The use of Cornu spirals in drawing planar curves of controlled curvature
Journal of Computational and Applied Mathematics
IBM Journal of Research and Development
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
A mark-based interaction paradigm for free-hand drawing
UIST '94 Proceedings of the 7th annual ACM symposium on User interface software and technology
The algorithmic beauty of plants
The algorithmic beauty of plants
Computer-generated floral ornament
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Interactive curve design using digital French curves
I3D '99 Proceedings of the 1999 symposium on Interactive 3D graphics
Planar G2 transition with a fair Pythagorean hodograph quintic curve
Journal of Computational and Applied Mathematics
On PH quintic spirals joining two circles with one circle inside the other
Computer-Aided Design
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In this paper we will present a novel design element creator tool for the digital artist. The purpose of our tool is to support the creation of vines, swirls, swooshes and floral components. To create visually pleasing and gentle curves we employ Pythagorean Hodograph quintic curves to join a hierarchy of control circles defined by the user. The control circles are joined by spiral segments with at least G2 continuity, ensuring smooth and seamless transitions. The control circles give the user a fast and intuitive way to define the desired curve. The resulting curves can be exported as cubic Bézier curves for further use in vector graphics applications.