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Heart Surface

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Heart surface
HeartSurfaceCrossSection

A heart-shaped surface given by the sextic equation

(x^2+9/4y^2+z^2-1)^3-x^2z^3-9/(80)y^2z^3=0

(Taubin 1993, 1994). The figures above show a ray-traced rendering (left) and the y=0 cross section (right) of the surface.

A slight variation of the same surface is given by

(2x^2+2y^2+z^2-1)^3-1/(10)x^2z^3-y^2z^3=0

(Nordstrand, Kuska 2004).

See also

Archimedean Spiral, Bonne Projection, Cardioid, Heart Curve, Piriform Curve

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References

Beutel, E. Algebraische Kurven. Leipzig, Germany: Teubner, 1909.Kuska, J.-P, C. "RE: Drawing a Heart in Mathematica?" comp.soft-sys.math.mathematica posting. Feb. 13, 2004. http://forums.wolfram.com/mathgroup/archive/2004/Feb/msg00303.html.Callahan, P. "RE: Re: Plot3D ? or sth [sic]." comp.soft-sys.math.mathematica posting. Feb. 10, 2003. http://forums.wolfram.com/mathgroup/archive/2003/Feb/msg00131.html.Nordstrand, T. "Heart." http://jalape.no/math/hearttxt.Peterson, I. "MathTrek: Algebraic Hearts." Feb. 9, 2002. http://www.sciencenews.org/20020209/mathtrek.asp.Taubin, G. "An Accurate Algorithm for Rasterizing Algebraic Curves." In Second ACM/IEEE Symposium on Solid Modeling and Applications Proceedings. 221-230, May 1993.Taubin, G. "An Accurate Algorithm for Rasterizing Algebraic Curves and Surfaces." IEEE Comput. Graphics Appl. 14, 14-23, 1994.

Cite this as:

Weisstein, Eric W. "Heart Surface." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HeartSurface.html

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