Abstract
This chapter focuses on computational geometry. Geometric information means data points or characteristic polygons that determine certain geometric objects, such as curves on a plane or surfaces in space. In mathematical lofting for ship bodies, derivatives specified at the end-points of the spline curve represent information for the curve. To investigate whether there are loops, cusps, or unwanted inflection-points on the curve is referred to as analysis and synthesis. Computational geometry is closely related to “computer aided geometric design.” The objects studied in computational geometry are curves and surfaces. In geometric design, a surface is generally divided into several patches such that each boundary shared by two adjacent patches is a plane curve and such that the projection of four boundaries of each patch into the xy-plane forms a rectangle. Techniques of interpolation and approximation are frequently applied to curves and surfaces. Properties of geometric shapes are different from those of functions, and ordinary techniques for interpolation and approximation of functions may not be suitable for geometric shapes.
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