# Final Project: Rendering Lily Pads

### Tom Brow, Ranjitha Kumar

## 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 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.

## Subsurface Scattering