A heart surface is a heart-shaped surface given by the sextic
equation
(1)
(Callahan 2003). The figures above show a ray-traced rendering (left) and the cross
section (right) of the surface. This sextic heart surface is also called "Süss"
(German for "sweet") in Hauser's gallery.
Nordstrand and Kuska use a slight variation of this sextic heart surface, given by
(2)
(Nordstrand, Kuska 2004).
Hauser's Herz surface , whose German name means "heart,"
is a distinct quartic surface defined by
(3)
See also Archimedean Spiral ,
Bonne Projection ,
Cardioid ,
Heart
Curve ,
Herz Surface ,
Piriform
Curve
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References Beutel, E. Algebraische Kurven. Leipzig, Germany: Teubner, 1909. Callahan, P. "RE: Re: Plot3D ? or sth [sic]."
comp.soft-sys.math.mathematica posting. Feb. 10, 2003. https://forums.wolfram.com/mathgroup/archive/2003/Feb/msg00131.html . Hauser,
H. "Gallery of Singular Algebraic Surfaces: Herz and Süss." https://homepage.univie.ac.at/herwig.hauser/gallery.html . Kuska,
J.-P, C. "RE: Drawing a Heart in Mathematica ?" comp.soft-sys.math.mathematica
posting. Feb. 13, 2004. https://forums.wolfram.com/mathgroup/archive/2004/Feb/msg00303.html . Nordstrand,
T. "Heart." http://jalape.no/math/hearttxt.htm . Peterson,
I. "MathTrek: Algebraic Hearts." Feb. 9, 2002. https://www.sciencenews.org/article/algebraic-hearts . 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. "Rasterizing Algebraic Curves and Surfaces."
IEEE Comput. Graphics Appl. 14 , 14-23, 1994. Referenced on
Wolfram|Alpha Heart Surface
Cite this as:
Weisstein, Eric W. "Heart Surface." From
MathWorld https://mathworld.wolfram.com/HeartSurface.html
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cross
section (right) of the surface. This sextic heart surface is also called "Süss"
(German for "sweet") in Hauser's gallery.
