Real-Time Rendering Corrigenda for 2nd print: minors

Very minor errors (mostly for the authors and the publisher)

• On page 24, in the table, the orthographic projection matrix is affine. (thanks to Steve Worley)
• Page 45, section 3.3.2, last paragraph, first sentence on that page ends "...represents the same rotation." Should be "...represent the same rotation." (thanks to Mike Day)
• Page 71, first full paragraph, 3rd line: change "amply" to "amplify".
• Page 75, after equation 4.10, add "Also, as with the diffuse contribution, if $\mb n\cdot\mb l$ is less than zero (i.e.~the light is below the surface), then the specular term is zero."
• Page 88, third from last line says "... the premultiplied RGB component (0.48, 0.42, 0.06), would be what is displayed..." - remove the comma after the right parenthesis, i.e. ")," to ")". equation can be broken..." (thanks to Ulf Assarsson).
• Page 115, Equation (5.1), delete the parenthesis in the numerator. (thanks to Adrian Lopez).
• Page 128, equation 5.4, should be negated, that is, r=v-2(n.v)n (thanks for Alex Linde and Jay Fong)
• Page 147 and 148, once on each page, there references to color plates followed by the text: "(following p. 194)". This should be written as ""(following p.~194)" in LaTeX to get correct spacing.
• Page 149, in the paragraph that starts "The Lumigraph and light-field rendering...", at the end of the fourth sentence it says "...for even small image sets), than those solved by QuickTime VR." It should rather be "...for even small image sets) than that solved by QuickTime VR." (note: remove the comma, too).
• Page 162, Equation 6.4, the last parenthese ")" should be removed. (thanks to Jim Nilsson)
• Page 177, second paragraph, sentence "Third, Z-buffering and writing to the color buffer are turned off,..." should instead be "Third, Z-buffer updates and writing to the color buffer are turned off (Z-buffer compares are still done),..." (thanks to Jim Napier)
• Page 177, second paragraph, sentence "Incrementing and decrementing are done only when the pixels of the rendered shadow-volume face are visible." should be "Incrementing and decrementing are done only when the pixels of the rendered shadow-volume face are visible (i.e. not hidden by any real geometry)." (thanks to Jim Napier)
• Page 178, third paragraph, last sentence which starts "In the final pass..." should rather be "In the final pass of the algorithm, the stencil buffer should be compared to $2^{n-1}$ (which is 128 when $n=8$) instead of 0. (thanks to Jacob Ström).
• On page 180, second paragraph, which starts "This technique can be..." In this paragraph we use both $\alpha_p$ and $\alpha$. This is wrong, $\alpha$ should instead also be $\alpha_p$. (thanks to Jacob Ström).
• Color Plate XVIII, should be "Chris Georges" rather than "Chris George".
• Page 211, in "The HOM algorithm", third paragraph, last sentence, says "If the object occluded by the....". This should be "If the object is occluded by the....". (thanks to Jacob Ström).
• Page 213, in the Example, it says "O=1-2^2/8^8=0.9375", when it should be "O=1-2^2/8^2=0.9375". (thanks to Hitoshi Ueda)
• Page 239, caption for figure 7.32: this example gets incorrect orientation of the triangles after the doubled vertex. To get it right, send vertex 9 three times (though this is not efficient). (A swap is equal to one extra vertex!). Need a better example. (thanks to Pai-Hung Chen).
• Page 262, in the caption of Figure 8.6, the next to last sentence says "...if APP has more much more work than the others." It should be "...if APP has much more work than the others.". (thanks to Jacob Ström).
• Figure 10.3, caption, change last sentence to: "The half-lentghs, h^B_u, h^B_v, and h^B_w, are the distances from the center of the box to the center of the corresponding face of the box. (thanks to Adrian Lopez)
• Page 294, increment (add 1) the index on each slab as the first slab is indexed 1 (not 0) in the definition on page 293. (thanks to Jim Nilsson)
• Page 297, section 10.3.2, second sentence says "..., and if the test fails,...". This should be "..., and if the test succeeds,..." (thanks to Jacob Ström).
• Page 301, the first two sentences (both start with "Recall...") should be replaced with "Recall that $\mb a^c$ is the center of the box, and $\mb a^u$, $\mb a^v$, and $\mb a^w$ are the normalized side directions of the box; $h_u$, $h_v$, and $h_w$ are the positive half-lentghs (from the center to a box face)."
• Page 301, sentence after pseudocode: replace "parallel to" with "perpendicular to". (thanks to Adrian Lopez).
• Page 304, Figure 10.9, in the leftmost part of the illustration, the right most "v_0" should be "v_1". (thanks to Ben Watson)
• Page 306, section 10.6, at the end of the first paragraph, the plane equation should be "=0", i.e., add "=0" after "+d_p". (thanks to Jim Nilsson)
• Page 308, last paragraph, second sentence should read "These problems are solved..." rather than "This problem is solved..."
• Page 319, second paragraph in section 10.9, the first two sentences (which start "Several intersection methods..." and "Finally, Green and Hatch...") should be replaced by: "In 1992, Voorhies \cite{Voorhies92} presented one algoritm to solve this problem. Later, Green and Hatch \cite{Green95} expanded on the gem by Voorhies, which handled only triangles."
• Page 325, in the pseudocode for "kDOP_intersect()" the parameter list is incorrect: there should be "min" and "max" for each slab (not "max":s twice). (thanks to Hector Yee)
• Page 337, figure 10.28 would be nice to have it closer to the text about frustum/box intersection testing (not sure how easy that is to do in LaTeX though). (thanks to Tommy Fortes)
• Page 338, second sentence has an opening parthesis: "t=e/f (by replacing...", but not an ending. Add ending parenthesis add end of sentence. (thanks to Tommy Fortes)
• Page 339, at the end of the first sentence, should be "0<=s<=l_1", that is, "l_1" instead of "1". (thanks to Adrian Lopez)
• Page 348, second paragraph, first sentence starts "Also, note that when two..." In this sentence, change to "line 9", and to "the children of A". (thanks to Adrian Lopez)
• Page 361, last sentence, reference [212], there is a space in his last name that should not be there (between the e and the c).
• Page 371, figure 12.4, the third buffer for triple buffering should be called "buffer 2", not "buffer 3". (thanks to Adrian Lopez)
• Page 386, in "Further Reading and Resources", first sentence starts "Blinn offer...", should be "Blinn offers..." (thanks to Jacob Ström).
• Page 398, section A.2, just after Equation A.12, replace "u_1=(-8,-6)" by "u_1=(8,6)" (thanks to Aaryn Flynn)
• In the caption of plate I, following page 194, change third sentence to: "The water reflection is created by mirroring polygons through the water's surface and blending them with the textured water polygon." (thanks to Mike Day)
• Page 434, reference [85], should be "Differential Geometry *of* Curves and Surfaces", not "for".
• Page 441, reference [162] should get updated "Computer Graphics, C Version" for the title, and the date is 1996.
• Page 447, reference [231], "Obfuscated C and Other Mysteries", the title of the book should be italicized instead of quoted.
• Page 448, reference [248], "The Programmer's Guide to Compressed Image Files", the title of the book should be "Compressed Image File Formats: JPEG, PNG, GIF, XBM, BMP" (it changed between the draft and the release), and should be italicized instead of quoted.
• Page 450, reference [258], says "Chalmers University of October 1998.", should be "Chalmers University of Technology, October 1998".
• Page 450, reference [264], "Advanced Compiler Design and Implementation", the title of the book should be italicized instead of quoted.
• Page 453, reference [293], "Digital Signal Processing--Principles, Algorithms, and Applications", change the "--" to a ":". Also change the year to 1995.
• Page 453, reference [300], "Procedural Elements for Computer Graphics", the date should be 1998.
• Page, 459, reference [357], change "--" to ":", i.e., "The RenderMan Companion: A Programmer's Guide to Realistic Computer"
• Page, 462. reference [394} should say "Elliptical" not "Eliptical".