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Eric Lengyel

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  1.   Thanks for the mention. My book goes into much more detail about all of this: https://www.amazon.com/dp/0985811749/?tag=terathon-20
  2.   Could you please stop using a pirated copy of my book? Moderator, can you please remove the link?
  3.   Very cheap. Only about two dozen scalar instructions in the pixel shader.   Yes, that's exactly what it does. (And the horizon map contains the sine of the angle to the horizon, which is the highest feature in the bump map in a local neighborhood around each texel.)
  4.   There is actually a way to do horizon mapping well, and I describe it in Chapter 5 of Game Engine Gems 3: https://www.amazon.com/dp/1498755658/?tag=terathon-20
  5. Here's one solution, but I'm not sure if it's what you're looking for:   http://transvoxel.org/
  6. These 200 pages correspond to the same range of topics that were covered in about 70 pages of my old math book. The new book goes into a lot more detail and covers new topics like Grassmann algebra that are not discussed in my old book at all. Topics related to graphics, animation, and physics that constitute the bulk of my old math book are going to be covered separately in future volumes of the Foundations of Game Engine Development series.
  7. The first volume in my new book series, Foundations of Game Engine Development, has been released on Amazon.com!   [attachment=33228:vol1.jpg]   This book covers the mathematics needed by game developers. The full table of contents and more information about the series can be found here:   http://foundationsofgameenginedev.com/  
  8.   I'm not seeing that on Amazon. Where can one obtain a copy?     It's not out yet. I'll put a link to the Amazon page on the above website when it's available. And I'll tweet it. (@EricLengyel)
  9. Thanks for the plug, Ravyne. I also have a new book coming out this month that covers more topics and goes into a lot more detail:   http://foundationsofgameenginedev.com/
  10.   This part doesn't sound right. One side should increase, and the other side should decrease. Your shadow is where the stencil ends up being nonzero.
  11. A plane (a,b,c,d) is really a four-dimensional trivector, not an ordinary vector. When you take the wedge product of three points P, Q, and R, it naturally produces a plane in which d = -dot(N, P) = -dot(N, Q) = -dot(N, R), where N = (a,b,c). When you take the dot product between a homogeneous point (x,y,z,w) and a plane (a,b,c,d), you get a*x + b*y + c*z + d*w, which gives you the signed distance between the point and the plane multiplied by w and the magnitude of N. A positive sign in front of the d is the correct choice.   This kind of stuff is discussed very thoroughly in my new book that comes out in August:   http://foundationsofgameenginedev.com/   Dirk, when a homogeneous point is treated as a single-column matrix that is transformed by multiplying on the left by a 4x4 matrix M, a 4D plane must be treated as a single-row matrix that is transformed by multiplying on the right by the adjugate of the matrix M. If the translation portion of the matrix M is not zero, then a plane will not be transformed correctly if you treat it the same as a point.
  12. Judging by your description, you will like the Tombstone Engine when it is released at the end of May:   http://tombstoneengine.com/
  13. The wedge product mentioned in that pseudocode is between two 2D vectors. Calling them U and V, this wedge product gives the following numerical quantity (which is technically a pseudoscalar or antiscalar, but it doesn't matter):   U ? V = U.x * V.y - U.y * V.x   I have a Grassmann algebra talk that provides an introduction to the wedge product:   http://www.terathon.com/gdc14_lengyel.pdf
  14. I have begun writing a new series of books entitled Foundations of Game Engine Development. The first volume covers essential mathematics, including conventional linear algebra and geometry as well as modern topics like Grassmann algebra and geometric algebra. If a high-quality book about this subject interests you, please help me self-publish it by contributing to my Indiegogo campaign:   https://www.indiegogo.com/projects/foundations-of-game-engine-development-volume-1   The success of this campaign will also mean that future volumes on rendering, animation, and physics will be written sooner.   [attachment=30312:Cover1x.png]