Creating Cross-Section Lines

Purpose

Display cross-sections on the picked geometry, according to the current construction plane.

Overview

The Cross section tool can produce two types of cross-section lines: Parallel and Radial.

• Parallel cross-section lines are created by intersecting a series of parallel planes with the geometry. These planes are perpendicular to the main axes (X, Y or Z).

• Radial cross-section lines are created by intersecting a rotating plane with the geometry. The plane passes through a user-defined pivot point and axis, around which it rotates. This axis is parallel to either the X, Y or Z axis.

You can use the Cross section tool on shells as well as surfaces and trimmed surfaces.

How To

To show cross-section lines on a model:

1

Pick the surfaces on which you want to show cross-sections.

2

Click the Cross section icon, or choose Cross section from the Evaluate palette menu.

3

If the Section type option is set to Radial, you must position the radial pivot.

4

A locator appears in the scene. Move the locator with the mouse, then click Go.

The Cross section tool creates cross section curves from the picked geometry.

If Create History is on, you can modify the model and the cross-section lines will automatically update.

To remove cross-section lines:

1

Pick only the group of cross-section curves.

2

Choose Delete > Active.

Tips and Notes

• Try to avoid situations where cross-sections pass through the pole of an object (such as a sphere). Cross sections around poles are not created.

As a workaround, you can try to move the surface slightly.

• Cross-section lines are actually grouped degree 3 curves. They appear as a compressed node in the SBD window.

Options

See Overview above for more details on these two types.

Section Type

Parallel-the cross-section lines are parallel to each other.

Radial-the cross-section lines are created from intersections with a rotating plane.

This option appears when Section Type is Radial.

Radial pivot point

X,Y,Z coordinates of the pivot point for radial cross-section lines.

This option appears when Section Type is Radial.

Number of radial sections

Number of radial cross-section lines.

Axis Usage X/Y/Z

Choose the axes perpendicular to which you want to create parallel cross-sections, or around which you want to create radial cross-sections.

Auto Range

Use the bounding box of the picked objects to determine where to compute the cross-sections, independently of the obkect's position in space.

These options appears when Auto Range is off.

Start/End Coordinate

Enter the 3D coordinates of two corners of a bounding box. The cross-sections will be calculated for the region of the selected object(s) that intersect this box.

If Start Coord equals End Coord, a single cross-section line is created.

Step Size

The spacing between cross-section lines along the X, Y, and Z axes.

Rebuild Cross-section

Rebuild the cross-section curves to remove multi-knots. Leave this option off if you are using the cross-section lines for evaluation. If you want to use the cross-section curves for modeling, turn this option on.

Create History

Save the construction history of the cross-section curves. If you turn Create History on, you can modify the surfaces that were used to create the cross-section curves, and the cross-section curves will update.

See Also

• Viewing a Dynamic Cross-Section on page 538

• Creating Curves on Surface for Various Criteria on page 540

Viewing a Dynamic Cross-Section

Purpose

View cross-sections on surfaces by dragging a cross-section plane through the model.

Unlike the regular Cross section tool, this tool can produce cross-sections in an arbitrary orientation.

How To

To create a cross-section line:

1

Select one or more surfaces that you want to examine.

2

Click the Dynamic Section icon, or choose Dynamic Section from the Evaluate palette menu.

3

Use the plane manipulator to set the cross-section plane, as shown below.

As you modify the plane, the cross section (which appears as a red line) is updated. To create more sections, change the value of Number in the option window.

• Drag a handle to move/rotate interactively.

• Click an arrow to change the center handle to the free move handle. Then drag the center handle to move the plane freely.

• Click a sphere to change the center handle to the free rotate handle. Then drag the center handle to rotate the plane freely.

The visual lines created by the Dynamic section tool do not persist after you choose another tool.

4

Optionally, click one of the buttons in the bottom-right hand corner of the view window:

• Click Geom to create real curves from the cross-section lines.

• Click Curvature to create curvature combs on the cross-section lines.

Options

Step Size

The distance between cross-section lines (when Number is greater than 1).

Number

The number of cross-section lines to create.

See Also

• Creating Cross-Section Lines on page 535

• Curvature Button on page 503

Creating Curves on Surface for Various Criteria

Purpose

Create curves on surface corresponding to highlights, iso-curvature lines, contours, or horizon lines.

How To

To create curves-on-surface from highlights:

1

Pick the surfaces on which you want to create curves-on-surface.

2

Double click the Surface evaluate icon, or choose Surface evaluate- from the Evaluate palette menu.

The Surface Evaluate control window opens.

3

Set the Evaluation Type to Highlights.

The highlight manipulator appears.

4

Set the following options (see Highlights Options on page 544 for more details):

• The number of lights you want to create highlights from.

• The spacing between the lights (if there is more than one)

• The width of the light (if there is only one).

• Set the Subdivision option from 1 to 6. The higher the value, the more precise the result. Use low values for draft quality, use higher values for final results.

The manipulator reflects the changes.

5

Drag different handles on the manipulator to orient the light(s):

Or type exact values into the Light Origin, Light Direction, and Spacing Plane fields of the Surface Evaluate window.

6

Click Go to create the curves-on-surface.

You can click the Undo button in the control window to remove the curves on surface, or change the manipulator and click Recalc.

To create curves on surface along lines of constant curvature:

1

Pick the surfaces on which you want to create curves-on-surface.

2

Double click the Surface evaluate icon, or choose Surface evaluate- from the Evaluate palette menu.

The Surface Evaluate control window opens.

3

Set the Evaluation Type to Curvature.

4

Set the following options (see Curvature Options on page 545 for more details):

• The Curvature Type.

• The Curvature Value at which you want to create curves on surface. For example, enter 0 to create curves-on-surface along inflection lines.

• Set the Subdivision option from 1 to 6. The higher the value, the more precise the result. Use low values for draft quality, use higher values for final results.

5

Click Go to create the curves-on-surface.

You can click the Undo button to remove the curves on surface, or change the manipulator and click Recalc.

To create curves-on-surface along a contour line:

1

Pick the surfaces on which you want to create curves-on-surface.

2

Double click the Surface evaluate icon, or choose Surface evaluate- from the Evaluate palette menu.

The Surface Evaluate control window opens.

3

Set the Evaluation Type to Contour.

The contour manipulator appears.

4

Drag different handles on the manipulator to orient the cross-section plane:

Or type exact values in the Plane Origin and Plane Normal fields of the Surface Evaluate window. (See Contour Options on page 545 for details.)

5

Click Go to create the curves-on-surface.

You can click the Undo button to remove the curves on surface, or change the manipulator and click Recalc.

To create curves on surface along the horizon line:

1

Pick the surfaces on which you want to create curves-on-surface.

2

Double click the Surface evaluate icon, or choose Surface evaluate- from the Evaluate palette menu.

The Surface Evaluate control window opens.

3

Set the Evaluation Type to Horizon.

4

Set the Horizon Type.

If the Horizon Type is Perspective, a viewpoint locator appears. Drag this locator to move the viewpoint, or type exact coordinates in the View Point fields in the Surface Evaluate window.

If the Horizon Type is Orthogonal, type a direction in the View Direction fields in the Surface Evaluate window.

See Horizon Options on page 546 for more details on these options.

5

Click Go to create the curves-on-surface.

You can click the Undo button to remove the curves on surface, or change the manipulator and click Recalc.

Tips and Notes

• When using the Horizon evaluation type, note that if the horizon does not cross the surfaces when viewed from the point or direction you set, the Surface evaluate tool will not create any curves on surface.

Surface Evaluate Option Window

Evaluation Type

Highlights

Create curves-on-surface corresponding to highlight lines produced by light sources.

Curvature

Create curves-on-surface along lines of constant curvature.

Contour

Create curves-on-surface from a single-plane cross-section.

Horizon

Produce curves-on-surface from horizon lines as seen from a point in space or from a direction.

These options appear when Evaluation Type is Highlights.

Highlights Options

Light Origin

The 3D coordinates of the first light's origin (center point).

You can set this interactively with the highlight manipulator when you use the tool.

Light Direction

The direction in which the light sources point.

You can set this vector interactively with the highlight manipulator when you use the tool.

Number of Lights

The number of lights from which to create curves-on-surface highlights.

If you use more than one light, the multiple lights are always parallel to each other.

This option appears when Number of Lights is 1.

Light Width

The width of the single light source.

Set the width to 0 to create a single curve-on-surface. Set the width greater than 0 to create two curves-on-surface corresponding to the edges of a wide highlight.

This option has no effect if Visual is turned on.

This option appears when Number of Lights is greater than 1.

Light Spacing

The spacing between multiple light sources.

This option appears when Number of Lights is greater than 1.

Spacing Plane

The vector perpendicular to the plane of the lights.

You can set this vector interactively with the highlight manipulator when you use the tool.

Subdivision

The quality of the curve-on-surface projection, from 1 to 6. The higher the value, the more precise the result. Use low values for draft quality, use higher values for final results.

Visual

Draw fast polylines instead of curves-on-surface.

Unlike curves-on-surface, these lines are for display only, and cannot be picked or used to create geometry.

The lines are represented in the SBD window by one node that contains a white box and no text/name.

To delete these lines, open the SBD window and delete the node representing the lines.

These options appear when Evaluation Type is Curvature.

Curvature Options

Curvature Type

Choose the method of calculating curvature on the surface:

Mean-average the two principal curvatures at each point on the surface.

Gaussian-multiply the two principal curvatures at each point on the surface.

Principal Min/Principal Max-use the minimum or maximum curvature values (that is, the curvature of the steepest or flattest curves that pass through each point).

Mean or Gaussian curvature is most useful for detecting surface irregularities. Principal Min or Max curvature is most useful for detecting inflection points.

Curvature Value

Enter the curvature value for the iso-curvature lines you want to create.

The Surface evaluate tool will create curves-on-surface along these lines of constant curvature.

These options appear when Evaluation Type is Contour.

Contour Options

Plane Origin

The 3D coordinates of the origin of the plane which will intersect the surfaces to create curves-on-surface.

You can set this interactively with the contour manipulator when you use the tool.

Plane Normal

The vector perpendicular to the plane.

You can set this vector interactively with the contour manipulator when you use the tool.

These options appear when Evaluation Type is Horizon.

Horizon Options

Horizon Type

Choose how to project the horizon line onto the surfaces.

Perspective-use the horizon as seen from a certain point in space.

Orthogonal-view the horizon from a certain direction. With this technique, the "sightlines" are parallel and the viewpoint is infinity.

Note that if the horizon does not cross the surfaces when viewed from this point or direction, the Surface evaluate tool will not create any curves on surface.

This option appears when Horizon Type is Perspective.

View Point

The point in space from which to look at the picked surfaces and the horizon.

You can set this interactively with the viewpoint locator when you use the tool.

This option appears when Horizon Type is Orthogonal.

View Direction

The view direction from which to look at the picked surfaces and the horizon.

Control Options

Create History

Save the history of the new curves-on-surface for later editing. If you turn Create History on, you can modify the surfaces and the curves-on-surface will update.

Auto Recalc.

Update the curves-on-surface automatically as you change the values in the Surface Evaluate window.

Buttons

Recalc

When Auto Recalc. is off, use this button to update the curves on surface to correspond to the current options.

Undo

Undo all the changes made by the Evaluate surface tool and return to the original surface.

Next

Finish creating curves-on-surface on the current surface and prompt for a new surface to evaluate.

See Also

• Showing Surface Curvature on page 523

• Showing Surface Features with Highlights on page 530

Measuring Minimum and Maximum Curvature

Purpose

Find the points with minimum and maximum curvature on a surface or a set of surfaces.

How To

To show the minimum and maximum curvature values on one or more surface(s):

1

Pick the surface(s) you want to evaluate.

2

Double-click the Min/max curvature icon, or choose Min/max curvature- from the Evaluate palette menu.

3

In the option window, set Mode to Active.

The Min/max curvature tool places temporary locators at the minimum and maximum curvature points on the surface(s), and opens a window displaying detailed information about the points.

Options

Mode

Choose whether to compute the curvatures on only Active (picked) objects, or All objects. All is the default.

Curvature Type

Choose how to calculate the curvature values:

Mean-use the average of the two principal curvatures to approximate the average curvature through each point.

Gaussian-use the product of the two principal curvatures.

Princ Min/Princ Max-use the minimum or maximum curvature values (that is, the curvature of the steepest or flattest curves that pass through each point).

From Curvature Texture-use the same type as in the Surface Curvature > Surf curv params window.

The Mean and Gaussian options are most useful for detecting surface irregularities. The Princ Min/Max options are most useful for finding inflection points.

See Also

• Showing Surface Curvature on page 523

Measuring Mass Properties

Purpose

Display mass properties (such as volume) of a model.

Overview

The Mass properties tool provides three ways of specifying the object to measure:

• Solid: the surfaces you pick represent the boundaries of a closed, solid object.

• Shell Interior and Shell Exterior: the surfaces you pick represent one side of a thin shell enclosing a hollow space (e.g. modeling a bottle with a single surface of revolution). You specify the thickness of the shell.

Restrictions

To get accurate statistics on an object, the following conditions must be met:

• The surfaces must completely enclose a volume. The edges of surfaces must meet within the tolerance value set in the Mass properties option window.

• The normals on all NURBS surfaces must point out of the solid, and, when moving along a face boundary in the increasing U direction, the face area must be to the left when viewed from outside the solid.

or

The normals on all NURBS surfaces must point into the solid, and, when moving along a face boundary in the increasing U direction, the face area must be to the right when viewed from outside the solid.

You can check the seam between two surfaces by placing a Deviation measurement on the seam (see page 515). You can check the orientation of normals using the Reverse direction tool (see Reversing Direction and Normals on page 120)

Display

The Mass properties window displays the following information:

Label	Description	Formula
volume	Volume enclosed by the picked surfaces, or volume occupied by shell surface with given thickness.
origin inertia	Moment of inertia about the origin.
area	Area of the picked surfaces.
cur. dimen	Current unit of measurement (default is centimeters).
centroid	X, Y, Z coordinates of the center of the object
inertia	Moments of inertia about the X, Y, and Z axes.	(X axis) (Y axis) (Z axis)
1st moment	First moments along the X, Y, and Z axes.
2nd moment	Second moments along the X, Y, and Z axes.

How To

To show the mass properties of a model:

1

Pick all the surfaces that make up the model. Make sure the surfaces completely enclose the volume of the object.

2

Click the Mass properties icon, or choose Mass properties from the Evaluate palette menu.

When the Mass properties tool completes its calculations, the Mass properties window appears, containing statistics about the object.

If you change the options of the Mass properties tool, the window will update.

Tips and Notes

• Using the Mass properties tool with the Solid option on a group of surfaces with gaps will not produce an error.

In fact, the results are still meaningful if the gaps between surfaces are not too large.

See Reversing Direction and Normals on page 120.

• If some of the inertia and moment values are negative, some of the surfaces probably have normals pointing inward. Use the Reverse direction tool to find and reverse the surfaces so they have normals pointing out.

• Depending on surfaces and normals, it is possible to confuse Shell Int. and Shell Ext. as to which are the exterior and which are the interior surfaces.

When in doubt, run the calculations with both and compare. The results with the smaller volume and surface area are those associated with Shell Int (i.e the picked surfaces are the exterior surfaces).

Options

Volume, Surface Area, Centroid,
Inertia, 1st Moment, 2nd Moment

Check the values you want to display in the Mass properties window.

Type

Describe the way the selected surfaces or faces define the solid.

Solid: the surfaces you pick represent the boundaries of a closed, solid object.

Shell Int/Shell Ext: the surfaces you pick represent the exterior/interior of a thin shell enclosing a hollow space (e.g. modeling a bottle with a single surface of revolution). The Thickness option (below) specifies the thickness of that shell.

Bounded

Turn this option on to calculate mass properties for only that part of a solid bounded between two planes (see below).

Axis

Specify whether the two bounding planes are perpendicular to the X, Y or Z axis (in the current corrdinate system).

In the diagram on the left, the Axis is Z.

The Axis, Min and Max options appear when Bounded is on.

Min
Max

Specify the values for the position of the planes along the chosen axis.

In the diagram on the left, the Min and Max are -1.0 and 1.0.

This appears only when Solid is on.

Tolerance

The maximum distance allowed between adjacent surfaces for them to form a closed volume

The Thickness and Precision options appear only when Shell Int or Shell Ext is on.

Thickness

The uniform thickness of the shell when using the Shell Int or Shell Ext options (above). In these cases, the Volume corresponds to the volume of the shell, rather than that of the enclosed space. The Area corresponds to the sum of the interior and exterior surface areas.

Precsion

Control the accuracy of the result. The higher this value is, the more accurate the result. The default value of 16 results in less than 1% error. Doubling the precision number usually quadruples the amount of calculations and the computational time.