Tuesday, January 24, 2017

NOT entirely subjective !!!


"It" is not entirely subjective as there are some mathematical and geometric truths I have discovered that govern the position of the ellipses and other lines that determine the positions of the facial and head features, that I have established ways of graphically calculating similar to the graphic calculations made in Perspective Projection drawings. These mathematical and geometric truths are far easier to discern in freehand line drawings than they would ever be in a drafting software tool, and are more practical, essential and efficient than any software calculation.

This, I would have thought, would have been taught in animation at Sheridan College, but in fact there was not any understanding of this at that school, to the best of my knowledge.  Evidence of this shortcoming is prominent in the animation of Belle in Beauty and the Beast, although that film was animated before I attended Sheridan College.

The first image is the solution to the problem posed by four of sixteen positions (32 positions if you count both front and back of the sphere) that are problematic due to not being forward or side positions, when the circle of the sphere is divided into 12 positions both horizontally (medians) and vertically (lines of latitude). From these 12 divisions one may extrapolate any further divisions, by thirds or halves.  Fifths are another problem, but can be subjectively assumed to be a leaning toward or away from divisions of these twelve, to not put too fine a point on it.

The second image is examples of those sixteen positions.

An assumption made in generating this solution is that the line between the ears remains level, but rotates around the vertical y axis.
The arrow points out of the nose from the inside of the head indicating the forward direction, the line with the circle on the end indicates a line projecting out the top of the head, and the right and left ear positions are indicated by the "R" and "L".

This solution took several months at about 3 hours per week, requiring about 10 to 15 similar drawings to identify the problem and ask the better questions. I have another book in me, waiting for an opportunity to write and publish, that would include anatomy and comparative anatomy for artists, as well as the geometry of head rotations.

David Foster, 2017-01-24.