Heart Surface
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 CurveExplore with Wolfram|Alpha
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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.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. "An Accurate Algorithm for Rasterizing Algebraic Curves and Surfaces." IEEE Comput. Graphics Appl. 14, 14-23, 1994.Referenced on Wolfram|Alpha
Heart SurfaceCite this as:
Weisstein, Eric W. "Heart Surface." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HeartSurface.html