Real-Time Rendering Corrigenda for 1st print: minors

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

• Page 3, last sentence before section 1.2: it looks as that sentence belongs to chapter 13, so there should be no indentation there (thanks to Tommy Fortes).
• On page 24, in the table, the orthographic projection matrix is affine. (thanks to Steve Worley)
• Page 25, figure 3.1: the font used in that figure is wrong (not the one we used on the other images). Also change to T(5,2,0) both in the illustration and in the caption (for readability).
• Page 30, last sentence: the formula (X=H_xy...) is on two pages. It would be easier to read if the entire formula was on one page. (thanks to Tommy Fortes).
• Page 31, figure 3.4, the last transformation says "H_yx(c)". This should be "H_xy(c)". (thanks to Jonas Jalminger)
• 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 69, Figure 4.3, there should be a whitespace between the first and the second image.
• Page 71, first full paragraph, 3rd line: change "amply" to "amplify".
• Page 74, caption of figure 4.7, fith row says "...for the another...". It should rather be "...for another..." (thanks to Jacob Ström)
• 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 76, figure 4.9, it says "-p/2", "-p/4", etc, it should be "pi" (i.e., the greek letter), not p. (thanks to Jim Nilsson)
• Page 88, fourth paragraph, next to last sentence says "...save the RGB values at the pixels as well as the alpha value." should end with "... alpha values."
• Page 88, addenda, added at the end of the Example: "If the teapot were viewed against a black background, the premultiplied RGB component, (0.48,0.42,0.06), would be what is displayed, as it would be the surface's computed shade multiplied by the amount of pixel coverage."
• Page 100, section 5.1, paragraph 2, last sentence says: "Once we have presented the entire process we will examine, the various..." Remove the comma.
• Page 106, section 5.2, second paragraph, last sentence should be removed. According to the OpenGL Reference Manual there is no lower limit. (thanks to Tommy Fortes).
• 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 132, second sentence says "...and r going to the right" change to "and h going horizontally to the right" (could leave off "horizontally"). Also, replace "r" with "h" in equation 5.5. (thanks to Jacob Ström)
• Page 135, last words on that page "specular color" are truncated.
• Page 145, second paragraph, last sentence says "...elaborate lighting equation can broken...", it should be "...elaborate lighting equation can be broken..." (thanks to Ulf Assarsson).
• 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 153, the paragraph before "World-Aligned Billboard", third sentence says "Each would then be rotated to the correct straight-on orientation for the current view, then translated to their final three-dimensional positions."
  It should say "Each would then be rotated to the correct straight-on orientation for the current view, then translated to its final three-dimensional position."
• 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).
• Page 191, last sentence before section 7.1 starts: "triangle fan, strip, and polygon mesh techniques" should be italic since the algorithms of the previous sentence are.
• Color Plate XVIII, should be "Chris Georges" rather than "Chris George".
• Page 197, the footnote does not end with a period.
• Page 200, section 7.1.3, fourth sentence ends "for an area of space." This is somehow a contradiction, so it might be better to end it like : "for a set of viewpoints."
• Page 200, section 7.1.3, third paragraph, last sentence says "..., however, and shadows volumes...", it should be "..., however, and shadow volumes..." (thanks to Jonas Jalminger)
• Page 202, last paragraph, first sentence says: "See Plate VIII..." It should be "See Plate XVIII..." (thanks to Tommy Fortes)
• Page 206, caption of figure 7.9, add at the end "(after Zhang \cite{Zhang98})". (thanks to Hansong Zhang)
• 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 218, paragraph 3, first sentence should say "approximately" instead of "approximatley". (thanks to Fredrik Warg)
• 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 240, second bullet, it says "STRIPE gets it better...", it should be "STRIPE gets its better..." (i.e., "its" not "it").
• Page 245, last bullet, add at the end "However, this makes the code bigger and thus may degrade cache performance. Also, branch prediction usually works very well on loops." (thanks to Haim Barad)
• Page 246, first bullet, add at the end "However, a mispredicted branch may be very expensive on some architectures." (thanks to Haim Barad)
• Page 246, the bullet before "Memory Issues" says "C is usually faster than C++". Change to: "Virtual methods, dynamic casting and sending structs by value has some efficiency penalties." (thanks to Tommy Fortes)
• Page 253, third bullet, the sentence that starts "For k-ary trees, where..." should rather be "For k-ary trees (scene graphs), where..."
• 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).
• Page 265, in "Further Reading...", it should say "Kempf and Hartman's manual [202]", not "book". Also in the references [202] should be written as a book, i.e., the title should be italic. Also add URL if we can find it.
• Page 272, fourth line down starts, "Any of these...". This sentence is misplaced, and should be after the first paragraph on page 273 ends, i.e., it should say "... connect the two most different in height. Any of these...".
• Page 278, first sentence "..., with each edge pointing back to the face (polygon)..." should rather be "..., with each edge referring back to the face (polygon)..."
• Page 293, the definition of the OBB. Remove "positively oriented" and its associated footnote.
• 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, 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 311, in the pseudocode, on line 8 and 9: the two "else"'s should be removed. (thanks to Peter Rundberg)
• Page 315, Figure 10.16, the rightmost "k_0" in the illustration should be a "k_1". (thanks to Jonas Jalminger)
• Page 315, in the paragraph after Equation (10.21), it says "triangle v_1 b k_1". It should say "triangle u_1 b k_1". (thanks to Jonas Jalminger)
• 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 324, title of section 10.10.3: the k in k-DOP should be larger. Same error on section title 11.4.
• 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 344, row 3, says "...use these distance...". This should be "...use these distances..." (thanks to Jonas Jalminger)
• 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 368, title of section 12.1.3: the z and the w in should be capital letters.
• Page 371, figure 12.4, the third buffer for triple buffering should be called "buffer 2", not "buffer 3". (thanks to Adrian Lopez)
• Page 380, at the end of the first sentence in section 12.2.3, there should be a reference to [320], i.e., \cite{Scott98}.
• Page 386, in "Further Reading and Resources", first sentence starts "Blinn offer...", should be "Blinn offers..." (thanks to Jacob Ström).
• Page 398, the Cauchy-Scwartz inequality should read: |u.v|<=||u||||v|| instead of ||u.v||<=||u||||v|| (thanks to Tommy Fortes)
• Page 398, section A.2, just after Equation A.12, replace "u_1=(-8,-6)" by "u_1=(8,6)" (thanks to Aaryn Flynn)
• Page 409, the second sentence after Equation A.40, says "..., $\lambda_0,\dots,\lamba_{n1}$...". It should be "..., $\lambda_0,\dots,\lamba_{n-1}$..." (thanks to Rodrigo Marchant)
• Page 420, says "Taylor series:", they are actually "MacLaurin series". (thanks to Peter Rundberg)
• Page 440, reference [144]. The title of the PHD title should be italic.
• Reference 174 on page 442, the SIGGRAPH 99 paper by Heidrich & Seidel, has page numbers "pp. 171-178," just before "August 1999".
• Page 445, reference [212], there is a space in his last name that should not be there (between the e and the c).
• Page 458, at the bottom, reference [355], the first website should be: "http://www.worldserver.com/turk/computergraphics/index.html", and the second should be deleted.
• 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