# Final Project: Rendering Lily Pads

### Tom Brow, Ranjitha Kumar

Upload new attachment "lilypads_big.jpg"

## Lily Pad Models

All the lily pads and stems were modelled in Mathematica; the screen shot below shows the basic form of the equations used to model both the pads and the stems. The intuition used to create the lily pad models is as follows:

- {x(u,v,) = cos(u), y(u,v) = sin(u), z(u, v) = C} creates a circle in the z(u, v) = C plane.
- To create a circle with frills on the outer edge, and varying frequency cosine terms to x(u, v) and varying frequency sine terms to y(u, v).
- Varying u from 0 to a value less than 2*Pi, results in an incomplete circle. To make the circle pucker inwards like a cardiod, multiply x(u,v) and y(u,v) by some degree of v.
- The other terms in x(u,v) and y(u,v) are used to move the location of the center of the lilypad.
- Finally, to get it to radially curve into the center in z multiply by sin(v), or some other function of z for the desired effect.

The lily pad stems can be thought of as sweeping circle along a curve defined by sines and cosines.

After creating all of the models in Mathematica, the geometry was outputted to PBRT scene files and referenced in the main scene file. We used the Mathemathematica to PBRT converter available at http://pbrt.org/downloads.php.

## Subsurface Scattering