The characteristic curve of the envelope generated by the tool motions is an important medium for measuring the distance between the tool and the desired surface. Via the single parametric surface envelope theory in differential geometry, this article proved the correctness of the characteristic curve obtained by minimum distance pairs. Simultaneously, combined with the existing envelope theory and the longitude method, an algorithm based on a velocity field is proposed to approach the characteristic curve. The torus cutter is first dispersed into longitudes and then the characteristic point on each longitude is determined with the estimated velocity. In the experiments, the actual velocity of the estimated characteristic point is computed by the true trajectory simulation of the tool. Therefore, the deviation of the proposed method could be measured comparing with the actual velocity. In the implementations, the proposed method is validated in machining a flat, a spiral, and a blade surfaces. In machining the spiral, our algorithm improves approximately 7 times accuracy with 1/7 time cost compared with the existing methods. The results in the blade surface example prove the stableness of the proposed algorithm.