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I hereby authorize whoever it may concern to post my comments as answers if they wish, whether as community wiki or otherwise if you like imaginary internet points.


11h
comment verifying the geometric relationship in the Blinn-Phong reflection model.
The only things you need are that (i) the angle between $R$ and $N$ is equal to the angle between $N$ and $L$, and that (ii) the angle between $E$ and $H$ is equal to the angle between $H$ and $L$.
Oct
21
comment What is $log( b,a)$ according to google?
It appears to be $\log 4.2$. Further reading: en.wikipedia.org/wiki/…
Oct
21
comment Defining ellipse using points and normal vectors from them
You'll definitely need a third point because two points and their associated normals do not determine an ellipse.
Oct
21
comment Defining ellipse using points and normal vectors from them
What exactly is the input? Do you have two or three "gradients" (point-vector pairs) that you know belong to the same ellipse? Or do you just have an unorganized collection of gradients corresponding to several unknown ellipses?
Oct
16
comment Is there a more appropriate SI unit of measure to use to determine the surface area of the playground equipment
The SI unit of area is $\mathrm m^2$. SI does not specify alternative units for use in playgrounds.
Oct
16
comment If -log(f) is convex, is f automatically convex?
Consider $f(x)=\exp(-x^2)$.
Oct
15
comment Is $\nabla\cdot{F} = F\cdot\nabla$?
Appropriate user image.
Oct
11
comment How to integrate Gravitational force?
en.wikipedia.org/wiki/Classical_central-force_problem
Oct
11
comment Interpolation polynomial Challenge
Say $p(x)=x^2-x^3$. You can match this with a degree-1 polynomial?
Oct
10
comment How can I approximate the logarithm of the sum?
Since $b>a$, a better approximation would be $\log b+\log(1+a/b)\approx\log b+(a/b)=\beta+\exp(\alpha-\beta)$.
Oct
10
comment Scalar value of similarity between Two Square Matrices
$\|B-A\|$ where $\|\cdot\|$ is any matrix norm.
Oct
10
comment Can a smooth function $f\colon\partial D^n\to\partial D^n$ be extended to a smooth function $\hat{f}\colon D^n\to D^n$?
Why not $g(|x|)f(x/|x|)$ where $g$ is a smooth function with all derivatives vanishing at $0$, such as $e^{1-1/|x|}$?
Oct
8
comment Geometric interpretation of mixed partial derivatives?
+1 for a very elegant geometric interpretation. However, I'd reconsider your last sentence -- the surface $f(x,y)=x^2-y^2$ is just as saddle-like as $f(x,y)=2xy$ even though the former has $f_{xy}=0$.
Oct
8
comment How many balls of radius 1 can be packed into a sphere of radius 10?
@Ross: Your link is for circles, not spheres.
Oct
7
comment Is a minimum a minimum in every norm? (for finite-dimensional vector spaces)
Equivalence of norms is a topological property. It means that if a sequence of vectors converges to a limit under one norm, the sequence also converges to the same limit under any other equivalent norm.
Oct
7
comment Is there any standard way to handle fractions of bilinear constraints in optimization?
Then it's equivalent to $(a_1+a_2+\cdots)(c_1+c_2+\cdots) = \mathrm{const}\cdot(b_1+b_2+\cdots)(d_1+d_2+\cdots)$, which is a quadratic constraint.
Oct
7
comment Geometry question: ray paths and circles
What exactly is the "lower trajectory" you are looking for? Do you want the length of the tiny segment of the red line to the right of the shaded gray region and to the left of the green diagonal line?
Oct
7
comment Is there any standard way to handle fractions of bilinear constraints in optimization?
What you've written there is the product of two fractions. What is the constraint exactly?
Oct
6
comment Is a minimum a minimum in every norm? (for finite-dimensional vector spaces)
By $\|\cdot\|_A$ you mean the norm $\|y\|_A=y^TAy$, do you?
Oct
6
comment Loonies and Toonies Combinatorics
Perhaps you should clarify that loonies and toonies are the Canadian \$1 and \$2 coins.