ABSTRACT
A.1 Four-point interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 A.2 Comparison to other approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 A.3 Computationally friendly expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
Assume an interaction that serves to preserve an angle between two neighboring triangles in a spring network. The basic principle widely used is to apply forces to the vertices increasing the angle in case that the current angle is smaller than the one to be preserved, or the opposite forces otherwise. Clearly, such forces will be applied out-of-plane and it is natural to apply them perpendicularly to the triangles. This choice leaves us with the scenario depicted in Figure A.1. Here, two triangles ABC and ABD have common edge AB and they enclose angle θ. Denote θ0 the angle to be preserved and assume θ > θ0. The forces to be applied thus have directions as depicted in Figure A.1. The forces FA,F
1 B and F
1 C are applied to triangle ABC and FD,F
F2C are applied to triangle ABD. The magnitudes of the forces are in principle free to choose in order to
FIGURE A.1: Two adjacent triangles with bending forces.
