A new model for 3D graphical rendering

Abstract

One of the most important tasks of a traditional 3D Rendering engine is the projection on the image plane of geometrical structures (such as triangles or lines). This operation takes place in the middle of the rendering pipeline, between the vertex shader and the fragment shader: its aim is just that of creating fragment data from vertex data. The solution of the projection problem is necessarily bound to the solution of a great number of systems of equations, where the complexity of the equations is in general related to the properties of the geometrical structures. To make this process fast, the most adopted solution is that of using linear models, so that the systems become linear and the module gets the simplest implementation. Unfortunately, linear models have some limitations: the solution is to use approximation, but to get good models they are necessary a lot of linear structures, in particular a lot of triangles; modern 3D Rendering Engines may automate the process of converting non linear models in triangles, but this does not reduce the occupation of memory and doesn’t eliminate linear approximation. In this article I consider a non linear model (the Lembo model) for geometrical structures in a 3D rendering engine: firstly I show the properties of the model; then I show an efficient algorithm to solve the projection problem directly on the model equations