Constraint-based LN curves

We consider the design of parametric curves from geometric constraints such as distance from lines or points and tangency to lines or circles. We solve the Hermite problem with such additional geometric constraints. We use a family of curves with linearly varying normals, LN curves. The nonlinear equations that arise can be of algebraic degree 60. We solve them using the GPU on commodity graphics cards and achieve interactive performance. The family of curves considered has the additional property that the convolution of two curves in the family is again a curve in the family, assuming common Gauss maps, making the class more useful to applications. Further, we consider valid ranges in which the line tangency constraint can be imposed without the curve segment becoming singular. Finally, we remark on the larger class of LN curves and how it relates to Bézier curves.

► The tangent direction of LN spline is locally linear. ► LN Hermite splines can be made tangent to given circles and lines. ► Criteria for nonsingular solutions and feasibility range given. ► Fast GPU algorithms implemented. ► LN curves have polynomial convolutions.