Already in the Portrait of Oswolt Krel, whose head is circumscribed by a parallelogram, there is an indication that Dürer also made use of planar basic geometric figures for describing forms.
The head in the Berlin Portrait of a Young Venetian Woman, for example, is circumscribed by a square, and a rectangle with an oval inscribed within it shapes the form of the head of The Moorish Woman Katherina in Florence.
A section of the head square of the unknown Venetian woman is separated by a line that runs from the upper left to the middle of the lower edge of the image, grazing the cheekbone and the chin. Striking on this portrait is the frequency with which Dürer deployed compass strokes – shown as arrows (with the radius of the inner circle, shown as a dotted black line) – to determine position and create forms.
In the case of The Moorish Woman Katherina, the quadrilateral is bound much more closely – at several points of intersection – to the linear grid of nine fields. The oval is perfectly embedded within it and closely determines the curve of her face and the tight bonnet. Various relationships of equivalence complement this portrait of a servant of a royal trade representative, whom Dürer met on his trip to the Netherlands (1520–21).
The crown is measured in accordance with the width of the mouth, and the distance between the inner corners of the eyes can be found again in several places. Thus, doubts whether this work is in fact an example of a spontaneously captured verisimilitude (“ricerca della verosimiglianza”) are reasonable. Giovanni Maria Fara stated Dürer’s “preciso interesse non lascia spazio ad alcuna idealità”. 
Dürer himself noted, “der moren angesicht sind gar selten hübsch an zw sehen” (the Moorish faces are seldom pretty to behold) and that there was little shapeliness to their bodies.  Apparently a scarcely noticeable measurement-aesthetic correction underlies the different physiognomy of the dark-skinned woman, which Dürer studied inquisitively. 
Dürer’s drawing The Architect Hieronymus of Augsburg, in Berlin, represents a special case, which was part of the preparatory work for the Feast of the Rose Garlands. It was produced during Dürer’s second trip to Italy, the same year as the Venetian woman, but with a greater emphasis on the circle.
Dürer used several of these as construction lines for the portrait of the architect: Not only is the upper head circular in shape, but the artist also used circles to determine the extensions of one cheek, the chin, the hair in the neck and to place individual elements in the face.
 Giovanni Maria FARA, cat. No. I.8 ‘Albrecht Dürer, La mora Caterina, 1521’, in exhib. cat. Dürer e l'Italia, Scuderie del
Quirinale / Rome, 10 March–10 June, 2007, ed. by Kristina Herrmann Fiore (Milan, 2007), 81–87, here 117.
 Hans RUPPRICH, Dürer. Schriftlicher Nachlass, vol. 2 (Berlin, 1966), 459.
 FARA, La mora Caterina, 117.