Curve Modeling With Controlling Over Geometric Feature Points

Curve modeling by interpolating a given sequence of points is prevalently used for interactive shape design in the art community.The interpolating curve segments are smoothly connected to form a desired pattern.The user can adjust the curve shapes by interactively modifying the position of given points.The existing interpolation-based modeling method aims at constructing curves with desired fairness,regardless of the controlling over geometric feature points,including cusps,loops,and inflection points.In this thesis,we propose an interpolation curve modeling method for interactively planar curve design.The final shape consists of smoothly connected curve segments,with each interpolating a given points,and the geometric feature points only occur at the given point or the joints of two segments.A cubic spline is the lowest degree of planar polynomial curve which possess a cusp,a loop or up to two inflection points.In this thesis,we adopt cubic Bezier curves to interpolate the given data.Geometric feature points only occur at the interpolation points and segments are smoothly connected.Since the interpolating curves constructed in this thesis is able to control the feature points,we refer to these curves as feature point controlled curves,or FPC-curves for short.We also tailor an iterative algorithm for FPC-curves computation based on results of theoretical derivation.By specifying the type and position of the interpolation point,the corresponding is generated in real time.Further,users can also make adjustments to the type and position of interpolation points so as to interactively adjust the shape of the curve.Experimental results have shown that the proposed modeling method is efficient and intuitive for designing visually pleasant shapes,where the number and positions of geometric feature points are well controlled.The resultant curves are G2 continuous almost everywhere,excepting at the joints where the sign of curvature changes.