C-Edge via Vector Equation (3-D)

You can also use vector equations to define composite edges, the support points being connected with lines oder circular arcs , depending on the respective function.

Vector equation

Sketch > Draw > Freehand > Vector equation

The support points are connected by means of lines here. To construct the composite edge, for each of the x-, y- and z-components separately either a parametric equation with parameter T is specified or a composite edge the x-, y- or z-coordinate of which is adopted is identified.

Approximated helixes with 5 windings, 50 segments and start angle 0 (between number of points and x-axis)
(1) Segment, (2) Average winding diameter, (3) Height, (4) Number of points

You need to specify each of the equations for the x-, y and z-component in turn, depending on T.

The following parameters are relevant for the helix:

r	Average winding radius
a1	Number of windings
t1	Height of the helix
i1	Number of points (= number of segments +1)
w	Start angle

This gives rise to the central angle of the segment: a=a1*360/i1

For the helix T can be defined as an increment in the direction of the z-axis.

T=t1/i1, =a2*T with a2=a1*360/t1

If a start angle w is taken into account, the following vector equations result:

X(T)=r*cos(w + ), Y(T)=r*sin(w + ), Z(T)=T

Next, the scope and the increment need to be specified for T, e.g..

Initial value=0, increment=t1/i1, end value=t1

You can also identify composite edges the x/y/z-positions of which are used instead of a formula for x/y/z. In so doing, you need to make sure of the same number of points and the orientation of the composite edges. Composite edges are treated like polylines in this case, i.e. only the start and end points are considered.

This method allows composite edges to be averaged and to be created from drafts. It is usually worthwhile to combine the parametric equations and the scope in a HiCAD macro, thus enabling the values for the input parameters to be varied.

Macro for helix creation

The figure shows helixes for different input values that have been created with the macro:

Variant	1	2	3	4
Average winding radius	50	50	50	50
Number of windings	5	5	5	5
Height	100	100	100	100
Number bof segments	10	5	20	300
Start angle	0	90	180	0

Variant 2 has "degenerated" into a straight-line composite edge consisting of 5 segments (points bound the segments), variant 1 into a zigzag line and variant 4 shows a very well approximated helix of 300 segments.

Circular vector equation

Sketch > Draw > Freehand > Circular vector equation

In contrast to the Vector equation function, 2 circular arcs that merge into one another tangentially are calculated at each of the support points here.

You can apply the specifications for the vector equation in the same way to the circle vector equation - except for parameter w. This gives rise to the following vector equations: X(T)=r*cos( ), Y(T)=r*sin( ), Z(T)=T Y(T)=r*sin(), Z(T)=T