Description

By themselves, closed curves in FRED have no optical significance (they simply define a path through space).  In FRED, the Aperture Curve Collection construct is used to assign an optical meaning (clear aperture, edge, obscuration, hole) to a collection of closed curves and specify how the curves are combined together using AND/OR logic. 

An example of a surface trimmed by an aperture curve collection

Navigation

An Aperture Curve Collection can be created by selecting the Aperture Curve Collection type in the Create New Curve dialog (see Create - New Curve).

Controls

Application Notes

Aperture Curve Collection rules

•Line and arc segments must be joined together as a Composite Curve prior to specification as an Aperture Curve Collection.

•The curves defining the aperture curve collection must be closed. That is, the end point and the start point are the same and there are no gaps anywhere along the length of the curve.  Curves that are not closed to the precision required by an aperture curve will not be available for selection in the aperture curve GUI.  This scenario is often encountered when using composite curves.

•An aperture curve collection can contain one or more closed curve but the closed curves do not have to be connected.

Definitions of the Aperture Curve Collection usage

Clear Aperture (default) – Keep the area of the surface inside the curve boundary.  In the absence of an Edge specification, the surface is trimmed to the shape specified by the Clear Aperture.  If an Edge is specified, then the Edge becomes the outer boundary of the surface and the Clear Aperture defines the region of the surface that will interact with the incident rays.

Edge – The curve represents the physical outer boundary of the surface. In the absence of a Clear Aperture, any ray striking the surface inside the Edge is halted. When used in conjunction with a Clear Aperture, the following rules apply:

•Rays incident outside of the area delineated by the Edge miss the surface

•Rays incident on the surface area inside of the Edge and outside of the Clear Aperture are halted on the surface

•Rays incident on the surface area inside of both the Edge and the Clear Aperture will interact with the surface according to the Raytrace Control and Coating specifications

Obscuration – Halt all rays incident on the area of the surface that lies inside the curve. This control does not trim the surface.

Hole – The area inside the curve is removed from the surface.   

Group definitions

Curve designations in the Aperture Curve Collection can be grouped together using Group #'s.  Curves in the same group number are logically AND'ed together and different group #'s are OR'ed together.

AND – The resulting surface is the area represented by the intersection (overlap) of all the curves in the group. An annular ring is a Clear Aperture “AND”ed with a Hole.

OR – The resulting surface is the area represented by the union (combination) of all the curves in the group. A segmented surface can be represented by a collection of “OR”ed apertures.

What to do when an aperture curve doesn't look right

Algorithmically, the aperture curve that gets applied to the geometry is determined by walking along the individual base curves with a given sampling.  If you have applied an aperture curve to the geometry and the aperture that is created looks incorrect, it is likely that the default sampling along the curves is insufficient to capture the topology of the curve(s) (i.e. regions of the curve may be "jumped" by the sampling algorithm).  The "Scale Factor" parameter on the Visualization tab of the aperture curve dialog controls the sampling of the curve profile. This value allows you to control how well the curve is sampled, with a value of 1 using the default sampling rate.  A scale factor less than 1 would result in a smaller sampling step size (better sampling of the aperture curve).

If adjusting the visualization properties of the aperture curve still does not result in the expected appearance/behavior, then it is possible that selecting one of the other Algorithms may resolve  the behavior.

Example: Trimming with an Aperture Curve Collection

The following example illustrates the use of an aperture curve collection (Algorithm = Use group numbers) to trim the outer edge of a surface and cut an unusual hole shape through the center.  The reflecting surface to be trimmed is an XY Toroidal Asphere type with a rectangular outer trimming volume.  The aperture curve collection is comprised of two curves: a segmented curve for the inner hole and a composite curve for the outer boundary (clear aperture).

The following steps will be taken to perform the surface trimming operation:

1.Create the base surface

2.Create the outer boundary (composite curve)

3.Create the inner hole (segmented curve)

4.Create the aperture curve collection

5.Trim the surface

Create the base surface

Add a Custom Element to the FRED document.  Right mouse click on the custom element node and select Create a New Surface from the list menu.  On the Surface tab of the surface dialog, select the surface type XY Toroidal Asphere and enter the following parameters:

Name: ellipse reflector

Traceable: Checked

Type: Y toroid

X Rad: 0

Y Rad: -150

Y Conic: -1

Hit Apply to accept these settings.

On the Aperture tab of the surface dialog, enter the following parameters:

Trimming Volume Outer Boundary X-Semi Aperture: 18

Trimming Volume Outer Boundary X-Center: 0

Trimming Volume Outer Boundary Y-Semi Aperture: 30

Trimming Volume Outer Boundary Y-Center: 20

Trimming Volume Outer Boundary Z-Semi Aperture: 15

Trimming Volume Outer Boundary Z-Center: -14

Trimming Volume Outer Boundary Shape: Box

Hit Apply to accept these settings, which specify a rectangular aperture 36 units wide in X centered at X = 0, 60 units wide in Y centered at Y = 20 and 30 units wide in Z centered at Z = -14 with a rectangular trimming volume.

On the Coating/RayControl tab make the following changes:

Assigned Coating: Reflect (100% Reflective Coating)

Assigned Raytrace Control: Reflect Specular (Allow reflected specular ray only)

Ray Colors: Reflect checked, set ray color to red

Hit Apply to accept these settings, then hit OK to close the dialog box.

The base surface should look like the following image in the 3D view (with some Visualization properties changed).

Create the outer boundary

The outer boundary of the surface will be a Composite Curve, which is a connected set of line segments and/or arcs.  Each segment is a separate curve.  FRED parameterizes every curve along its length from 0 to 1 so that every curve, regardless of its shape, begins at u=0 and ends at u=1.  A Composite curve connects multiple segments in the following fashion:

Start₁ > End₁, Start₂ > End₂, … , Start_n > End _n

The end of Curve N must coincide exactly with the start of Curve N+1 in order for the two to join.  FRED re-normalizes the parameterization after joining so that the new curve is fully parameterized from u=0 to u=1.  In order for a Composite curve to be used in an Aperture Curve Collection the composite curve must be ‘closed’, meaning that the end point of Curve N coincides with the start point of Curve 1.

Create a new curve in the custom element of the Circular Arc type with the following parameters entered on the Curve tab:

Name = "semi-circular arc"

Center X = 0

Center Y = 32

Radius = 18

Start Angle = 0

Sweep Angle = 180 

These settings specify a semi-circular arc with a radius of 18 units centered at Y = 32.  The start angle is simply the angle, in degrees, of the starting point of the arc as measured counter-clockwise from the local X axis.  Note that since the arc is not centered in the local coordinate system, the starting point will be physically located at (X,Y) = (18,32).  The sweep angle is the angle subtended by the arc, in degrees, beginning at the start angle.  Both the sweep angle and the start angle can take any value between 0 and 360 degrees.

On the Visualization tab of the dialog, check the Draw box to render the curve in the selected color.

Click OK to accept the changes and close the dialog box.

The remaining three curves that will be used in the Composite curve are all line segments.  Create a new curve in the custom element node of type "Line segment" with the following properties:

Name = "-x"

X Start = -18

X End = -18

Y Start = 32

Y End = 5

Z Start = 0

Z End = 0

Note that the start of the line segment is coincident with the end of the semi-circular arc created previously (at X=-18, Y=32).  Make the curve visible (check Draw on the Visualization tab), and click OK to accept the changes and close the dialog.

Create (and draw) another curve in the custom element node of type "Line segment" with the following properties:

Name = "bottom segment"

X Start = -18

X End = 18

Y Start = 5

Y End = 5

Z Start = 0

Z End = 0

Create (and draw) the last curve in the custom element node of type "Line segment" with the following properties:

Name = "+x"

X Start = 18

X End = 18

Y Start = 5

Y End = 32

Z Start = 0

Z End = 0

The four curves just created, the Circular Arc and the three line segments, should appear in the 3D View as shown below.

Finally a Composite Curve that combines the Circular Arc and the three Line Segments into a single closed curve to be used in the Aperture Curve Collection.

Create a new curve in the custom element node of type Composite Curve named "outer composite".  In the Curve Designation list select the curve named "semi-circular arc".  Add the remaining three line segments in the following order, "-x", "bottom segment" and "+x".  Adding the curves in this order guarantees that they form a closed composite curve.

NOTE: The end of each curve must coincide exactly with the start of the subsequent curve in order for FRED to create a composite curve. If this condition is not met, then FRED pops up a warning dialog and omits the curve in question from the final construction.

NOTE: Checking the Reverse Sense box switches the start and end points of the curve in question, as may be required to successfully connect adjacent curves.

TIP: To avoid inadvertently separating the curves at some later time, either make the coordinate system of every curve in the referenced list coincident with the coordinate system of the composite curve, or put all the curves, including the composite curve, into the same coordinate system.

Create the inner hole

The hole in the center of the surface will be defined using a Segmented curve type. This curve consists of a collection of (X,Y,Z) points connected by simple line segments and can used, for example, to create a square or a rectangle. The data points can be entered manually in the curve dialog, read from an ASCII text file containing rows of (X,Y,Z) coordinates or created using the Generate Points utility available from the list menu opened by right mouse clicking in the spreadsheet area for entering points.  The manual entry will be used in this example.

Create a new curve in the custom element node of type "Segmented (points connected by line segments) with the name "inner segmented".

By default, the curve is created with two points pre-defined. Add four more rows by right mouse clicking inside the spreadsheet area and selecting the Append Point option from the list menu to create a total of six points.  When all the rows have been added, enter the following values for the (X,Y,Z) coordinates:

Point 1: (-6,10,0)

Point 2: (6,10,0)

Point 3: (6,16,0)

Point 4: (0,20,0)

Point 5: (-6,16,10)

Point 6: (-6,10,0)

NOTE: In order to fully enclose an area with a segmented curve, the start and end coordinates must be the same.

Check the Draw box on the Visualization tab and then hit OK to accept the settings and close the dialog box.  The outer and inner curves should look like the following figure in the 3D View.

Create the Aperture Curve Collection

Now create the Aperture Curve Collection using both the composite curve, "outer composite", and the segmented curve, "inner segmented".  Create a new curve in the custom element node of type Aperture curve collection and name it "aperture collection".

Internally, FRED uses the Aperture curve collection to create an extruded surface that modifies the boundaries of the surface to be trimmed.  In this example the curve extrusion method is "The collection curve’s local Z-axis" and the Algorithm is, "Use group numbers". NOTE: the extrusion is never rendered or raytraced, it is only used to project the member curves onto the surface where the Aperture Curve Collection is applied as a trimming designation. 

Use the entity picker in the Curve Designation list to select the curve "outer composite".  NOTE: FRED will only list closed curves in this dialog.   Append a new row by right clicking in the spreadsheet area and selecting Append Curve Row from the list menu. Once again, use the entity picker in the Curve Designation list to select the curve "inner segmented" from the list menu.

Set the "inner segmented" curve usage to "Hole".  The "outer composite" curve usage should be set to "Clear Aperture"

Notice that the group number for the two curves is the same, meaning that their operations will be “AND”ed together.  In this combination FRED will keep the area outside of the "Hole" and inside of the "Clear Aperture".

Select OK to keep these settings and close the dialog box.

Trim the surface with the Aperture Collection Curve

At this point the Aperture Curve Collection can now be used to trim the surface created in the first step of of this example.

Double click on the surface node in the object tree view to Edit/View the surface definition.  On the Aperture tab in Trimming Surface Specification section's Operation list, right mouse click and choose "Select Entity" from the list menu to initiate the object picker.  Using the object picker, select the Aperture Collection Curve.  Hit OK to accept the settings and close the dialog box.

The trimmed surface should now look like the following in the 3D View.

Related Topics

Curve and Curve-based Surfaces

Curves and Curve-based Surfaces

Surface - Apertures, Trimming Volumes and Trimming Surfaces