Geometry

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.
Following geometrical types are available:
Text
Geometry type
Type definition
Insertion data explanation
SAF geometry strings
Notes
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Line
Straight-line between two nodes
Start point , End point
N1;N2
Line
-
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​
Circular Arc
Arch defined with 3 nodes
Start point, Intermediate point, End point
N3;N4;N5
Circular Arc
-
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​
Parabolic Arc
Parabolic arch defined with 3 nodes

Start point, Intermediate point, End point
N6;N7;N8
Parabolic Arc
-
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​
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)
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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
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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

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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)=∑i=03PiBi(t)Q(t)=\sum_{i=0}^{3}P_iB_i(t)Q(t)=∑i=03​Pi​Bi​(t)
 ; tϵ<0,1>t\epsilon<0,1>tϵ<0,1>
 B0t=(1−t)3,B1t=3t(1−t)2,B2t=3t2(1−t),B3t=t3B_{0t}=(1-t)^3,B_{1t}=3t(1-t)^2,B_{2t}=3t^2(1-t),B_{3t}=t^3B0t​=(1−t)3,B1t​=3t(1−t)2,B2t​=3t2(1−t),B3t​=t3
 Q(t)Q(t)Q(t)
 is for the Bezier curve PiP_{i}Pi​
 is for coodinates, and BitB_{it}Bit​
is for basis function
Spline Q(t)=∑i=0mPiNin(t)Q(t)=\sum_{i=0}^{m}P_iN_i^n(t)Q(t)=∑i=0m​Pi​Nin​(t)
 ; tϵ<ti,ti+1>t\epsilon<t_i,t_{i+1}>tϵ<ti​,ti+1​>
 Ni0(t)=1N_i^0(t)=1Ni0​(t)=1
fortϵ<ti,ti+1>t\epsilon<t_i,t_{i+1}>tϵ<ti​,ti+1​>
 Ni0(t)=0N_i^0(t)=0Ni0​(t)=0
otherwise Nik(t)=t−titi+k−tiNik−1(t)+ti+k+1−tti+k+1−ti+1Ni+1k−1(t)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)}Nik(t)=ti+k​−ti​t−ti​​Nik−1​(t)+ti+k+1​−ti+1​ti+k+1​−t​Ni+1k−1​(t)
 Q(t)Q(t)Q(t)
is for the Spline curve PiP_iPi​
is for the coordinates Nin(t)N_i^n(t)Nin​(t)
is for basis function nnn
is for the degree of curve mmm
is for points of the control polygon
Polyline schematics:
1

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

Last modified 1yr ago