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# Sketch splines

1. 1. Work with splines

2D and 3D splines are curves of constantly changing radius. Inventor supports two types of splines: interpolation and control vertex. Interpolation splines pass through a series of points. Control vertex splines are defined by a control frame which influences the spline curves.

There are two spline commands, one for each type of spline. The type of spline that is created is determined by the command you select. After a spline is created, you can change the type of spline in the right-click menu.

Interpolation splines

For visual separation, spline endpoints are square, and spline fit points along the curve are diamond shaped.

If the spline Fit Method is set to Standard (default setting) or Minimum energy, you can manipulate the handles displayed in a passive state at each point to shape the curve. A 3D spline contains a tangent handle but does not have curvature or flatness controls.

If the Fit Method is set to AutoCAD, the spline does not have handles. A spline using the AutoCAD fit method is not suitable for creating class A surfaces.

You can partially or fully constrain spline points by either inferring constraints to existing geometry as you draw the curve, or by adding constraints and dimensions later.

Determine a fit method

You can choose how the spline data points are fit along the spline by right-clicking a spline, and then choosing Fit Method. Choose between Standard (the default method), AutoCAD , and Minimum Energy .

A basic understanding of curve terminology is required in order to choose the fit method that will provide the best results. The continuity described in the following section is the result of joining two or more curves or faces together and applying constraints or fillets to smooth the transition as required.

Curvature is a mathematical indication of the smoothness between two curves or surfaces. The rate of change of direction is called curvature. The smoothness of a curve is specified by the letter G and followed by a number.

 G0 G0 (point) continuity means the endpoints touch. The transition between the two edges or surfaces is noticeable. It can be a sharp or gradual transition. For example, a reflection in one surface disappears at the boundary and a different reflection appears in the next surface.  The following image shows a Zebra Analysis of a G0 intersection between two faces. The faces meet, but no fillet exists to smooth the transition. The stripes do not line up and there is an abrupt change between the faces. G1 G1 (tangent) continuity is a smooth transition between curves. The two curves or surfaces appear to be traveling in the same direction at the join, but the rate of curvature change (speed) is noticeable.  For example, a reflection spans two surfaces but there is a visible edge at the boundary.  The following image shows a Zebra Analysis of a G1 intersection between two faces. A tangent fillet exists between the faces. The stripes meet, but the transition between the faces is sharp and angular. G2 G2 (curvature) continuity is a very smooth transition between curves. The two curves match at the endpoints, are tangent, and have the same "speed" (curvature) at the join.  For example, a reflection appears in both surfaces with no obvious boundary.  The following image shows a Zebra Analysis of a G2 intersection between two faces. A Smooth (G2) fillet exists between the faces. The stripes meet and the transition between faces is smooth with no detectable boundary. G3 G3 (curvature with constant rate of change) continuity is the same as G2, plus the rate of change in the curvature matches between the curves. This is an even smoother transition with no detectable boundaries. Class A surfaces require G3 or higher continuity.  For example, a reflection shows no detectable boundary changes between two surfaces with a high gloss finish in bright lights.

The following images show a spline using the same fit points solved using each of the different fit methods. The Standard and the Minimum Energy fit methods are suitable for creating Class A surfaces. The AutoCAD fit method is not suitable for creating Class A surfaces. The spline curvature comb (Display Curvature) is on to show the smoothness of each curve. The curvature comb display has no relation to the number of fit points or control points in the spline. The smaller graphic in each image depicts the complexity of an extruded surface created from the spline using each fit method. The surface lines (U,V) are not visible in Inventor.

 Standard mathematical fit method AutoCAD polyline fit method Minimum Energy mathematical fit method

This table compares spline fit methods:

 Characteristic Standard AutoCAD Minimum Energy Minimum continuity G3 G2 G3 Suitable for class A surface Yes No Yes Supports tangents at endpoints Yes Yes Yes Supports tangent handles Yes No Yes Supports curvature handles Yes No Yes Moves unconstrained internal points to maintain styling intent Yes No Yes Distributes curvature and tension over the entire spline No No Yes Allows tension control No (see Note below) No (see Note below) Yes Matches fit point splines created by AutoCAD No Yes No Creates large amount of data No No Yes
NoteThe spline tension control slider is available for all splines. Adjusting the spline tension automatically converts the spline to a Minimum Energy fit method.
TipTo visualize the differences among the three methods, right-click the spline and select Display Curvature to turn on the curvature comb of the spline.

Splines created using the Standard or Minimum Energy fit method can be manipulated with handles. When you create a spline using either of these fit methods, the tangent handle is displayed in a passive state at each fit point. A passive handle does not affect the spline shape.

You can manipulate the spline fit points or add dimensions to them without using the tangent handles.

Activate a handle with a press and drag on a passive handle or right-click on a fit point and choose Activate Handle from the context menu.

Right-click on a fit point to enable the Curvature or the Flat option from the context menu. If you enable Curvature, you can place a radial dimension on a fit point. If you enable Flat, the curvature is set to zero at the fit point.

You can apply constraints to handles to specify relationships to other geometry.

• Use the context menu to enable or disable handle options.
• Use the context menu option Reset Handle to reverse a handle edit.
• Use the context menu option Reset All Handles to restore the spline to the original solve state.

Offset splines

The Offset command on the Sketch tab offsets geometry from an ellipse or trimmed ellipse. Use this technique to represent a uniform wall thickness.

When using Offset, the selection point on the ellipse determines the offset geometry type: a mathematical ellipse or an associative spline offset equidistant from the ellipse.

The Offset command has two default settings that affect the results of an offset ellipse:

• Loop Select chooses closed loops.
• Constrain Offset constrains the distance between the offset geometry and the original ellipse to be equidistant.

Control vertex splines

Control vertex splines are defined specifying control vertices. Adjusting the shape of a spline by moving control vertices often provides more predicable results than using fit points.

The control frame of the spline is displayed with the construction line style. The control vertices are displayed as circles.

You can constrain spline endpoints, the control frame, or the spline itself. You can dimension spline endpoints and the control frame.

Using the control frame to adjust spline curvature

Control vertex splines can be manipulated with the control frame. When the spline is created, the control frame is displayed as construction lines.

You can drag the vertices of the control frame to change the shape.

You can drag the lines of the control frame to change the shape.

Visualize spline curvature

You can visualize spline curvature and overall smoothness by turning on its curvature comb. To turn on the curvature comb, right-click a spline, and then choose Display Curvature.

The curvature comb displays spines along the spline. The length of each spine is equal to the curvature of the spline at that point, adjusted for the view scale. By observing the progression of the tips of the spines you can get a feel for how continuous the curvature of the spline is, and how smooth it is.

Procedures

Create an interpolation spline

First select a part face or work plane to use as the sketch plane . In an empty file, the sketch plane is preset, and you can start to sketch.

1. On the ribbon, click Sketch tab Draw panel Interpolation Spline.
2. In the graphics window, click to set the first point or select an existing point.
3. Continue clicking to create more points on the spline.
4. Click OK to create the spline and exit the command. Click Apply to create the spline and remain in the spline command.
Note

Alternatively, you can import points from a Microsoft Excel spreadsheet and automatically create splines or lines through the imported points (see Sketch points).

Work with splines

• To delete the spline without deleting the spline fit points, convert the points to center points.
• To create a spline tangent to a line or arc, with the spline command active, click and drag from an endpoint of the line or arc.
• To edit the position of spline fit points, select the spline, and then click and drag a point. Internal fit points are diamond shaped, end fit points are square.
• Reposition the spline by adding dimensions and constraints to spline fit points, and between the fit points and other geometry.
• Hold down Alt while you drag a spline point to move other nonconstrained spline points to preserve the spline shape. If some points that are constrained do not move.
• To activate a handle, press and drag anywhere on a passive handle, or right-click the handle or a fit point and choose Activate Handle from the context menu.
• To reverse a handle edit, select the spline and choose Reset Handle from the context menu. Reset Handle uses the handle closest to the cursor location, unless a specific fit point or handle is selected. Reset Handle does not always change the spline handle back to the original solve state if other handles are modified. The reset is based on the current spline shape.
• To reverse all handle edits and restore the spline back to the natural solve state, select the spline and choose Reset All Handles from the context menu.
• Use the context menu options to:
• Activate or de-activate the tangent, curvature, or flat handles.
• Choose the fit method.
• Close the spline.
• Reset Handle.
• Reset All Handles.
• Convert to a control vertex spline.
NoteAdjusting the spline tension automatically changes the spline fit method to Minimum Energy.

Edit an interpolation spline

In an active sketch, use one or more of these methods to edit an interpolation spline:

• Use the Select command to click an endpoint or any internal point on the spline , and then drag the point to a new location.

• Drag geometry that is constrained to a spline point to a new location.
• Add constraints to control relationships between the spline and other geometry:
• Place a tangent constraint between the spline and another curve.
• Add constraints to spline points, or between a spline point and other geometry.
• Add constraints to active tangent and curvature handles to specify relationships between a spline and other geometry.
• Add dimensions to control spline size.
• Add dimensions between fit points on the spline, or between a fit point and other geometry.
• Add a radial dimension to an active curvature handle to control the spline arc radius at the fit point.
• Add a unitless length dimension to an active tangent handle to control the distance the handle is tangent to the spline. The initial dimension value indicates a natural state. Normal values usually range between .5 and 2. Begin with a 1.0 dimension and observe the effect of changing it to values ranging from .5 to 2.0 or greater.
NoteTo analyze the curvature of a spline, right-click a spline, and then choose Display Curvature.

Right-click to use context menu options:

• Setup Curvature Display Set the spacing between the comb points.
• Display Curvature Display the comb points and display a visual analysis of the curvature and overall smoothness.
• Activate Handle Enable a tangent handle.
• Curvature Enable the curvature handle, and activate the tangent handle if it was not previously enabled.
• Flat Specify zero curvature at a fit point.
• Reset All Handles Restore the spline to the natural solve state.
• Reset Handle Reverse an edit to a selected handle or the handle nearest the cursor position.
• Convert to CV Spline Change the spline type to a control vertex spline.
• Fit Method Set the transition of the spline curve between fit points. An AutoCAD fit method is not suitable for class A surfaces.
• Insert Point Add a spline fit point.
• Close Spline Join start and endpoints of the spline.
• Spline Tension Add or reduce tension with a slider control, which converts the spline to a Minimum Energy fit method.

In addition, right-click the spline to:

• Add points along the spline curve.
• Examine the radius of curvature at points along the curve.
• Show constraints.
• Change the fit method.
• Close open splines.
NoteReset Handle does not always change the handle back to the original solve condition if other handles are modified.

Create a control vertex spline

Show Me how to create and use control vertex splines

First select a part face or work plane to use as the sketch plane . In an empty file, the sketch plane is preset, and you can start to sketch.

1. On the ribbon, click Sketch tab Draw panel Control Vertex Spline.
2. In the graphics window, click to set the first point or select an existing point.
3. Continue clicking to place more vertices.
4. Click OK to create the spline and exit the command. Click Apply to create the spline and remain in the spline command.
NoteThe spline is tangent to the control frame at the start point and end point.

## Work with splines

• To delete the spline without deleting the spline fit points, convert the points to center points.
• To edit the position of spline control vertices, click and drag a vertex.
• To edit the position of the spline control frame, click and drag a line.
• Reposition the spline by adding dimensions and constraints to the control frame or between the control frame and other geometry.
• Use the context menu options to:
• Close the spline.
• Convert to an interpolation spline.
• Change the control frame polygon visibility.

Edit a control vertex spline

In an active sketch, use one or more of these methods to edit a control vertex spline:

• Use the Select command to click an endpoint , vertex, or control frame and then drag the geometry to a new location.
• Drag geometry that is constrained to a spline endpoint, control vertex, or control frame.
• Add constraints to control relationships between the spline and other geometry:
• Place a tangent constraint between the spline and another curve.
• Add constraints to the spline endpoints or vertices.
• Add constraints to the control frame.
• Add dimensions to the control frame.

Right-click and use the context menu options:

• Setup Curvature Display Set the spacing between the comb points.
• Display Curvature Display the comb points and display a visual analysis of the curvature and overall smoothness.
• Insert Vertex Insert a control vertex to the control frame.
• Convert to Interpolation Change the spline type to an interpolation spline.
• Polygon Visibility Turn on/off the display of the control frame polygon.

To delete control points:

1. Select the control point.
2. Right-click and select Delete.
NoteYou can only delete control points if there are 4 or more points, including the start point and end point.

Convert the spline type

You can convert an interpolation spline to a control vertex spline or convert a control vertex spline to an interpolation spline. Right-click the spline and select Convert to Interpolation or Convert to CV Spline to change the type.

If you convert the type then convert back, the spline will not have the same fit points or control frame as the original. The initial conversion creates a best-fit spline and adds more points or vertices.

Offset geometry from an ellipse

Offset geometry from an ellipse or trimmed ellipse. Use this technique to represent a uniform wall thickness.

1. On the ribbonSketch tab Draw panel , click Ellipse, and create an ellipse.
2. On the ribbon, click Sketch tab Modify panel Offset.
NoteThe ellipse responds to cursor movements. Pause the cursor near the ellipse quadrants to display an axis. When the axis is visible, the offset produces an ellipse. If the axis is not visible, the offset produces an associative spline.
3. (Optional) Right-click, and clear check marks to remove the default settings that affect the results of an offset ellipse.

• Loop Select chooses closed loops.
• Constrain Offset constrains the distance between the offset geometry and the original ellipse to be equidistant.
4. Click the ellipse.
5. Move the cursor in the direction you want to place the offset geometry, and then click to create.
6. To quit, right-click, and then select Done.
7. If the new offset is an associative spline, use Dimension to specify an offset distance.
8. (Optional) You can break the association between the ellipse and the offset spline. Right-click and select Convert to Spline.

Right-click the spline, and then use spline shape adjustment options as needed.

Show Me how to offset an ellipse

When the association between the offset spline and the ellipse is removed, you can add dimensions and constraints separately.

Remove offset spline association to an ellipse

1. If necessary, right-click the sketch geometry in the graphics window or the sketch icon in the browser, and then select Edit Sketch.
2. Right-click the associative spline offset from the ellipse, and then select Convert to Spline.

The offset ellipse is converted to an unassociative spline, and you can control it separately. A fit point and multiple shape points are added to the spline.

You can dimension and constrain to the fit point or drag a shape point. Right-click, and then use any of the spline editing options to add points, display curvature, choose the fit method, adjust spline tension, and use the Bowtie to modify curve shape.

References

Interpolation Splines

 Access: Ribbon: Sketch tab Draw panel Interpolation Spline

Control vertex splines

 Access: Ribbon: Sketch tab Draw panel Control Vertex Spline
 Resize Drag an endpoint. The endpoint on the opposite end of the spline remains in a fixed position. Move Click the spline, and then drag. Reshape Drag a spline vertex or control frame to move the control vertex locations. The control frame can be constrained and dimensioned to increase control of the spline shape. In an active sketch, select the spline or control frame and right-click to access the context menu options. Select the spline and right-click then select one or more of the context menu options to adjust spline shape. Display Curvature Curvature combs help visualize the spline smoothness. Curvature combs amplify discontinuities in a curve. Insert Vertex Inserts a new vertex on the control frame. Convert to Interpolation Changes the spline type to an interpolation spline. Close Loop Creates a closed loop by joining the beginning and endpoints of the spline. Polygon Visibility Turns on/off the display of the control frame polygon.

Curvature Settings

Provides a visual analysis of the curvature and overall smoothness. The curvature comb plot shows curvature with a series of connected spines radiating outward from the curve. The relative length of the curve is equal to the curvature of the curve at the point where the spine originates. Longer spines indicate areas of higher curvature, and shorter spines indicate lower curvature.

 Access: Select one or more sketched curves (spline, circle, or ellipse) in the graphics window that have curvature displayed, right-click and select Setup Curvature Display from the context menu.

Definition

 Sets appearance of analysis results along each curve and edge of the selected geometry. Comb Density Specifies the spacing between spines. Comb Scale Specifies the scale (length) of the spines.

Interpolation Spline Tension

Controls the tension for an interpolation spline created using the Minimum Energy fit method. Interpolation splines created with other fit methods automatically convert to Minimum Energy splines when tension is applied, and change shape.

 Access Right-click an interpolation spline to see the context menu options.
 Slider bar Set the initial position of the slider bar in the Application Options for Sketch. The default position is zero. A low value (closer to 1) is a loose tension setting. A high value (closer to 100) tightens the spline between the fit points. The spline updates with a preview graphic as you move the slider position Check box Select to apply the current setting to the active spline. Default box Select to write the current spline tension to the Application Options for Sketch. “x” in the upper right corner Click to close the dialog box.