1. A computer-implemented method, comprising: receiving, at a computing device having one or more processors, a first control point and a second control point; determining, at the computing device, a first set of constraints for curvature continuity at the first control point, the first set of constraints including at least one of tangent angle, curvature, first derivative of curvature and second derivative of curvature at the first control point; determining, at the computing device, a second set of constraints for curvature continuity at the second control point, the second set of constraints including at least one of tangent angle, curvature, first derivative of curvature and second derivative of curvature at the second control point; and computing, at the computing device, a curve having a curvature and an arclength at each point along the curve, the curvature at each specific point of the curve being a polynomial function of the arclength corresponding to that specific point, wherein the curve satisfies the first set of constraints at the first control point and wherein the curve satisfies the second set of constraints at the second control point.