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Richard Baker

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Meson (3/13)



  1. Now my son wants a statistics textbook. (for the uninitiated, I am only his humble scribe and mother). I remember my stats textbooks from 35 years ago in grad school (Statistics: An Intuitive Approach: Weinberg, George H.: 9780818504266: Amazon.com: Books), but they are not necessarily the best today. He wants one that will take him from relatively basic stuff up to regression analysis. If not one, then two in a series. Hopefully something that is inexpensive and/or available secondhand through Amazon. Suggestions? Thank you.
  2. The normalizing factor m = 1/(pi2*{2pi}2*{3pi}2*...{npi}2) I derived this from the products formula but it is only valid for x in the neighborhood of 0. It was a neat exercise but I don't totally understand why m should equal this but it is cool nonetheless.
  3. Thank you. I will be watching the thread for other responses.
  4. If you look at the graph of sin (x) you see that all the zeroes are located at multiples of pi. So if you were to factor sin (x) as if it were a polynomial you would get m * x * (x-pi) * (x + pi) * ( x-2pi) * (x + 2pi) * ( x - 3pi ) * (x + 3pi) ..... (x - n pi) * ( x + n pi) as n approaches infinity. Question: what is m? I figured this much from computer experiments, m is not a constant, it is a function of x and n. m is less than 0 if n is odd, m is greater than 0 if n is even. If you graph abs (x) and scaled it by the appropriate very large factor you'd see that m (x) looks like a bump centered at x =0 which morphs as n increases, it retains the bump figure. It is not of the form c * exp ( - k x2), although it looks like it could be. What is this mystery function m? Please help me figure this out.
  5. I already used back face culling on some polygons but not all of them. I tried using the average z value of the vertices of the polygon but that doesn't work because some polygons have closer points but are further away from the average. Thank you. Be back later in a rush right now.
  6. I am working on a platform that does not have z buffering hardware support. I am trying to sort polygons in a scene according to z distance so I can implement the painter's algorithm, but I am having no luck. Currently I divide the game into regions and sort the polygons manually in each region according to what looks right. But I would like to know the mathematical solution. I don't have any cyclical overlaps and I don't have any intersecting objects but I do have polygons that touch. Thank you for your help.
  7. He has decided that William of Occam had a better idea.
  8. Sensei or others-- I have received a copy of the code for his problem. Others, ask and you shall receive.
  9. He has very limited access to word-processor, and handwriting is difficult for him. For I in range 0, pixel columns, sample frequency (:enter l for j in range 0 pixel rows, sample frequency initialize ray of (i, j) --> unitvector for k in range numberofreflections enter findintersection (origin, unitvector) --> parameter enter parameter times unitvector plus origin --> x, y, z evaluate derivatives (x, y, z) equals partialderivatives reflection (normalvector), unitvector --> unitvector x, y, z --> origin #now for the second pass nested within the i and j loops more later.
  10. He is eager to be able to interact directly. I will see what can be done to make communication easier. Glad you responded. I will be gone for a good part of today.
  11. The way I was taught to conceptualize it on scratchapixel.com the focus point is behind the screen plane so it was probably awkward wording on my part because some people conceptualize the focus point in front of the screen plane. My question still stands; in the case of the interpolating quadric with two intersection points how do I determine which intersection point is a valid interpolation of the implicit surface. Thanks.
  12. I am using bi-quadratic interpolation but the coefficients of the interpolating quadric surface are weighted according to the position in screen-space. I know it seems unorthodox but it seems like a real viable method. If anybody has ever ray-traced a sphere (a quadric surface) they would know that no meshes are required; you simply find the ray-sphere intersection using the quadratic formula. My solution didn't work for weeding out the false hits. What I currently do is calculate the local Lipschitz constant and divide the value of f at the surface of the quadric where the intersection of the ray occurs. Then subtract c, and divide that difference by the Lipschitz constant. This doesn't work because it is overzealous; it eliminates a lot of true hits. Thank you for showing interest in my problem. Specific language is difficult, my scribe is not perfect .
  13. OK. I got it figured out. Would be easy with a larger computer, but I am limited to my TI super-calculator.
  14. Let me rephrase my question: I think the problem is the hyperboloid of two sheets. How do I determine whether the interpolant quadric surface is on the same sheet as the implicit surface I am interpolating?
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