Keenan Crane

 Email Office 329 Annenberg Phone (502) 821-3239 Mail MC 305-16 California Institute of Technology 1200 E California Blvd Pasadena, CA 91125 Calendar
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 Data & Source Code Cheat Sheets Variational Principles Cheat Sheet - useful for remembering which combinations of "Hamilton," "Euler," "Lagrange," "Gauss," "Pontryagin," and "d'Alembert" correspond to which principle. Triangle Areas Cheat Sheet - areas of regions in the circumcentric dual of a triangle mesh can usually be written via simple expressions involving the cotangents of the interior angles of the primal triangles. فارسی <=> 日本語 Decoder Ring Farsi alphabet in Japanese [PDF] [XeTeX] Japanese alphabet in Farsi [PDF] [XeTeX] (hiragana and katakana) Homework & Lecture Slides Introduction to Discrete Differential Geometry (DDG) and Discrete Exterior Calculus (DEC) - lecture notes, homework assignments, and code for CS 177 (Discrete Differential Geometry), Fall 2011 at Caltech.   Notes on differential geometry of curves and surfaces and discrete curvature flow from SGP 2012 Grad School.   Discrete Differential Geometry (DDG) Homework Exercises - several sets of homework exercises I created for CS 177 at Caltech in Fall 2008.   Importance Sampling for Monte Carlo Ray Tracing - 3/8/2006 CS419 (Advanced Graphics) at UIUC. Fundamental MCRT issues, importance sampling, multiple importance sampling, Metropolis-Hastings, resampled importance sampling, defensive sampling, rejection, inversion, the alias method   GPU Algorithms - 5/30/2006 CMPS 160 (Introduction to Computer Graphics) at UC Santa Cruz. Cg, object- and tangent-space normal mapping, displacement mapping, "bumpy shiny," convolution, framebuffer objects. Briefly: fluid simulaion, ray tracing, fractals.   Shaders - 2/13/2006 CS418 (Intro to Graphics) at UIUC. Basic intro to shaders, programmable shaders in Cg/OpenGL, texturing, parameterization, normal mapping, cube mapping, barycentric coordinates. Pedagogical Articles Fun
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