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## 3D heart from the heart.

If you're chasing this years' Valentine's Day, or maybe next year...

With the LISP utility 3DPlot (Download) you may not only create raw mathematical surfaces, but by choosing the appropriate math function you can generate some pretty heartbreaking models. You never know when they might come in handy...

```(defun fXYHeart (u v)
(list
(* 16.0 (sin u)(sin u)(sin u) (- 1.0 (* v v v)))
(* (- (* 13.0 (cos u)) (* 5.0 (cos (* 2.0 u))) (* 2.0 (cos (* 3.0 u)) (cos (* 4.0 u))) (- 1.0 (* v v v)) ) )
(* v 3.0)
))
(setq nods (3DPlot fXYHeart (- pi) pi (/ (* 2 pi) 50) -0.999 0.999 (/ 2.0 50)))
```

You can then smooth the resulting 3D heart model using _MESHSMOOTH, assign the appropriate material (here Glazed Metallic) and render the result:

click to enlarge

A similar mathematical expression can be used to generate a heart shape in Inventor or Fusion. As the "Expression Curve", enter:

x(t) = sin(t)*sin(t)
y(t) = (13*cos(t)-5*cos(2*t)-2*cos(3*t)-cos(4*t))/16

A 3D sketch with a heart-shaped contour (half)curve will be created, which you can complete by mirroring and extruding (see Heart.ipt in the CAD Block Library):

applies to: AutoCAD · Inventor · Fusion 360 360 ·

 See also: Tip 13847: Pringles in AutoCAD - a hyperbolic paraboloid. Tip 12749: Generate parametric mathematical 3D surfaces (meshes) in Fusion 360. Tip 9711: 3DConstruct - converting a 3D mesh to a frame construct Tip 9651: Convert a DWG 3D mesh model to an Inventor 3D solid part. Tip 9625: How to color 3D topo surface model by slope?