A rapid Prototyping system that laser-cuts and laminates thick layers can fabricate 3D objects promptly with a variety of materials. Building such a system must consider the surface distortions due to both vertical-cut layers and triangular surfaces. We developed a tangential layer-cutting algorithm by rearranging tangential lines such that they reconstruct 3D surfaces more closely and also constitute smoother laser trajectories. An energy function that reflects the surface-closeness with the tangential lines was formulated and then the energy was minimized by a gradient descent method. Since this simple method tends to cause many local minima for complex 3D objects, we tried to solve this problem by adding a simulated annealing process to the proposed method. To view and manipulate 3D objects, we also implemented a 3D visual environment. Under this environment, experiments on various 3D objects showed that our algorithm effectively approximates 3D surfaces and makes laser-trajectory feasibly smooth.