Sketching Clothoid Splines

Curves and surfaces modeling is a fundamental research topic in Computer AidedGeometric Design (CAGD) and Computer Graphics (CG). It has been extensively ap-plied to CAD/CAM/CAE, 3D feature films, digital visual effects in film, 3D videogames and so on. Along with the development of computer technology, more and morepeople begin to use computer as tools to design geometric shapes, and some excellentsoftware for this purpose has been emerged. A key component among them is how toinput freeform curves or surfaces. Based on previous work, we investigate and design asketch-based system using clothoid splines. The users input some data points by mov-ing mouse, our system then automatically output a clothoid spline which approximatesthe given data. Through adjusting some parameters, the users can control fairness, ap-proximation error and the number of segments of the resulting curve. Here, a clothoidspline consists of lines, arcs and clothoid curves, which are joined with ??2 continuity.This approach does not need a global parameterization for the input data, and outputcurves have fine fairness. In addition, we present an algorithm to perform re-samplingprocedure for the input data so as to eliminate the effect of non-uniform distribution. Inorder to reduce approximation error for the input data with sharp features, we introducean algorithm to detect cusp and join them with ??1 continuity. The experiments showthat our system can process input data well, and output pleasing curves.