Keenan Crane

@keenanisalive

Digital Geometer. Assistant Professor of Computer Science and Robotics , and member of the .

Pittsburgh, PA
Vrijeme pridruživanja: siječanj 2008.

Medijski sadržaj

  1. 25. sij
    Odgovor korisnicima

    Seems only for the committee:

  2. 11. sij
  3. 10. sij

    Most useful thing I have learned about Mathematica in the past year: you *can* actually tell it that some variables are (always!) real, positive, etc., using the global $Assumptions list.

  4. 5. sij

    I find that many students struggle early on to write good figure captions. A good caption doesn't just explain what’s already apparent in an image—it highlights how a specific example supports a more general principle, and explains why that principle is relevant or interesting.

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  5. 30. pro 2019.
    Odgovor korisnicima

    Right. Here's a picture of the subdivision is talking about, which can be used to trivially convert any tetrahedral mesh into a hexahedral mesh—but with poor angles near tet vertices. Any other way to split up a tet into cubes? :-)

  6. 29. pro 2019.

    How do you chop up a tetrahedron into nicely-shaped little cubes? Here's one way, obtained a la symmetric moving frames (). How else can you do it?

  7. 29. stu 2019.

    Want to change the way the world thinks about geometric computing? The Geometry Collective at Carnegie Mellon University is looking for PhD students for 2020/2021. Topics include mesh processing, discrete differential geometry, and computational design.

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  8. 24. stu 2019.

    The SIGGRAPH Technical Awards Committee is soliciting nominations for the 2020 Computer Graphics Achievement and Significant New Researcher Awards: Help our community flourish by nominating the (many!) deserving graphics researchers. Deadline Jan 31 2020

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  9. 6. stu 2019.
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  10. 6. stu 2019.

    In college I recreated “The Gibson” from Hackers as an interactive OpenGL program. As of tonight it still runs on my 2004 PowerBook G4.

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  11. 6. stu 2019.

    How do you ensure that a cubic Bézier* f(x)=∑ᵢ cᵢBᵢ(x), is strictly increasing? A: Pick coefficients such that c₁>c₀, c₃>c₂ and (c₁²+c₂²+c₀(c₃−c₂)−c₁(c₂+c₃))/(c₀−3c₁+3c₂−c₃) > 0. (Who says you don't learn anything useful in high school math?)

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  12. 25. lis 2019.

    Three integers satisfying a² + b² = c² form a Pythagorean triple, which can be drawn as a right triangle, or a point (a/c, b/c) on the unit circle. Amazing fact: starting with the four Pythagorean triples (±1,0,1), (0,±1,1) all others can be generated via hyperbolic reflections.

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  13. 22. lis 2019.
    Odgovor korisniku/ci

    Very nice! Reminds me of a little demo we wrote for the GeForce 8 launch: Was exciting at the time to think of the possibilities for real time fluids... fun to see it happening in the wild (and at much higher quality).

  14. 5. lis 2019.

    Computer graphics is one of the priority hiring areas for tenure-track hiring in the CMU Computer Science Department this year, at all levels. Please apply! More info here:

  15. 5. lis 2019.
    Odgovor korisniku/ci

    I briefly mention some of the longer history of the cotan formula in the introduction of this note: The oldest reference I know is MacNeal’s 1949 PhD thesis, but I’d be glad to learn of older (or even just other) historical references. Cuneiform maybe?

  16. 2. lis 2019.

    No, Mathematica, when I told you to rotate my polygon that is *not* what I meant! 😆 (Must be how a computer tells a …)

  17. 1. lis 2019.

    We adopted this perspective in "Globally Optimal Direction Fields" to generate the smoothest rotationally symmetric direction field on a curved surface (). and others built on our approach to handle other symmetries

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  18. 1. lis 2019.

    In particular, a function f: ℂ → ℂ can be interpreted as a vector field whose components are the real and imaginary parts of f. Around a point z0 ∈ ℂ, a pole or zero looks something like (z−z₀)^n. Fractional powers capture singularities in line fields, cross fields, etc.

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  19. 1. lis 2019.

    Poles of a complex function can be nicely visualized as vector field singularities—but are rarely drawn that way (try Google images!). In computer graphics, vector field singularities can be thought of as poles and zeros of complex functions—but are rarely understood that way!

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  20. 28. ruj 2019.

    Q: How do you know your baker uses ideal hyperbolic triangles? A: He can only make pie.

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