What is parameterization? - Mathematics Stack Exchange
2015年4月25日 · The idea of parameterization is that you have some equation for a subset X of a space (often Rn), e.g., the usual equation x2 + y2 = 1 for the unit circle C in R2, and you want …
Parametrization of a line - Mathematics Stack Exchange
A direction is given by a vector (u, v). So if your line goes through the point (a, b), and has direction (u, v), then one possible parametrization just says: "start at x = a and y = b, and then …
Parametrization for the ellipsoids - Mathematics Stack Exchange
If you want to use spherical coordinates, you need to parameterize r as a function of θ and ϕ. Plug into the equation for an ellipsoid and get. r = 1 √((cos(ϕ) / a)2 + (sin(ϕ) / b)2)sin(θ)2 + (cos(θ) / …
Parametrization of $y^2 - x^2=1$ - Mathematics Stack Exchange
A parametrization for the given level curve is therefore. γ(t) = (tan t, sec t), − π/2 <t <π/2, π/2 <t <3π/2. A plot shows that this is indeed the case. However, for the other parametrization. γ(t) = …
How to tell whether a curve has a regular parametrization?
2015年7月20日 · and this second parametrization is regular because its velocity anywhere is at least 1. So, my question is: given a non-regular parametrization of a curve, is there an …
linear algebra - Parametrization of $SO(N)$ using unit vectors ...
2018年5月31日 · The group SO(N) has m = N(N − 1) / 2 generators and one thus needs m angles to parametrize it. In the case of SO(2) and SO(3), one can also parametrize using unit vectors …
Parametric form of square - Mathematics Stack Exchange
2014年10月17日 · A parametrization of a straight line from P to Q is r(t) = tP + (1 − t)Q as t goes from 0 to 1. Four of these pieces with suitable start and stop values for t will take you round …
Find a vector parametrization - Mathematics Stack Exchange
The vector equation of a line always looks like. r(t) = vt + b r (t) = v t + b. where v v is a vector parallel to your line, b b is a point on your line, and t t is your variable. So you just need to …
Parametrizing a circle in a counterclockwise direction
2022年4月29日 · Sorted by: 1. A parametrization is not unique. Suppose you parametrize the circle as (r cost, r sint) (r cos t, r sin t) with t ∈ [0, 2π) t ∈ [0, 2 π). Then, when t = 0 t = 0 you …
How to parameterize an ellipse? - Mathematics Stack Exchange
2018年7月15日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …