You could use a conformal map based on the Koebe–Andreev–Thurston circle packing theorem.

---

          [![enter image description here][1]][1]
          ^{Image from [Wikipedia](https://en.wikipedia.org/wiki/Circle_packing_theorem).}

---

It would not be a simple implementation from scratch, but it is very general, mapping any shape to any other. Used in computer graphics quite a bit, e.g., for texture mapping.

You could use a conformal map based on the Koebe–Andreev–Thurston circle packing theorem.

---

          [![enter image description here][1]][1]
          ^{Image from [Wikipedia](https://en.wikipedia.org/wiki/Circle_packing_theorem).}

---

It would not be a simple implementation from scratch, but it is very general, mapping any shape to any other. Used in computer graphics quite a bit, e.g., for texture mapping.

---

          [![CirclePacking][2]][2]
          ^{Image from Peter Schröder.}

---

Maybe visit Ken Stephenson's [circle packing web pages](http://www.circlepack.com/).

You could use a conformal map based on the Koebe–Andreev–Thurston circle packing theorem.

---

          [![enter image description here][1]][1]
          ^{Image from [Wikipedia](https://en.wikipedia.org/wiki/Circle_packing_theorem).}

---

You could use a conformal map based on the Koebe–Andreev–Thurston circle packing theorem.

---

          [![enter image description here][1]][1]
          ^{Image from [Wikipedia](https://en.wikipedia.org/wiki/Circle_packing_theorem).}

---

It would not be a simple implementation from scratch, but it is very general, mapping any shape to any other. Used in computer graphics quite a bit, e.g., for texture mapping.