| This thesis presents a computational method for mesh-based free-form functional surface design that consists of two surface design schemes: the V-spring scheme and the selective scheme. The two schemes are targeted for two different design issues: generating surfaces of minimized mean curvature variation and addressing the dilemma of reducing curvature and area.; The first scheme—the V-spring scheme—creates surfaces of minimized mean curvature variation. The displacement of a vertex is determined by a V-shaped spring which is formed by the vertex and each of its adjacent vertices. The spring length of the V-spring is an approximation of the radius of normal curvature associated with the adjacent vertex. By keeping equal the two spring lengths of a V-spring, and thus minimizing the variation in normal curvature, the mean curvature variation, which is the mean value of all the normal curvatures, is minimized. The V-spring scheme is especially suitable for generating specific functional surfaces such as fillets, which are of constant mean curvature.; The goal of the second scheme—the selective scheme—is to create a surface that satisfies two often contradictory demands in surface design: reducing area and reducing curvature. Decreasing the area reduces the material cost, and in most cases, improves overall performance, due to the reduced weight. Area-minimized shapes, however, often include cusps or sharp ridges, which cause manufacturing difficulties and undesirable stress concentration. Although conventional smoothing operators can eliminate cusps and ridges by reducing the surface curvature, they also increase the surface area as a by-product. The selective scheme addresses the two contradictory demands by selectively applying a curvature reduction operator to the large curvature regions, while applying an area reduction operator to the entire surface. The selective scheme also provides flexibility for surface design by allowing the user to specify the curvature threshold, or the allowable maximum principal curvature.; The industrial applications of the two surface design schemes are demonstrated. The V-spring scheme is used for generating fillets. Its versatility is exemplified in three different fillets. The selective scheme is applied to the design of an automobile structural part. The result shows that, compared to other fairing schemes applied on the entire surface, the selective scheme smooths out large curvature regions and effectively reduces surface area. With these industrial applications, the two surface design schemes show promise for extensive uses in the future. |
