analytic geometry - Superellipse parametric equation
2017年12月20日 · $\begingroup$ 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 ...
2019年4月4日 · 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).
SuperEllipse - Autodesk Community
2010年5月5日 · 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 ...
Circumference of a superellipse? - Mathematics Stack Exchange
Do you know there's a general formula for the area of a superellipse, the one you have there you can approximate it by cutting it according to the grid of the graph $\endgroup$ – Aderinsola Joshua Commented Apr 8, 2021 at 7:02
Cartesian equation for the curvature of a superellipse?
2020年5月9日 · $\begingroup$ 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.
trigonometry - Derivation of parametric superellipse equation ...
2023年10月5日 · If I plug in the Cartesian equation into something like Geogebra it plots the superellipse from the get go, but to reach the same results through programming it feels like I'm just introducing these exponents to produce the desired result, and I would love to understand how we come to these seemingly magic numbers.
The area of the superellipse - Mathematics Stack Exchange
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Polar form of a superellipse? - Mathematics Stack Exchange
For the ones still interested, two forms of a super ellipse in Cartesian and polar form: Cartesian non-continuous:
geometry - How to determine a point is inside a superellipse ...
2011年10月21日 · Take the equation of the Lamé curve to be $$\left|\frac{x}{a}\right|^p+\left|\frac{y}{b}\right|^p=1$$ Taking your specified order of operations, the result after rotating by an anticlockwise angle $\varphi$ and translating the center of the superellipse to $(h,k)$ is
Volume and surface area of a fourth degree superellipse
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