Amos Frank

Mathematica Summer Camp

Class of 2014


Hi, my name is Amos Frank. I am from Edina, Minnesota. I have done some programming in Python, Java, and BASIC. My math experience so far involves multivariable calculus, linear algebra, and some differential equations. I enjoy playing chess, ultimate Frisbee, and skiing in the winter.

Project: Visualization and Rating of Mountains Based Upon Slope

Mountains are typically rated for skiing on a scale of green circle, blue square, and black diamond. Using high-definition grayscale images, elevation data can be pulled and analyzed to obtain slope at every point. Based on that data, the mountain's difficulty can be assessed.

The algorithm used to determine slope is an image convolution. It takes the points around the desired point at some range and, using some function, applies them to the center point. That function is the convolution matrix. In this case, the matrix determines slope by taking nearby points for several pixels and applies an exponential function to give heightened importance to nearer pixels. This is then computed as a slope and given a color function that determines difficulty.