This paper aims to provide a series of new methods for projecting a three-dimensional (3D) object onto a free-form surface. The projection algorithms presented can be divided into three types, namely, orthogonal, perspective and parallel projection.
For parametric surfaces, the computing strategy of the algorithm is to obtain an approximate solution by using a geometric algorithm, then improve the accuracy of the approximate solution using the Newton–Raphson iteration. For perspective projection and parallel projection on an implicit surface, the strategy replaces Newton–Raphson iteration by multi-segment tracing. The implementation takes two mesh objects as an example of calculating an image projected onto parametric and implicit surfaces. Moreover, a comparison is made for orthogonal projections with Hu’s and Liu’s methods.
The results show that the new method can solve the 3D objects projection problem in an effective manner. For orthogonal projection, the time taken by the new method is substantially less than that required for Hu’s method. The new method is also more accurate and faster than Liu’s approach, particularly when the 3D object has a large number of points.
The algorithms presented in this paper can be applied in many industrial applications such as computer aided design, computer graphics and computer vision.
