Resumen de Optimal bases of spaces with trigonometric functions

Jesús Miguel Carnicer , Esmeralda Mainar Maza , Juan Manuel Peña Fernández

• We present a procedure to obtain the normalized B-basis, that is, the basis with optimal shape preserving properties of a space. We illustrate this construction with the space ¯ T1/2 generated by 1, t, cos t, sin t, cos(t/2), sin(t/2). We also obtain the control polygons for the representation of complete cycloidal arcs, cardioids, deltoids, Descartes' trifolium and the lima¿con of Pascal.