The goal of our project was to model a tumbler that one might add coffee or tea to. We chose this project because we always come to math class with coffee or tea, and we wanted to see if we could use what we had learned in our multivariable class to model it. We utilized Mathematica to create individual graphs of different elements, often combining multiple graphs to make one component. The final image was produced using a mixture of Mathematica and Photoshop to achieve the desired look.
The first component of our project was the cup itself. To make this piece, and many of the others, we employed 3D parametric plots. The cup combined a parametric plot of a cone that was cut off above the tip, and a disc. We used the“show” command in Mathematica to merge the two graphs together and create the image. The mesh, or lines, on the graphs were removed. The cup and the ice also employed reduced opacity commands to make them transparent. For the straw we created a stretched-out cylinder with a small radius using cylindrical coordinates. We also changed the color to red to make it stand out. Next, we made the lid using half of an ellipsoid that was manipulated to be more angular. The last component was the ice, which was made from six planes merged into one graph. The ice cubes were combined in one graph to create five different ones. Photoshop was used to add the lid, straw and cup together, and add the ice into the cup, as Mathematica would not combine the elements in the desired manner.
