Errata -- First Revised Edition)
(Second printing, March 2009)
You have a First Revised Edition of the book if the Morgan-Kauffmann logo is at the lower right corner of the cover. If not, check the Errata for the First Edition.
In the second printing of the First Edition, we have fixed all major first edition errata, and almost all of the minor errata. However, there were some non-erroneous additions that would have involved too much additional text and have led to impermissible page roll-overs. Here they are, together with any errata that may have been found after publication.
Not all browsers support all standard html symbols (older versions of Internet Explorer, for example). If you think that this symbol "⌋" looks like a square, you may want to view the bitmap symbol version.Those errata in bold correspond to Major Corrections; those marked with '*' correspond to Minor Corrections, and those that are unmarked correspond to Typos.
- Pg 160, a simpler example is grade 2 of the product of the blades e1 ∧ e3 and (e1-e2) ∧ (e3-e4) . [20100201 AS]
- *Pg 225, bottom derivation:
AC reports a more compact derivation:
limε→0 ((x+εa)-1-x-1)/ε = limε→0 -x-1 ((x+εa)-x)/ε) (x+εa)-1 = -x-1 a x-1. [20071127 AC] - *Pg 286, section 11.5.3: This would be a good place to be more precise about the definition of weight. Write the direction A of a finite k-flat X in terms of a chosen pseudoscalar Ik for its subspace as A = ω Ik , then ω is the weight of the blade. For an infinite (k+1)-blade X, choose a pseudoscalar Ik+1 and write X = ω Ik+1, then ω is the weight of the blade. In both cases, the sign of the weight is determined by the chosen orientation of the pseudoscalar, but its magnitude is geometrically objective. It is simple to prove from the definition that a weight is translation invariant. Note also that unit weight and unit norm are different concepts; for the point representation e0+p has weight 1, but norm √(e02+p2) [20080326 AC]
- *Pg 296, figure 11.7: Because of the counter-intuitive signs resulting in (a) and (c), AC has the sensible suggestion to redefine the relative orientation of A to B as B ∩ A (so that the orientator is written first, the orientatee last). [20080326 AC]
- *Pg 407-409:
We should have defined more clearly what we mean by weight and orientation as the split of the geometrical concept direction into a scalar and a unit blade element. In the caption of Table 14.2, weight is defined in a manner that makes it always positive -- but this then presumes that the orientation will pick up the sign. AC clarifies the issue raised in the second paragraph of page 409:
-
Let D = Ek ∞
be the direction of a conformal blade X.
If a unit orientation Ik has been given for the k-D vectorspace of Ek, and Ek = α Ik, then α is the weight of Ek, and the orientation of X is sign(α) Ik.
If k=0, the standard orientation is 1, and if k=n, the standard orientation is In. These are invariant under rigid body motions; for the other k-values the orientations are still invariant under translations.