José F. M. Morgado

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In 1960, José Morgado gave a necessary and sufficient condition on a poset P in order that closure operators on P , ordered pointwise, form a complete lattice. This result was based on a notion of relative quasi-infimum in posets. This note shows that Morgado's result is flawed. One important issue of the research on closure operators (closures for short)(More)
Graphics systems usually have primitives for rendering straight-line segments, circles, Bézier curves and surfaces. However, they do not have generalized primitives for implicit curves and surfaces. This is so because current algorithms have serious difficulties in dealing with differential singularities (e.g. self-intersections). This paper is about a(More)
Mathematical systems (e.g., Mathematica, Maple, Matlab, and DPGraph) easily plot planar algebraic curves implicitly defined by polynomial functions. However, these systems, and most algorithms found in the literature, cannot draw many implicit curves correctly; in particular, those with singularities (self-intersections, cusps, and isolated points). They do(More)
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