Parametric Design using Digital Project

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Parametric Design using Digital Project

• 22. Developable surface

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Developable surface

• a surface with zero Gaussian curvature
• flattened onto a plane without distortion (i.e.
  stretching, compressing, tearing).
• a surface that can be made by transforming a
  plane (i.e. folding, bending, rolling, cutting,
  and gluing).
• A surface that can be unrolled or flattened
  without stretching / with zero deformation
• A ruled surface with a constant or parallel
  normal direction / vector along each ruling
  line (isoparm)
• Tangentially linked planes cones and cylinders

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Gaussian Curvature

• product of the principal curvatures
• Principal curvature
• the minimum and maximum of the curvatures at that
  point of all the curves on the surface passing
  through the point

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Curvature
http//www.geo-texture.com/curvature_what.htm?row2
col2curvature_whatrow2col2.htm
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Curvature
http//www.geo-texture.com/curvature_what.htm?row2
col2curvature_whatrow2col2.htm
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Curvature
http//www.geo-texture.com/curvature_what.htm?row2
col2curvature_whatrow2col2.htm
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Curvature
http//www.geo-texture.com/curvature_what.htm?row2
col2curvature_whatrow2col2.htm
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Blend
Developable Surface
MultiSection
Fill
MultiSectionwith guideline
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Curvature analysis

• Checking curvature of surface
• Min, max, Gaussian curvature
• Preparation
• Set Isoparms on in display
• Set length unit as mm
• Set display mode to material mode
• Adjust value range of curvature

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Isoparametric curves

• Isoparametric curves are line running along the
  surface in the U and V directions
• Isoparametric curves are sometimes called
  isoparms.

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Blend
Developable Surface
MultiSection
Fill
MultiSectionwith guideline
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Blend

• Even though the Blend Surface command is
  generally reserved for an association for
  blending, if a user restricts its implementation
  to just two curves without tangency, a surface
  with a stabile, straight structure will result.
  The isoparametric structure is based upon a
  parallel associativity. The neighboring isoparms
  have an equal distance from each other as per the
  divisions of the driving splines.

http//www.gtwiki.org/mwiki/index.php?titleDiffer
ent_Surfacing_Methods
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Developable surface

• The Developable Surface is a special command that
  optimizes the isoparms through an algorithm so
  that the resultant surface can be unrolled
  without any positive or negative Gaussian
  curvature. The algorithm follows the edge of the
  splines and finds where the perpendiculars are
  identical. Then it produces an isoparm for each
  of these coincidences.

http//www.gtwiki.org/mwiki/index.php?titleDiffer
ent_Surfacing_Methods
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Fill

• The Fill Command is probably the most stabile
  surfacing function in the Digital Project
  interface. It most simulates the behavior of
  cloth and is, in most cases, the antithesis of
  the developable surface. To produce this
  particular example, two guide curves were added
  to make a "Boundary" for which to contain the
  Fill Surface. Real life examples of this behavior
  could describe the material of a tent or soap
  film in a hoop.

http//www.gtwiki.org/mwiki/index.php?titleDiffer
ent_Surfacing_Methods
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Multi section

• Multi-Sectioning takes the profiles' orientation
  into account. When you loft using this command,
  the start directionality of the edge is
  perpendicular spline plane. Isoparm analysis
  displays an even distribution of lines.

http//www.gtwiki.org/mwiki/index.php?titleDiffer
ent_Surfacing_Methods
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Multi section with guide

• If you want to force the directionality of the
  Multi-Section from perpendicular to a direct
  connection, create a guide curve for the Loft.
  Connect the both first points from the spline
  curve startpoints with a typical straight line.
  This scenario does not force the surface to be
  homogeneous with Gaussian analysis, and its
  isoparametric structure is still evenly
  distributed.

http//www.gtwiki.org/mwiki/index.php?titleDiffer
ent_Surfacing_Methods
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Surface patterning with unfold
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