Geometry

Basic construction elements are simple geometry types, that are used for shape definition of structural members and geometrical object. With defining the further attributes to these elements from the lists Structural analysis elements, Supports and hinges and Loads the complete structural model is created. All values refer to the list StrucutralPointConnection.

Geometry types

	Geometry type	Type definition	Insertion data explanation	SAF geometry strings	Notes
	Line	Straight-line between two nodes	Start point , End point N1;N2	Line	-
	Circular Arc	Arch defined with 3 nodes	Start point, Intermediate point, End point N3;N4;N5	Circular Arc	-
	Parabolic Arc	Parabolic arch defined with 3 nodes	Start point, Intermediate point, End point N6;N7;N8	Parabolic Arc	-
	Bezier	Cubic Bezier curve	Start point, 2nd point of control polygon (vertex), 3rd point of control polygon (vertex), End point N9;Vertex_B1_1; Vertex_B1_2;N10	Bezier	N9 and N10 stands for start and end node Vertex_B1_1, Vertex_B1_2 define vertexes of bezier curve All values refers to list StrucutralPointConnection Bezier curve is parabolic, when 2nd and 3rd control points are the identical (values of coordinates are the same)
	Spline	Curved line defined by polynomial function	Start point, Set of mid points, End point N11;N12;N13;N14; N15;N16;N17;N18	Spline-8	“Spline-#” where “#” stands for number of nodes defining the spline
	Circle	Circle	Center Point, Point on the perimeter N36;N37 Or Three point on perimeter N36;N37;N38	Circle and Point or Circle by 3 points	Circle is not valid to define StrucutralCurveMember
	Polyline	Combination of in nodes connected geometric types	List of nodes N21;N22;N23;N24;N25; N26;N27;N28;N29;N30; N31;N32;N33;Vertex_B1_1; VertexB_1_2;N34;N35	Line;Line;Spline-7;Line;Circular Arc;Line;Bezier;Line	Detail explanation can be found in notes below

Notes

Mathematical definitions:

• Bezier
  \(Q(t)=\sum_{i=0}^{3}P_iB_i(t)\) ; \(t\epsilon<0,1>\)
  \(B_{0t}=(1-t)^3,B_{1t}=3t(1-t)^2,B_{2t}=3t^2(1-t),B_{3t}=t^3\)
  \(Q(t)\) is for the Bezier curve
  \(P_{i}\) is for coodinates, and
  \(B_{it}\) is for basis function
  
  

• Spline
  \(Q(t)=\sum_{i=0}^{m}P_iN_i^n(t)\) ; \(t\epsilon<t_i,t_{i+1}>\)
  \(N_i^0(t)=1\) for \(t\epsilon<t_i,t_{i+1}>\)
  \(N_i^0(t)=0\) otherwise
  \(N{i}^{k}{(t)}=\frac{t-t_i}{t_{i+k}-t_i}N_{i}^{k-1}{(t)}+\frac{t_{i+k+1}-t}{t_{i+k+1}-t_{i+1}}N_{i+1}^{k-1}{(t)}\)
  \(Q(t)\) is for the Spline curve
  \(P_i\) is for the coordinates
  \(N_i^n(t)\) is for basis function
  \(n\) is for the degree of curve
  \(m\) is for points of the control polygon
  

Polyline schematics: