Artistic Representation of Facial Expressions

It is well known that many find themselves confused.
Since we know that most people rely on guessing, using examples from other masters, or only follow the guidance of their own eyes in life, we do not doubt in any way that an honest practitioner of art would gladly acknowledge that when asked to depict a face, where the head is at a specific angle, leaning forward or backward, they would struggle to do so accurately without a fixed rule. This rule would guide the depiction of the oval shortening and the crossing alignment, ensuring accuracy. In this method that I've provided, it is important to note that the accidental tilting of the head, forward or backward, viewed directly from the front, is most characteristic of a certain type. Regarding such facial depictions, one must pay particular attention to the shrinking or shortening circumference of the oval, and the curvature of the arc or horizontal circle of the face, which belongs to the cross of the face. The rest can be done easily with the help of side views; and those views are direct from the front, as we will notice in this part.
Let us then, for the aforementioned proposal, according to the first draft of this accidental facial representation, draw an oval as in Sketch A B C D, divided as you see by a straight-angled cross A C.B.D. You want to depict a face in this same manner, where the head is tilted forward...

Mathematical Facial Representation of a head tilted randomly forward or backward, viewed directly from the front,

Translation Notes

- Tronie: In this context, it refers to a depiction or portrait specifically addressing facial expressions.
- Ovaal (Oval): This refers to the shape that is the basis for constructing the face in art.
- Kruys (Cross): This refers to spatial alignment guides used in artistic depictions.