Objectives  In the case of uneven distribution of map features, the density difference breaks the visual balance and reduces the beauty of the map. A large number of spatial features are concentrated in the small area, resulting in the contradiction between the display of features and the size of the area. Map details are not prominent, which increases difficulties in obtaining spatial information and is not conducive to decision analysis. The uneven distribution of feature density in mapping area increases the difficulty of map expression. Conventional map expression cannot solve the problem of visual imbalance.

  Methods  Based on Gastner-Newman cartogram algorithm, this paper proposes a map transformation algorithm that balances the feature density and achieve consistent public perception. Various cartograms can be generated through five steps: Designing deformation unit scales, configuring density weight combination of features, applying linear diffusion equation, constructing deformation grids and mapping discrete control points.

  Results  Taking Qingxiu district of Nanning city, China as the research area, we select two scale deformation units of sub-district and custom grid, and configure density weights with different combinations of point of interest and road network geometry features to generate various cartograms. The deformation measurement values of the deformation map are calculated respectively. After cognitive experiments, 56 questionnaires were obtained. Regarding the morphological control of the administrative map of Qingxiu District in Nanning, the parameters configurations should be controlled as in S_perimeter > 0.975, S_{perimeter area ratio} > 0.961 and S_{shape ratio} > 0.966. In this way, public cognition can be consistent.

  Conclusions  This study provides a new idea to solve the problem of uneven density of map features. The deformed map reaches visual balance.The area where the original features are dense increases while the area where the features are sparse decreases. By adjusting the deformation weight parameters to maintain the consistency of public map cognition. Subsequently, we will further study how to determine the optimal parameter combination to achieve the optimal deformation expression and cognitive effect.