Exploring the Optimal Curves of Intersection for Enhanced 3D Shape Designing A Comprehensive Study on Geometric Optimization Techniques

Surface and solid intersection is emerging swiftly in many applications of computer graphics, engineering and mathematical models. In engineering science, several algorithms are produced for some unique purposes like intersection of prism/cone, cone/cone, prism/cylinder etc. All such procedures used different 3D drawing tools for creating geometrical interpretation of their required models. Surface intersection deals with numerous algorithms in computational and applied mathematics, needed for intersection of different surfaces such as rational polynomial parametric, implicit algebraic etc. In this paper, a novel surface intersection approach is proposed which works for all types of intersection like; parametric-parametric, explicit-explicit, implicit-explicit surfaces. This scheme includes a method for determination of significant points (boundary and turning points) from surface intersection sequence points. Optimal curve is fitted to these points by rational quadratic spline and a soft computing technique Genetic Algorithm (GA) is applied for attaining optimized curve, by allotting specific shape parameter values in the depiction of rational quadratic spline. However, some experimental results show the efficiency and robustness of this technique.