January 2008 Archives

Cache's definition of inflection contradicts mathematical terminology in that it is not a transition through a smooth point, but either a smooth point or a singular point. He further contradicts mathematical definitions when he states that inflection is never the product of a reflection but rather two separate entities: concave curvature and convex curvature.
















Cache's inflection is produced when any concave curve meets any convex curve at any junction.  It is not a reflection because concave and convex are separate entities.




Mathematically speaking, the curves that meet at an inflection point could be the product of a reflection or a variety of other transformations.

This is the exterior inflecting pleating pattern. I want to begin manipulating it so that it articulates the form of the surface it is navigating, as in the bodice of the pink Versace gown I had discussed previously.

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When the stitches are gathered, to return the structural pattern to a consistent scale, the outcome is a fabric manipulation with a graded density. When used as a wall the densities can be used in the service of structure and light modulation.

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When the stitches are gathered, to return the structural pattern to a consistent scale, the outcome is a fabric manipulation with a graded density. When used as a wall the densities can be used in the service of structure and light modulation.

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This chart defines the formal hierarchies for the different types of spaces.

 

The following charts provide two possible formal approaches for the spaces. The oval elements that define the spaces are cut into segments which work together to create a hierarchy of glamorous entrance, enclosure, and exit. Two different methods were employed to join the corresponding sets of curves.

1. The first set uses parallel tangency to create a connection between the curving elements. This creates a connection through a smooth point (mathematical inflection).

 

   

   

 

 

2. The second set uses a hierarchy of tangential angles to connect the elements. This creates a connection through a smooth or singular point (Cache's inflection).

 

    

 

From what I understand of the Cache text he seems to be using the term inflection somewhat loosely, or perhaps with reference to another philosopher's work. Cache uses the term inflection to define any curve that changes from being concave to convex. This is not the case in the mathematical definition of the term inflection.

Mathematically speaking the inflection point is a point on a curve at which the curvature changes sign via a smooth transition. The curve changes from being positive curvature to a negative curvature, or vice versa. For example when driving a vehicle along a curve, the point of inflection is a moment at which the steering-wheel is momentarily straight, being turned from left to right or right to left.

Cache's inflection rococo changes curvature from concave to convex but not at a smooth point. It changes at a singular point (one which is not smooth) so therefore it is not mathematical inflection.

 

Mathematical inflection occurs only through a smooth point. Cache's inflection occurs through a smooth point or a or a singular point.

 

 

  

 

When an oval is divided at equal lengths along its perimeter, it becomes clear that because of its irregular shape its dividing lines produce spaces with differing angles.

If a person travels along the edge of the oval at a fixed speed they will cover more ground (more angles), in some areas, in the same amount of time that it would take them to traverse another part of the oval.  

I am going to infer that this is why baroque architects thought the area, surrounding and including that which is parallel to the maximum axis, facilitated circulation. Taking this into account, I am going to define my spaces so that the most glamorous moments take place in the slow parts of the curvature; parallel to the minimum axis, where the angles are smaller. This could be a way to generate a dramatic entrance or to create a glamorous focus within a space.

The slowness of the segments of the oval with smaller angles, is also supported by the fact that they have larger areas, than the segments created with larger angles. As a result, these areas take longer to move through.  

 

 

This was an experiment with a different type of plaster. This one dries as hard as stone. The idea behind using this was that because the plaster dried so hard, it would produce a detailed, delicate cast but it would be easy to remove the waxed fabric from the mold using a heat gun. The heat gun would soften the wax and then it would easily be able to come loose from the mold without damaging the plaster. Not the case...because of the complexity of the form and the hardness of the plaster, the cast is gripping the fabric quite tightly and the fabric is very much stuck :P

One solution may be to apply a thin coat of oil to the the waxed fabric next time.