A version of quartic rational triangular patches is used to C1 construct a surface comprising two composite triangles. Like previous scheme such as cubic Ball and cubic Bézier, they have no free parameter that can be adjusted for surface interpolant. Thus, our proposed method has three free shape parameters, α, β, and γ. This study shows the comparison of the three methods�quartic rational, cubic Ball and cubic Bézier triangular patches. To validate the performances, the error measurement used are root mean square errors (RMSE), maximum error and Central Processing Unit (CPU) times. Besides that, we also made a comparison between C1 and G1 continuity. Based on the results, the proposed scheme is better than the three previous schemes in terms of a smaller value of RMSE, and maximum error. Meanwhile, G1 continuity gives less computation rather than C1. © 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.