On The 2D Shape Metamorphosis And Implement

Morphing (metamorphosis) refers to the process of transforming one shape (the source) into another (the target). This operation is also known variously as shape blending, shape averaging or shape interpolation. It has been widely used in computer graphics, animation, CAD/CAM, advertisement and so on.In this area, though many works have been down, a perfect one is still hardly to find. And commercial software packages which greatly depends on man-machine interaction sometimes yields undesired results. This thesis presents some effective and robust algorithms to resolve the 2D object metamorphosis including polygon morphing and freeform curve metamorphosis. The major works involved are as follows:1. In 2D polygon blending, a method of morphing planar polygons is presented. The source polygon and target polygon are described by the centroid and the lines between centroid and every vertex. According to the lines of centroid and vertex, and angles between the two adjacent lines, a correspondent lengths and angles are interpolated to create interpolation polygons. The algorithm is simple and effective. If the number of vertices of the polygon which has more vertices is n, the algorithm is 0{n2). The advantage of this approach is that it yields intermediate polygons which are closed and have natural shapes.2. Based on the matching method of freeform curves presented by S. Cohen, the correspondent vertex pairs of the two key polygons are established automatically with no manual intervention. The two polygons are converted to multi-resolution representations based on evolution schemes. Intermediate representation is generated from these two, from which intermediate polygons are reconstructed. The algorithm is O(nd), where n is the number of vertices of the polygon which has more vertices andd is the depth of evolution. Because this representation captures the geometric properties of a shape at different levels of detail, the algorithm is robust and really achieves good results.3. hi the freeform curve blending, we focused on the metamorphosis of Bezier curves, there are three algorithms that can be used to generate the intermediate curves employed the matching method of freeform curves. Two of them are also applicable for the general parametric curves. And then we indicate their limitations. Furthermore, an algorithm based on second order derivatives matching and an algorithm based on curvature matching are presented respectively. And then a comparison is made between the three methods above.4. We show that the proposed methods are useful in industrial design, such as the ruled surface which is generated by the affine combination of the two initial curves can be used in surface modeling. And the proposed methods can be extended in various domains, such as the metamorphosis of the two ruled surfaces, the multiple curve blending in which three curves blending is performed as an example, and the morphing of two tensor product surfaces. The results implied the approach is successful and the transformation is smooth.