Constrained modification of the cubic trigonometric Bézier curve with two shape parameters

A new type of cubic trigonometric Bézier curve has been introduced in [1]. This trigonometric curve has two global shape parameters λ and µ. We give a lower boundary to the shape parameters where the curve has lost the variation diminishing property. In this paper the relationship of the two shape parameters and their geometric effect on the curve is discussed. These shape parameters are independent and we prove that their geometric effect on the curve is linear. Because of the independence constrained modification is not unequivocal and it raises a number of problems which are also studied. These issues are generalized for surfaces with four shape parameters. We show that the geometric effect of the shape parameters on the surface is parabolic. Keywords: trigonometric curve, spline curve, constrained modificatio

Geometric properties and constrained modification of trigonometric spline curves of Han

New types of quadratic and cubic trigonometrial polynomial curves have been introduced in [2] and [3]. These trigonometric curves have a global shape parameter λ. In this paper the geometric effect of this shape parameter on the curves is discussed. We prove that this effect is linear. Moreover we show that the quadratic curve can interpolate the control points at λ = √2. Constrained modification of these curves is also studied. A curve passing through a given point is computed by an algorithm which includes numerical computations. These issues are generalized for surfaces with two shape parameters. We show that a point of the surface can move along a hyperbolic paraboloid

Continuous fusion of motion data using an axis-angle rotation representation with uniform B-spline

The fusion of motion data is key in the fields of robotic and automated driving. Most existing approaches are filter-based or pose-graph-based. By using filter-based approaches, parameters should be set very carefully and the motion data can usually only be fused in a time forward direction. Pose-graph-based approaches can fuse data in time forward and backward directions. However, pre-integration is needed by applying measurements from inertial measurement units. Additionally, both approaches only provide discrete fusion results. In this work, we address this problem and present a uniform B-spline-based continuous fusion approach, which can fuse motion measurements from an inertial measurement unit and pose data from other localization systems robustly, accurately and efficiently. In our continuous fusion approach, an axis-angle is applied as our rotation representation method and uniform B-spline as the back-end optimization base. Evaluation results performed on the real world data show that our approach provides accurate, robust and continuous fusion results, which again supports our continuous fusion concept