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Surfacing : Art or Science

Creating aesthetic shapes is an art (skill), but there are many logical considerations in creating the complex shapes, which make it a science.

Smooth and fair surfaces are required in shipbuilding (reducing water resistance, and fabrication ease), Aeroplanes (aerodynamics), Automobiles (aerodynamics, and styling), Consumer products (styling and ergonomics), Architecture (styling and manufacturability). These are art + science.


Complex surfaces are also required for functionality and performance in Hydraulics (flow through pumps and valves), Power transmission (involute profile), SPMs and packaging machines (scrolls, cam slots), Sheetmetal (developable surfaces), Plastics  (manufacturability). These are pure science.

Product look (styling) is subjective, and it needs lot of innovation. The artistic approach involves Polygonal and SubDivision approaches, which create basic shapes and allow to pull, rotate, twist some portion of it to create desired shape. The artistic approach can be used for models of humans, animals, plants, terrains and consumer products.

Alternately, the styled surfaces can also be conceptualized to be made up from 3D or 2D curves. If the curves are 2D, the plane (principal or oblique) is defined and the curves are drawn. If the curves are 3D, then either two 2D curves on different planes are projected only each other, or a 2D curve is projected on a 3D surface. These curves can be used as profile or guide curves to create the surfaces. The scientific methods to create surfaces are Sweep (one profile curve and many guide curves) or Loft (many profiles curves and many guide curves). There are many variations and controls in both the methods.

Some ways of further modifying the surfaces are freeform dragging of points on the surface, trimming / extending the surfaces, creating ruled surfaces using the surface boundary curves, etc.

Some approaches of styled surface design are : (A) insert image and trace curves, (B) project planar mesh on imported surface and trace the projected curves, (C) view U-V lines on basic surface and drag points to modify the surface.

To practice surfacing as a science, it is good idea to first consider whether the desired surface is Algebraic (flat, cylinder, sphere, conic, toroidal) or Ruled (developable) or Interpolated (NURBS surface has four boundaries as splines, and each point on the surface is defined by iso-parametric U-V mesh curves). Mathematical considerations can prove a be help in surfacing.


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