I am trying to create a graphics application where the user can use an arbitrary shape as a brush, which will be swept along the drawing path. The shape may be transformed along the path (rotated, resized, etc). I read this paper, and it seemed promising:Approximate General Sweep Boundary of a 2D Curved ObjectMy understanding of the method is this:Simplify the shape to a polygonSample the shape at various times t along the curveFor each t, connect each point of the polygon at t the corresponding point of the polygon at t-1Calculate the convex hull of the joined shapesMove to t+1Do I have it right? Is this the best way to approach this problem?To clarify what I mean by a Sweep Boundary: Examples would include a pen writing a line, Zorro marking the wall with his sword, a magic marker on a mirror. In each of these cases, there is a path that defines the movement (the Heartline) and a shape that defines the width and angle of the writing instrument (the Counterpoint). The counterpoint is independent of the heartline and can change at any point t along the path.The path would be convex only in the sense that an envelope is formed by the counterpoint as it travels along the heartline.
Algorithm for sweeping a 2d shape along a curve?
algorithms;graphics;geometry