Constrained, Interactive Design of Framed Curves : Interaktive Auslegung von Dreibeinkurven unter geometrischen und dynamischen Randbedingungen

This work covers methods that facilitate the design of spatial paths that are to be traced by a system of rigid bodies, such as a car, train or bobsled. In these applications, the path geometry and the resulting dynamics of the rigid bodies are closely tied to each other. The path is not only seen, but also felt by the bodies or any human patron sitting inside. This imposes additional constraints on the underlying geometric object. Similarly as for spatial trajectories of rigid bodies, we need to specify both the position and the orientation of the path. We will model such paths using framed curves, geometric objects composed of a spatial curve and its moving frame.

In this thesis, we introduce framed curves as a representation for spatial tracks in the context of layout design. We show how, given a particular framed curve, we can evaluate the fairness of the track it represents, check common design constraints and perform various geometric operations, such as constructing sweep surfaces and offset curves. Furthermore, framed curves can be implemented as general joints in the context of multi body analysis, allowing us to solve the related inverse kinematics problem using established multi body systems (MBS) libraries. ... mehrWe propose an algorithm that approximates the equations of motion of a vehicle efficiently and with sufficient accuracy for our application, the design of roller coaster layouts. The results of this algorithm is verified against both real-world measurements and theoretical ground truth data. We also propose two different modeling techniques for the design of framed curves in an interactive CAGD setting. First, using a curvature based curve definition, framed curves may be generated from three input functions using numerical integration. Second, using polynomial spline interpolation and non-linear optimization, energy minimizing curves and moving frames can be generated using several human-defined interpolation constraints and an application-defined loss function.