Enter the curvature as a function of the curvilinear abscissa s. The curve, passing through a given point and having a given tangent, is plotted.

Note the sign of the curvature in the [url=https://en.wikipedia.org/wiki/Frenet%E2%80%93Serret_formulas]Frénet frame[/url]. You can try the Cornu spiral, the [url=https://en.wikipedia.org/wiki/Euler_spiral]clothoid[/url], whose curvature is an affine function of the curvilinear abscissa.