Near Extensions and Alignment of Data in R(superscript)n

2 Building ε-distortions: Slow Twists, Slides

In this chapter, we introduce a key object in the near distorted Whitney extension problem, we call a -distorted diffeomorphisim which distorts distances by factors and where is small enough. We introduce two examples of these maps, we call Slow Twists and Slides. We look at their actions and how they can be used to construct -distorted diffeomorphisims which agree with Euclidean motions in . [39, 67]

We now begin to look at Problem 1 and Problem 2. We will translate “smooth” into the idea of a -distorted diffeomorphism (See Figures 2.1–2.12).

Figure 2.1 Initial points lying on the line , and the application of a Slow Twist with , with (top ...