Sunday, February 5, 2017

Hatching with Frederick Goltzius

Hendrick Goltzius was a German-born Dutch printmaker, draftsman, and painter. He was the leading Dutch engraver of the early Baroque period, noted for his sophisticated technique and the "exuberance" of his compositions. According to A, Hyatt Mayor, Goltzius was the last professional engraver who drew with the authority of a good painter, and the last who invented many pictures for others to copy".
According to Samuel van Hoogstraten, a student and biographer of Rembrandt, it was the master himself that encouraged his students to copy Goltzius engravings as a way to learn how to hatch.

Hatching with Robert Crumb

Illustrated here are various styles of hatching. Some are combinations of hatching techniques distributed to create contrasting effects. In the work of Robert Crumb, for example, the artist hatches a background with perpendicular fine cross hatching and contrasts this with and area of contour hatching, implying different textures. The masterful use of the contrasting hatching textures can create great luminosity and imply color.

Saturday, February 4, 2017

Hatching Topologies for the Artist

A methodology of drawing that emerged over the years as a way to describe form is known as hatching. Hatching is used as a way to organize lines to better communicate the concept of form to the viewer. Hatching is a kind of drawing language, comprised of groups of lines of varying lengths, that often appear as a series of parallel lines which describe the topology of the form in space. Hatching can also be a pattern of shapes that through proximity to one another create the illusion of light on an object- commonly referred to as the light model. All forms of hatching rely on patterns of alignment and orientation to describe how form reflects light thereby creating in the viewer's brain information about how that object occupies space. In this regard, hatching is very much like the matrix of polygons that describe a volume in CAD space, as demonstrated in previous posts.
As a primer, one might consider that there are six types of Hatching modalities.

Contour Hatching

Parallel Hatching

Cross Hatching

Fine Cross Hatching 

Tick Hatching

Basket Hatching

Wednesday, February 1, 2017

Topological strategies of Antony Gormley

These visual metaphors help us to visualize the volume of a figure by creating a virtual manikin in space. We are then able to transduce the visual information into a drawing or painting with a greater sense of that figure's occupancy of space. Consequently, the artist is then less dependent on measuring the contours of the image on the canvas because they can "project" a holographic facsimile of the volume with their visualization skills. 
One example of this is the work of Antony Gormley. The British sculptor fills the volumes of his figures with various forms that range from cubes to tangled wires, to colossal steel grids.Gormley can "see" the human form in space- he senses it's occupancy and displacement. This gives him free reign to experiment with all kinds of materials with which to describe these volumes.

Tuesday, January 31, 2017

The topology of the human form

What is topology?

"Basically, topology is the modern version of geometry, the study of all different sorts of spaces. The thing that distinguishes different kinds of geometry from each other (including topology here as a kind of geometry) is in the kinds of transformations that are allowed before you really consider something changed. (This point of view was first suggested by Felix Klein, a famous German mathematician of the late 1800 and early 1900's.)
In ordinary Euclidean geometry, you can move things around and flip them over, but you can't stretch or bend them. This is called "congruence" in geometry class. Two things are congruent if you can lay one on top of the other in such a way that they exactly match.
In projective geometry, invented during the Renaissance to understand perspective drawing, two things are considered the same if they are both views of the same object. For example, look at a plate on a table from directly above the table, and the plate looks round, like a circle. But walk away a few feet and look at it, and it looks much wider than long, like an ellipse, because of the angle you're at. The ellipse and circle are projectively equivalent.
This is one reason it is hard to learn to draw. The eye and the mind work projectively. They look at this elliptical plate on the table and think it's a circle because they know what happens when you look at things at an angle like that. To learn to draw, you have to learn to draw an ellipse even though your mind is saying `circle' so you can draw what you really see, instead of `what you know it is'.
In topology, any continuous change which can be continuously undone is allowed. So a circle is the same as a triangle or a square because you just `pull on' parts of the circle to make corners and then straighten the sides, to change a circle into a square. Then you just `smooth it out' to turn it back into a circle. These two processes are continuous in the sense that during each of them, nearby points at the start are still nearby at the end." Robert Brunner

More examples of the topology of the human form as mapped with various CAD solutions, i.e, the types of meshes that wrap the geometry. Each kind of mesh has certain parameters that it follows. This is determined by the mathematical algorithm that defines where various coordinates are in space,.For example, a mesh may be perpendicular to the ground plane, or it can be at a designated angle to the ground plane. The mesh is often thought of as being a regular matrix of polygons, projected on or dividing up a volume. The mesh by extension creates a way for the brain to visualize the displacement or occupancy of that volume in space.

Friday, January 20, 2017

Bilateral Symmetry and Congruency

Here are a few more examples of the curious visual phenomena that occur when the inverse surface of the volume ( the inner skin ) flips to look like the obverse or outer skin. This odd mirrored bi-symmetrical flipping occurs through z axis, (into the picture plane) and is illustrated here more clearly by observing the figure with and without hair. Notice that the form flips toward and away along a transverse axis (3/4 point of view.)
This phenomena is commonly referred to as congruency.

Convex or Concave?

Here, the first figure appears to be facing away looking up to the upper right. The lower figure appears to be facing us looking toward the lower right. They are in fact the same figure with and without hair.

Monday, January 16, 2017

From outline to spatial visualization

One visualization strategy is to conceptualize the figure as a mannikin rather than become too enamored of the anatomical details. A generalized approximation of geometry that resembles the masses of the figure emulates how the sculptor builds the volumes. For example, a peanut shape could be analogous with the torso, an ovoid for the head, cylinders for the arms and legs, etc.These primitive geometric forms are more easily mapped in the brain as we shall later find out, and create a volumetric placeholder which is ultimately more accurate than a finely placed contour.
What we are trying to train ourselves to see is the complete form in all its volumetric occupancy.
Illustrated here are CAD renderings of the human figure as groups of polygons that are "skinned" over a volume. From these renderings, it's possible to see more clearly the inner walls of the reverse side of the figure. Also noticeable is how the inner reverse wall exhibits the odd perceptual phenomena of appearing both concave and convex at the same time. Seeing through a wireframe CAD drawing or cross-sectioned rendering allows one to see the bi-symmetrically of the volume very clearly. In this example I sectioned a human figure into two halves along a natural lateral curve, dividing the figure into anterior and posterior halves. Separating the two halves it is possible to see the shell of the hidden back half of the volume.
The last picture illustrates the bi-lateral symmetry in action. I have duplicated the front half and mirrored its symmetry. By comparing the inner shell with the outer shell, it is virtually impossible to tell if the figure is convex or concave.

Convex or Concave???