Spline approximation of offset curves
β Scribed by Josef Hoschek
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 405 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0167-8396
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Offset curves are important in some aspects of computeraided design. Several authors have studied, and found, approximations to offset curves of cubic B-splines. Curves made of segments of clothoid spirals, arcs of circles, and straight line segments are used as centre lines of railways and highways
A simple and efficient method is developed for generating oftset curves interactively using a set ot control knots for a uniform cubic B-spline. ## geometry, curves, oEsets The construction of offset curves has many applications in industry. For example, it can be used in the numerical control of
A plene cubic spline segment is given. We wont to epproximote Its offset line by another cubic spline segment. Therefore we take the known curvotures end tangents ot the endpoints of the offset line end colculete the corresponding spline. Finally examples ore given.
Given a parametric plane curve \(\mathbf{p}\) and any BΓ©zier curve \(\mathbf{q}\) of degree \(n\) such that \(\mathbf{p}\) and \(q\) have contact of order \(k\) at the common end points, we use the normal vector field of \(\mathbf{p}\) to measure the distance of corresponding points of \(\mathbf{p}\