A controlled polygon plotter procedure

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A controlled polygon plotter procedure

• Dr. Lajos Szilassi and László Kóródi University
  of Szeged,Hungary

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A controlled polygon plotter procedure

• CAS have a serious shortcoming in displaying of
  polygons.

The algorithm that decomposes the polygons (given
by the list of vertices) into triangles obtained
by the diagonals started out from the first
vertex and displays these triangles without any
further examinations.
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A controlled polygon plotter procedure
Lets see the following polygon.

• If we dont use color, we cant see any problem
  in the displaying.

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A controlled polygon plotter procedure

• If we use color, we can see what is the problem
  with the plotting of a nonconvex polygon.

• We show some cases when the decomposition of the
  polygon gives wrong result.

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A controlled polygon plotter procedure

• If we give the vertex A at first, then the
  MAPLE tries to decompose the polygon into
  triangles from the vertex A.

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A controlled polygon plotter procedure

• If we give the vertex B at first, then the
  MAPLE tries to decompose the polygon into
  triangles from the vertex B.

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A controlled polygon plotter procedure

• If we give the vertex D at first, then the
  MAPLE tries to decompose the polygon into
  triangles from the vertex D.

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A controlled polygon plotter procedure

• If we give the vertex F at first, then the
  MAPLE tries to decompose the polygon into
  triangles from the vertex F.

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A controlled polygon plotter procedure

• This would be a right decomposition.

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A controlled polygon plotter procedure

• In the three dimensional space the situation is
  similar, but there are further problems

The CAS dont check that
- the first three points determine a plane.
- all subsequent vertices belong to the same
plane.
- the ordered sequence of vertices forms a simple
polygon.
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A controlled polygon plotter procedure

• In order to eliminate these shortcomings we have
  created two procedures cpolygonplot and
  cpolygonplot3d

The first of them works in 2D.
The second of them works in 3D.
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A controlled polygon plotter procedure

• Lets see the details of the first procedure.

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A controlled polygon plotter procedure

• The cpolygonplot procedure contains the following
  main procedures
• Disjunct It tests that two given segments has
  a intersecting point.
• Simple It tests that the given points
  determine a simple polygon.
• Out It tests that if the points A,B,C are
  given and determine a triangle, then a point P is
  out of the triangle.

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A controlled polygon plotter procedure

• The procedure Disjunct
• In this case the output of the procedure is
  true.

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A controlled polygon plotter procedure

• The procedure Disjunct
• In this case the output of the procedure is
  true.

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A controlled polygon plotter procedure

• The procedure Disjunct
• In this case the output of the procedure is
  false.

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A controlled polygon plotter procedure

• The procedure Disjunct
• In this case the output of the procedure is
  false.

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A controlled polygon plotter procedure

• The procedure Simple
• In this case the output of the procedure is
  false and procedure gives the vertices of the
  intersecting edges.

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A controlled polygon plotter procedure

• The procedure Outer
• In this case the output of the procedure is
  true.

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A controlled polygon plotter procedure

• The procedure Outer
• In this case the output of the procedure is
  false.

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A controlled polygon plotter procedure

• Lets see the details of the second procedure.

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A controlled polygon plotter procedure

• The cpolygonplot3d procedure contains the
  following main procedures
• Disjunctive
• Simple
• Outer
• Comp test that the first three points determine
  a plane and all subsequent points belong to the
  same plane.

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A controlled polygon plotter procedure

• Thank you for the attention.