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This paper proposes a geometrical construction interpretation of variational geometry for achieving parameterized object definition. Vector geometry is used to represent the various kinds of geometrical entities while dimensions are defined to have directional sense. Geometrical constructions are then used to link up all geometrical entities and dimensions of a solid in a meaningful way, to represent the variational geometry properly. The geometrical construction scheme is implemented in a prototype modeller using polyhedral solids as examples.