Lesson 9: Formulas for the Side View of the Human Head - Phase 1

In Lesson 9, we advance our invention of the human head by mastering Phase 1 of the Side View Formulas. This lesson is about moving beyond basic shapes into what Riven Phoenix describes as "speaking the sentences of the formula." These are logical, step-by-step mapping rules that allow you to construct a realistic skull without a single reference photo.

Flattening the cranial top: Most artists draw the head too round; the formula forces a realistic flat-top transition.

Defining the Cranial Top and Temples

A common mistake in figure drawing is making the skull perfectly spherical. In Lesson 9, we apply a specific formula to "flatten" the top of the cranium. By dividing the top half of our bounding box and mapping a horizontal line, we create the structural plateau where the skull's curve meets the flat area of the temples.

This phase also involves understanding the 95% Conceptual Rule: we don't need to know every microscopic bump on the bone, only the structural "sentences" that define the overall mechanical design. We map the curve of the occipital bone and the transition into the neck with simple subdivisions.

The Eye Socket Formula: Replacing complex anatomy with a simple, repeatable arc mapping.

Simplified Orbits and Cheekbones

Instead of struggling with the complex anatomy of the eye socket, we use a simplified arc formula. By finding the center point of the face box, we map a specific curvature that defines the orbit. This isn't an "organic" guess—it's a mechanical placement that ensures the eye sits correctly within the skeletal foundation.

We then extend this to the zygomatic bone (cheekbone). By connecting the eye socket arc to the jawline at a specific intersection, we define the cheek's structural width. This provides a rigid framework for the muscles of expression to be added in later phases.

Finding the Teeth and Nose: Precise grid intersections define the separation of the jaw and the nasal bone.

The Formulas for the Nose and Mouth

Placing the mouth and nose is no longer a matter of "feeling" the proportions. The formula dictates exactly where the nasal bone ends and the cartilage begins. By dividing the lower-front quarter of the head and mapping a specific descending angle, the structure of the nasal cavity is revealed.

Using these same grid lines, we locate the division of the teeth. This ensures that the mouth is always aligned with the depth of the skull, preventing the "floating mouth" error common in amateur drawings. Every feature is anchored to the bone.

The Hidden Axis: The fundamental tilt of the skull reveals why the eye line sits directly in the middle of a portrait.

The Axis of the Human Skull

The biggest "Aha!" moment of this lesson is discovering the Axis of the Skull. Many artists are taught that the eyes sit in the middle of the head, but they don't know why. Lesson 9 proves this mathematically: when a human looks straight ahead, the skull's structural axis is actually tilted.

By mapping a 90-degree intersection through the skull's center, we see that the tilt of the cranium combined with the depth of the jaw places the eye line at the exact geometric center of the head. Understanding this "invisible axis" allows you to rotate the head in 3D space with total confidence.