Planar Bisector CurvesBased on Developable
نویسنده
چکیده
This paper presents an algorithm to compute the bisector curve of two planar paramet-ric curves. We reduce the problem of computing a bisector curve to that of intersecting two developable surfaces. Given an input curve C (t) = (x(t); y(t)), the corresponding developable surface D C(t) is constructed symbolically as the envelope surface of a one-parameter family of tangent planes of the paraboloid z = x 2 + y 2 along a lifted curve b C (t) = ? x(t); y(t); x(t) 2 + y(t) 2. Compared with general surface/surface intersection, de-velopable surface/surface intersection is considerably more robust and eecient.
منابع مشابه
Möbius bands, unstretchable material sheets and developable surfaces
A Möbius band can be formed by bending a sufficiently long rectangular unstretchable material sheet and joining the two short ends after twisting by 180°. This process can be modelled by an isometric mapping from a rectangular region to a developable surface in three-dimensional Euclidean space. Attempts have been made to determine the equilibrium shape of a Möbius band by minimizing the bendin...
متن کاملBisector curves of planar rational curves
This paper presents a simple and robust method for computing the bisector of two planar rational curves. We represent the correspondence between the foot points on two planar rational curves C1(t) and C2(r) as an implicit curve F(t; r) = 0, where F(t; r) is a bivariate polynomial B-spline function. Given two rational curves of degree m in the xy-plane, the curve F(t; r) = 0 has degree 4m 2, whi...
متن کاملAnalysis and Design of Developable Surfaces
A developable surface can be formed by bending or rolling a planar surface without stretching or tearing; in other words, it can be developed or unrolled isometrically onto a plane. Developable surfaces are widely used in manufacturing with materials that are not amenable to stretching. A ship hull design entirely composed of developable surfaces would greatly reduce production costs of that hu...
متن کاملPiecewise Developable Surface Approximation of General NURBS Surfaces, with Global Error Bounds
Developable surfaces possess qualities that are desirable in the manufacturing processes of CAD/CAM models. Specifically, models formed out of developable surfaces can be manufactured from planar sheets of material without distortion. This quality proves most useful when dealing with materials such as paper, leather or sheet metal, which cannot be easily stretched or deformed during production....
متن کاملDesign of Rational Bézier Developable Surface Pencil Through A Common Isogeodesic
This paper studies the problem of designing a rational Bézier developable surface pencil with a common isogeodesic, and provides an algorithm for the representation of complicated geometric models in industrial applications which need to satisfy that the shape surface can be developed and a given curve is geodesic. By employing the local Frenet orthonormal frame, the explicit expression of the ...
متن کامل