Robust and Efficient Computation of the Closest Point on a Spline Curve
نویسندگان
چکیده
Parametric cubic spline curves are commonly used to model the geometry of road surfaces in real-time driving simulators. Roads are represented by space curves that define a curvilinear frame of reference in which three-dimensional points are expressed in coordinates of distance along the curve, offset from the central axis, and loft from the road surface. Simulators must map from global Cartesian coordinates to local road coordinates at very high frequencies. A key component in this mapping is the computation of the closest point on the central axis of the road to a three-dimensional point expressed in Cartesian coordinates. The paper investigates a two-step method that exploits the complementary strengths of two optimization techniques: Newton’s method and quadratic minimization.
منابع مشابه
Control point adjustment for B-spline curve approximation
Pottmann et al. propose an iterative optimization scheme for approximating a target curve with a B-spline curve based on square distance minimization, or SDM. The main advantage of SDM is that it does not need a parameterization of data points on the target curve. Starting with an initial B-spline curve, this scheme makes an active B-spline curve converge faster towards the target curve and pro...
متن کاملFitting B-Spline Curves to Point Clouds in the Presence of Obstacles
We consider the computation of an approximating curve to fit a given set of points. Such a curve fitting is a common problem in CAGD and we review three different approaches based upon minimization of the squared distance function: the point distance, tangent distance and squared distance error term. We enhance the classic setup comprising a point cloud and an approximating B-Spline curve by ob...
متن کاملA robust engineering approach for wind turbine blade profile aeroelastic computation
Wind turbines are important devices that extract clean energy from wind flow. The efficiency of wind turbines should be examined under various working conditions in order to estimate off-design performance. Numerous aerodynamic and structural research works have been carried out to compute aeroelastic effects on wind turbines. Most of them suffer from either the simplicity of the modelling ...
متن کاملTracking Point-Curve Critical Distances
This paper presents a novel approach to continuously and robustly tracking critical (geometrically, perpendicular and/or extremal) distances from a moving plane point p ∈ R to a static parametrized piecewise rational curve γ(s) (s ∈ R). The approach is a combination of local marching, and the detection and computation of global topological change, both based on the differential properties of a ...
متن کاملAn Application of Singularity Theory to Robust Geometric Calculation of Interactions among Dynamically Deforming Geometric Objects
This dissertation presents a general mathematical framework for geometric inquiries and geometric operations on dynamically deforming models, performing the efficient and robust computation of these events: 1. Evolution of an existing solution to a nearby one under small perturbation 2. Detection of transition events 3. Identification of the set of transition points where a structural change of...
متن کامل