Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Geometric concepts for geometric design
Geometric concepts for geometric design
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Polynomial curves controlled by points as well as by the tangents in them allow for a great margin of freedom, far from the conditions implied by the use of conventional curves, in the design of free-form curves. The lofting technique, in turn, permits us to generate surfaces that include a series of given curves. The algorithms propitiated to generate these curves and surfaces are very suitable for the geometric design of the arch dam, since they provide for a design of the curves forming the horizontal arches in which the dam can conceivably be divided taking into account, besides, the angle among the tangents to the arch at its ends as well as the hillsides of the closed arch. Once these curves are designed, the facings of a dam can be generated as the surfaces involving both series of previous curves. This paper presents the geometric calculations behind the generation of both surfaces and their computerized processing, in addition to a practical example of the use of the proposed methodology.