J₂(x)

Linear Map: (x₁,x₂) ↦ (x₂,-x₁).

areas(P,Q,R)

Area of triangle PQR

areasine(P,Q,R)

Area of triangle PQR weighted by the sine of the interior angle

auto_simp!(R₀,R,tolsmt,tolarea)

Automatic mode for polygon simplification. Subroutine for polygonal regions.

1. Delete points by ϵ-test
2. Polygon smoothing 
3. Delete points by ϵ-test
4. Rounding for digital curves

INPUT: - R₀ data structure of the original region - R data structure of the approximate region - tolsmt smoothing level - tolauto tolerance for automatic mode OUTPUT - nothing, (R is overwritten)

auto_simplification(Ω,tolsmt,tolcol,tolrad)

Automatic mode for polygon simplification. Subroutine for simply connected polygons

del_repts!(R,ltol)

Delete repeated points in a polygon using the length of segments

del_repts(Ω,ltol)

Delete repeated points in a polygon using the length of segments

distseg(a,b,p)

Compute euclidean distance from the segment ab to the point p.

edit_bnd3(plt,tab,R,tlabels,infovec,nH₀)

Routine for interactive edition of polygons by mouse clicks

get_cos(P,Q,R)

Compute cos(Q) in the triangle PQR using the dot product

perim(v)

Compute the perimeter of a simplgety-connected polgetygonal region

radiusine(A,B,C)

Get double product inradius r × circunradius R weighted by the sine of the interior angle

readGEO(A)

Get two-column array of countour points coordinates

from GEO file of GMSH

readPOLY(A)

Get two-column array of countour points coordinates

reverse_orientation!(R)

Reverse orientation of a polygonal region using its triangle areas

reverse_orientation!(Ω)

Reverse orientation of a clockwise oriented polygon using its triangle areas

save_region(R,dirpath)

Save polygonal region in GEO format of GMSH

tol2per(R₀,tol_range)

Get simplification percentages at the given simplification tolerances

INPUT - R₀ contour - tol_range tolerance range

αvec = triangle_areas(R)

Compute the areas of triangles generated by three consecutive vertices of a polygonal region.

triangle_areas(Ω)

Compute the areas of triangles generated by three consecutive vertices of a simple-connected polygon.

αvec == triangleareassorted(R)

Compute the areas of triangles generated by three consecutive vertices of a polygonal region.

The areas are scaled so that their average is equal to one.

α(Ω,p,q,r)

Compute the area of the triangle PQR in polygonal region Ω, where P = Ω[p], Q = Ω[q], R = Ω[r]

α(Ω)

Compute the area of a simply-connected polygonal region Ω: v₁,v₂,...,vₙ.

          ₙ₋₁

α(Ω) = 1/2 ∑ det(vₖ,vₖ₊₁) + 1/2⋅det(vₙ,v₁) ₖ₌₁

α(P,Q,R)

Evaluation of the area functional at the triangle PQR.

∂perim(v)

Let x be the two column arragety of contour coordinates.

Compute the gradient of the contour perimeter

with respect to its coordinates