Painting system based on texture mapping is often limited by the model's parameterization in a 2D texture space. For models with complex topologies or complicated distributions of the structural details, finding the parameterization can be very difficult and usually must be performed manually. Here a novel data representation and a system for direct painting on 3D surface are presented. By creating 3D colored points for each triangle, the system can support a great variety of painting operations similar to the conventional 2D pixels editor. One key ingredient of this method is a novel adaptive data representation including geometry, topology and color. This technique is called the imaged geometry, which allows users to treat each triangle as a triangle image, and to paint the points on 3D triangle surface without any parameterization. This system can take any triangle model as an input and produces an output with colored points on triangles of the model surface. Because this method is adaptive, details are created in the triangles required by the texture painting, which reduces memory usage. Based on the imaged geometry, the models with complex topologies can be painted in an easy way.