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What The Hare Said To Hector
Hector: Alright, explain your game to me, Mr. Hare. Hare: First, I will stand somewhere along the race track, but I won’t tell you where, and this wall hides me from view. Now, do you see this large contraption here? Hector: Indeed. There is a meter long net suspended from a high cable that extends […]
Comments Off on What The Hare Said To HectorJan 20th, 2012  Filed under Uncategorized 
Miss Register, I Presume?
In my AIM 2010 paper, I describe how to obtain a projective transformation from the image plane to the laser plane in a line laser 3D range imaging system. With the laser oriented vertically (i.e. perpendicular to the transport direction of the object being scanned), this allows for mapping of image coordinates directly to 3D […]
Comments Off on Miss Register, I Presume?Jun 4th, 2011  Filed under Uncategorized 
Rise of the Quaternions
Adolphus finally quit messing around and started using a quaternion representation for rotations internally! The quaternion class itself is simple, and conversion to and from rotation matrix and axisangle representations is fairly straightforward. The magic happens in converting from Euler angles — all twelve valid conventions! By solving the conversion to quaternion for all twelve […]
Comments Off on Rise of the QuaternionsOct 18th, 2010  Filed under Uncategorized 
Rotating Lines
Problem: Given a line of slope m in the Euclidean plane, what is the slope m’ of the line rotated (counterclockwise) by angle θ? Solution: Suppose we have an equation for the line of the form y = mx + b. We can ignore b as it is unrelated to the slope (in effect, we […]
Comments Off on Rotating LinesJun 28th, 2010  Filed under UncategorizedTags: math 
So Close, Yet So Far Away
I humbly entreat any analytical intellects of greater constitution than my own (of which, to be sure, there is no dearth) to enlighten me in matters mathematical. First of all, if I have a 5dimensional space which consists of a 3dimensional Euclidean space plus direction (defined by inclination and azimuth) — that is, the set […]
Comments Off on So Close, Yet So Far AwayJun 15th, 2010  Filed under Uncategorized 
Snap To Grid
I like Gabor Herman‘s definition of discrete Euclidean space. He defines, for any positive real number and any positive integer : This chops Nspace up into a square (cubic, etc.) Bravais lattice, with primitive vectors of magnitude . Each point in the discrete space is then associated with a primitive cell (or Voronoi neighbourhood, in […]
Comments Off on Snap To GridMar 17th, 2010  Filed under Uncategorized 
Pi Day Madness
You have a righthanded Cartesian coordinate basis of a threedimensional Euclidean space, with axes , , and . You’re given some spatialdirectional vectors of the form , where and are, respectively, the inclination angle (from the positive axis zenith) and the azimuth angle (measured righthanded from the positive axis) of an associated direction, which is […]
Comments Off on Pi Day MadnessMar 14th, 2010  Filed under Uncategorized 
On Path and Edge Strengths in Fuzzy Graphs
How does one define the strength of a path in a fuzzy graph? Mathew and Sunitha state that “the degree of membership of a weakest [edge] is defined as [a path’s] strength” without any apparent justification. Saha and Udupa mention that several measures, including sum, product, and minimum, all seem plausible, but also ultimately choose […]
Comments Off on On Path and Edge Strengths in Fuzzy GraphsOct 17th, 2009  Filed under Uncategorized 
Distributed Descriptive Statistics and Magic
Here’s an interesting problem. Anyone know of a solution to this? There are 24 wizards in the land of Network. They live spread out far from one another, because if too many of them got too close, the concentration of magical power would create a singularity and destroy the universe. They are all aware of […]
Comments Off on Distributed Descriptive Statistics and MagicOct 10th, 2008  Filed under Uncategorized