The invention belongs to the technical field of a three-dimensional gesture interaction method, and specifically relates to a gesture interaction method based on joint point transformation. The invention mainly solves the technical problems of expensive devices used and poor authenticity of obtained human hand models in the prior three-dimensional gesture interaction method. According to the invention, three-dimensional point clouds are processed with information in colour images synchronously obtained by a Kinect camera while acquiring point cloud data, in the scheme, a base function construction method based on geodesic distance is adopted in reconstruction, and a curved surface representation function is a high-order derivable parametric form and can guarantee topological property and surface smoothness of the human hand; meanwhile, joint points can be effectively extracted by a method of inter-dimensional matching between the three-dimensional point clouds and a two-dimensional image. The method in the scheme has the characteristics of more accurate, fast extraction speed and low computation load relative to the conventional method of reconstructing the three-dimensional joint points after performing matching between the images.