Annex E
(informative)
Examples
E.2.4 - Segmented Reference Curve
Example overview
A IfcSegmentedReferenceCurve is a curve defined in a “horizontal distance along base curve, deviating elevation” coordinate system. The IfcCurveSegment.ParentCurve defines the change in cross slope between rail heads over the length of the segment. When the IfcCurveSegment.Placement.Location differs from the IfcCurveSegmentPlacement.Location of the next segment (or the IfcSegmentedReferenceCurve.EndPoint for the last segment, if specified), the IfcCurveSegment.ParentCurve also defines the deviating elevation. If the IfcCurveSegment.Placement.Location is the same as for the start of the next segment, the deviating elevation along the length of the segment is constant.
Evaluation of a IfcCurveSegment that is part of a IfcSegmentedReferenceCurve is illustrated with an example. Consider a IfcCurveSegment with a IfcCosineSpiral parent curve. The curve segment has a position of (0.0,0.08,0.0) and an Axis of (0.0, 0.10606,0.99436). The curve segment has a length of 100. The next curve segment has a position of (100.0,0.0,0.0) and an Axis of (0.0, 0.0,1.0). The constant and cosine terms are both 2500.
The parent curve equation is $D(s)=\frac{L}{A_o} + \frac{L}{A_1}cos(\pi \frac{s}{L})$ where $A_0$ is the constant term and $A_1$ is the cosine term.
The deviating elevation at the start of the segment is $D_s=D(0)=0.08$
The deviating elevation at the end of the segment is $D_e=D(100)=0.0$
The deviating elevation at the segment mid-point is $D=\frac{100}{2500}+\frac{100}{2500}cos(\pi \frac{50}{100})=0.04$
The orientation of the Axis at the start of the segment is $\theta_s=tan^{-1}(\frac{0.99436}{0.10606})=1.46454$
The orientation of the Axis at the end of the segment is $\theta_e = tan^{-1}(\frac{1.0}{0.0}) = 1.570796$
The orientation of Axis at the segment mid-point is $\theta = \theta_s + \frac{(\theta_e -\theta_s)}{(D_e - D_s)}(D-D_s)=1.46484+\frac{(1.570796-1.46454)}{(0.0-0.08)}(0.04-0.08)=1.517968$
The slope of the deviating elevation is the derivative of the parent curve.
$slope = -\frac{\pi}{A_1}sin\pi\frac{s}{L} = -\frac{\pi}{2500}sin\pi\frac{50}{100}=-0.0012567$
$slope angle = tan^{-1}(slope) = -0.0012567$
RefDirection = ($cos(slope angle)$, $sin(slope angle)$ ,0.0)
The Z-Direction at the segment mid-point is (0.0, $cos\theta$, $sin\theta$) = $(0.0,0.05234,0.99863)$
The Y-Direction is the cross product of Z-Direction and RefDirection
Axis is the cross product of RefDirection and Y-Direction
Figure E.A shows the deviating elevation of the left rail, right rail, and centerline of track along the length of the segment.
Figure E.B shows the orientation variation of Axis along the length of the segment
Images
IFC-SPF source
ISO-10303-21;
HEADER;
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