Surface Intersections

I hit numerous impasses and sometimes spent hours at my local university’s library thinking and looking for theorems and tools. For example, when I started to parameterize my space curve, I ran into the problem that one of Wang et al.’s theorem that was crucial in parameterization failed for my intersection space curve projection. I was stuck, but I knew I could adapt it some way. I read ahead. I tried multiple ways of attacking this problem. Many times I failed. I didn’t give up. I just went back to my notes, and looked for new ideas that I had written down. Weeks later, while I was reading the parameterization section in Wang et al.’s paper, I suddenly realized that if I lowered the degree of the space curve projection, I could successfully adapt the failed theorem . . . Eventually I was able to derive the parameterization for a special case of the intersection curve.

• Mathematics