![]() Setting r = 2, t = 2.5, A = B = 3, C = 4 one obtains Piet Hein's superegg. The general super-ellipsoid is obtained by scaling the basic shape along each axis by factors A, B, C, the semi-diameters of the resulting solid. The basic shape above extends from −1 to +1 along each coordinate axis. Volume: Vrh2 2 Surface Area (with top and bottom): SA 2 2 + rh r Volume: Vsss s Volume: VLW H Surface Area (with top and bottom): SA 2 2 2 + +LW LH WH Surface Area (with top and bottom): SA 6 s2 Volume: V 1 2 3 rh Surface Area: SA 4 r2 Volume: V 4 3 3 r. In that case, the super-ellipsoid is a solid of revolution, obtained by rotating the Lamé curve with exponent t around the vertical axis. Surface Area 2bs + b2 Volume 1/3 b2h Another way to calculate this is to use the perimeter ( P) and the. For a triangle with only two known side lengths, a a and b b, the unknown side length. ![]() In other words, for a triangle with side lengths a a, b b, and c c: a+b>c a + b > c. In particular, if r is 2, the horizontal cross-sections are circles, and the horizontal stretching w of the vertical sections is 1 for all planes. Math Formulas for Basic Shapes and 3D Figures. What is the triangle inequality rule The triangle inequality rule states that the longest side of a triangle must be shorter than the combined lengths of the two other sides. Namely, if x = u cos θ and y = u sin θ, for a fixed θ, then Note that the formula becomes a special case of the superquadric's equation if (and only if) t = r.Īny "parallel of latitude" of the superellipsoid (a horizontal section at any constant z between -1 and +1) is a Lamé curve with exponent r, scaled by :Īny "meridian of longitude" (a section by any vertical plane through the origin) is a Lamé curve with exponent t, stretched horizontally by a factor w that depends on the sectioning plane. The parameters r and t are positive real numbers that control the amount of flattening at the tips and at the equator. ![]() The basic super-ellipsoid is defined by the implicit equation ![]()
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