A geometric idea to solve the eikonal equation

Given a closed plane curve <b>c</b>(<i>t</i>) = (<i>c</i><inf>1</inf>,<i>c</i><inf>2</inf>) (<i>t</i>) ∈ ε R² and associated function values g(<i>t</i>) we present a geometric idea and an algorithm to solve the equation ||∇<i>f</i>|| = <i>a</i> = const. with respect to the boundary values <i>g</i>(<i>t</i>) along the boundary <b>c</b>(<i>t</i>). This is equivalent to finding a developable surface <i>D</i> of constant slope <i>a</i> = tan α through the spatial curve <i>C</i> determined by (<i>c</i><inf>1</inf>, <i>c</i><inf>2</inf>, <i>g</i>) (<i>t</i>). The presented method constructs level curves of the surface <i>D.</i> We put some emphasis on the treatment of the singularities of the solution which are <i>D</i>'s self intersections.