences); [4/4/01]
    Found by V. Zafiris


  • p. 110, bottom: Figure 7.5 actually illustrates the bicubic case, not the bilinear case from the example. [1/5/01]
    Found by B. Ehrlich


  • p. 111, Figure 7.5. The caption should refer to Figure 7.4, not to Example 7.6. [1/5/01]
    Found by B. Ehrlich


  • p. 118, sketch 73. The radius of the shown circle is 2/3, but it should be 3/2. This means the center has to move to the right. Therefore, c(0) = [3/2, 0]^T. [11/17/01]
    Found by B. Ehrlich


  • p. 125, Sketch 80: "theta" should be "alpha". The unlabeled point and vector on the line L correspond to x and v, respectively. [4/9/01]
    Found by V. Zafiris


  • p. 126, top. Reflection lines may be defined differently; view a postscript version or pdf version.


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  • p. 130, middle of page, chain rule equation: {\bf s}_i should be {\rm d}{\bf s}_i. [4/9/01]
    Found by V. Zafiris



  • p. 130, sketch 81: it should say "Four cubic Bezier curves." [4/02]
    Found by Chris Cera


  • p. 150, eqn (10.6): The superscript for d should be n-r. [11/28/06]
    Found by S Mahbub Murshed

  • p. 151, eqn (10.8): the subscript k-3 should read k-n.   [11/1/00]
    Found by B. Seshadri


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  • p. 151, Property 5: K=2n-1 should read K=2n.   [11/5/00]
    Found by B. Ehrlich


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  • p. 154, Figure 10.7: The knot u_4=6 is not drawn.   [11/1/01]


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  • p. 155, Figure 10.8: The B-spline N^3_4 should be N^3_2.   [11/13/01]
     Found by R. Holmes


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  • p. 157, Example 10.8: After inserting u=1.5, the Greville abscissae become 0,1/3,5/6,3/2,13/6,8/3,3.   [6/24/02]

  • p. 157 (Last sentence of page): Insert each domain knot until it has full multiplicity in order to construct the Bezier points.   [6/24/02]
     Found by Chun Lee


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  • p. 158, Figure 10.10: The junction Bezier points (solid circles) are difficult to see in the figure.   [6/24/02]
     Found by Chun Lee


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  • p. 160: Twice in the first paragraph, instead of n+1 knot intervals, it should read 2n-2 knot intervals. Therefore, the knot sequence takes the form \delta_0, ..., \delta_{2n-3},...,\delta_{K-2n},\delta_0, ...\delta_{2n-3}. The list of de Boor points that must overlap is incorrect also. It should read \dd_0 = \dd_{D-n}, \dd_1 = \dd_{D-(n-1)}, ..., \dd_{n-1} = \dd_{D-1}. The footnote at the bottom of the page is a bit misleading: \dd_3 is not contrained by the periodic conditions.   [10/5/01]


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  • p. 161, eq. (10.11): the term N^{n-1}_1 should be N^{n-1}_{i-1}.   [11/28/00]
    Found by B. Ehrlich


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  • p. 161, eq. (10.13): the term N^{n-1}_1 should be N^{n-2}_{i-1}. All superscripts in this equation should be n-2.  [11/28/00]
    Found by B. Ehrlich


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  • p. 174, Ex. 11.4: the matrix should be:
    1 0 0 0 0
    3/2 7/2 1 0 0
    0 1 4 1 0
    0 0 1 7/2 3/2
    0 0 0 0 1
    . [12/05/01 and 6/20/03]
    Found by B. Ehrlich and T. Meyer


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  • p. 188, displayed equations: should all have a superscript "1". [4/9/01]
    Found by V. Zafiris

  • p. 190, Sketch 101: A dotted line is missing. Please see this updated sketch. [11/3/04]

  • p. 193, Problem 2: [3,0,0] should read [4,0,0].   [12/05/01]
    Found by B. Ehrlich


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  • p. 197, Example 13.2: The new weights in standard form are 1, 2/sqrt(2), 1.   [01/19/01]
    Found by M. Bara


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  • p. 198, Figure 13.2: "0.1 to 0.9" should say "0.1 to 10"   [11/14/01]
    Found by B. Ehrlich


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  • p. 211, Exercise 3.3: the x-coordinate of the point on the curve is -22/32. The derivative vector is missing a factor of 3.   [10/5/01]
    Found by B. Ehrlich


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  • p. 215, Exercise 6.8: the control point b_11 has a missing y-coordinate. It should be 1/2. The control point b_21 has a y-coordinate of 0, but this should be a 1.   [10/5/01]
    Found by B. Ehrlich


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  • p. 218, Exercise 12.3: the third row should have z-coordinates 0, 4/3, 8/3, 4.   [12/5/01]
    Found by B. Ehrlich