The arbitrary adoption of cell center to represent the whole cell is a compromise to the grid structure of the digital elevation models (DEMs), which greatly limits the accuracy of estimating flow distance and width functions. This study uses the triangulation with linear interpolation (TLI) method to approximate the missing flow distance values within a cell except for the cell center. A new flow distance algorithm (D∞-TLI) is proposed to improve the flow distance estimation by using a two-segment-distance strategy. The first segment distance from a cell center to a crossing point at the local 3 × 3 window boundary is modeled by the D∞ method. The second segment distance souring from the crossing point is estimated by the TLI using the flow distance values assigned for the two closest downstream cell centers, while these values have been assigned by iterating from lowest to highest cells. Then, using the continuous flow distance field approximated over a cell region, this cell can be divided into multiple equidistant belts (MEB) to estimate the width function. Four numerical terrains and two real-world terrains are used for assessments. The results demonstrate that D∞-TLI outperforms nine existing flow distance algorithms over any numerical terrains, and it is overall optimal for real-world terrains. Meanwhile, MEB extracts the width function which is less affected by unreasonable artificial fluctuation than the previous method. Hence, MEB combined with D∞-TLI can obtain a high-accuracy estimation of hydro-geomorphological attributes that may be conducive to the application of hydrologic modeling.