analytic geometry - Superellipse parametric equation
Dec 20, 2017 · $\begingroup$ Whatever is the sign of a and b the parametric equation s satisfy the superellipse equation. If a or b are negative nothing change. If a or b are negative nothing change. EG if a and b are both negative, the parametric equations with minus sign represent the equation in the first quadrant and so on. $\endgroup$
graphing functions - What is the formula for a superellipse with ...
Apr 4, 2019 · Starting at (0,0), count up 4 units to (0,3). Next count up 3 units and over 1 (3+1=N) to (1,5). Then up two and over two, then up one and over three, then over four, ending up at (6,6). Continue the process to complete the points on the superellipse. The arbitrary placement of this example places the center of the superellipse at (1.5,4.5).
Circumference of a superellipse? - Mathematics Stack Exchange
8. Could someone help me formulate the circumference of a superellipse? xn an + yn bn = 1 x n a n + y n b n = 1. If it makes things easier, I'm considering only the cases n> 2 n> 2, and n ∈ Q n ∈ Q. Since the formula for an ellipse (n = 2 n = 2) involves special functions, I assume the general case won't be any simpler, but I can't seem to ...
Polar form of a superellipse? - Mathematics Stack Exchange
To make it a superellipse, just change the exponent to n n giving r = ab |b cos(θ−θ0)|n+|a sin(θ−θ0)|n√n r = a b | b cos (θ − θ 0) | n + | a sin (θ − θ 0) | n n. Translations are hard in polar coordinates, so I would give up and go to Cartesian. Insert absolute value signs where needed...
Solved: Creating a detailed super ellipse - Autodesk Community
05-13-2016 06:29 AM. Ha I've worked it out! draw grid or overall measurement 2800x1200. then enter LAME command. mark centre point in grid. enter half length dim :1400. then enter half height dim :600. enter curve exponent :5.3.
The area of the superellipse - Mathematics Stack Exchange
The area of the superellipse. I'm watching this video, where D. Knuth explains the connection of π and factorials, and other matters (it is very interesting). Almost at the end of the talk he says the area of the superellipse. x1 α + y1 α = 1. is given by. A(α) = 2α ⋅ Γ(α)2 Γ(2α) whic would be. A(α) = 2αB(α, α) = 2α∫1 0(1 − ...
Volume and surface area of a fourth degree superellipse
The page had formulas for the area and perimeter of the shape in two dimensions with the equation: x4 +y4 = 1 x 4 + y 4 = 1. I was wondering how one could calculate the volume and surface area of the same shape in 3D (3D Rectellipse), with the equation: x4 +y4 +z4 = 1 x 4 + y 4 + z 4 = 1. I couldn't come up with much so I asked.
SuperEllipse - Autodesk Community
May 5, 2010 · Here's an all-purpose Lamé [anything but Lame] Curve routine, for SuperEllipse and SubEllipses and everything in between, complete with User choice of exponent 'n' and level of precision, and remembering choices for default offerings. I chose the Polyline & PEDIT approach rather than a Spline, so that [when appropriate] the four quadrants can ...
Cartesian equation for the curvature of a superellipse?
May 9, 2020 · $\begingroup$ Math24 is an excellent excellent site, and has the curvature equations for an ellipse in parametric form, but I'm looking for the equation for curvature for a superellipse in Cartesian form. Also, all my analytic geometry/calculus coursework was completed back in 1972, can't remember any of it, and can't do the derivations myself.
calculus - Points on a normal to a superellipse at distance $d
Nov 27, 2015 · Given a point P0 $(x0, y0)$ lying on a super ellipse, $(x/a)^n + (y/b)^n = 1$, where $2 <= n <= 5$, I'm trying to derive an equation to describe the point P1 (x1, y1) lying on the normal thro...