Create curves-on-surface from geometry

Create curves-on-surface from existing curves and surfaces by intersecting surfaces, projecting curves onto surfaces, and mapping curves onto surfaces.

Overview

There are four basic tools for creating curves-on-surface from existing curves:

• Intersect. This tool creates curves-on-surface where two surfaces intersect (See To create curves-on-surface at the intersection between two surfaces).

  This allows you to trim the surfaces back to the intersection.

  

• Project. This tool creates curves-on-surface by projecting a curve along a vector onto surfaces (see To project a curve or surface outline to create a curve-on-surface).

  This is like shining a flashlight at the curve, and turning the shadows on the target surfaces into curves-on-surface. The line between the flashlight, the curve, and the shadow is the projection vector.

  

• Project normal. This tool is like Project, but instead of projecting along a single vector, the curve is projected onto each point on the surface along the normal at that point (see To project a curve along the surface normals to create a curve-on-surface)

  This tool is very useful for projecting curves that are parallel to or surround the target surface.

  

• Geometry mapping. This tool maps world-space curves onto the target surface.

  Geometry mapping can produce curves-on-surface that are impossible with projection or intersection. For example, you can wrap text curves around a cylinder, rather than simply projecting them onto the sides.

  

To create curves-on-surface at the intersection between two surfaces

1. Pick the surfaces on which you want to create curves-on-surface (the target surfaces).
   TipAlternately, you can select the Intersect tool before selecting the surface on which you want to create curves-on-surface, and then click the Go button.
2. Click the Intersect icon, or choose Create CurvesOnSurface > Intersect from the Surface Edit palette menu.
3. Click the surface you want to intersect with the picked surfaces. This intersecting surface can not be one of the picked surfaces.
4. If a surface was picked in step 3, the Intersect tool creates curves-on-surface.
   • If the Create Curves on Surface option is set to On First Surface, the Intersect tool creates curves-on-surface on the target surfaces, but not on the intersecting surface you clicked in step 3.
   • If the Create Curves on Surface option is set to On Both Surfaces, the Intersect tool creates curves-on-surface on both the target and the intersecting surfaces.
5. Repeat step 3 for another intersecting surface if necessary.

To project a curve or surface outline to create a curve-on-surface

1. Pick the surfaces on which you want to create curves-on-surface.
   TipAlternately, you can select the Project tool before the surface on which you want to create curves-on-surface, and then click the Go button.
2. If you want to project a curve or surface outline along a view vector of a window, select that window.

   Otherwise, create a reference vector to represent the projection direction.

3. Click the Project icon, or choose Create CurvesOnSurface > Project from the Surface Edit palette menu.

   An indicator appears showing the projection vector.

4. Do one of the following:
   • Click the curve, isoparametric curve, or curve-on-surface you want to project onto the surface(s). The curve is projected along the view vector of the active window.
   • Click the reference vector (that you have previously created that represents the projection direction. The curve is projected along the vector direction.

   This operation can take some time depending on the complexity of the geometry. Press to cancel the operation.

5. You can now:
   • Continue to click curves to project.
   • Click another vector to change the projection direction.
   • Shift-click on the selected vector to project the curve or surface along the view vector of the active window.
   • Select new surfaces using a Pick tool and click the Project icon again.
   • Choose another tool.

To project a curve along the surface normals to create a curve-on-surface

1. Pick the surfaces on which you want to create curves-on-surface.
   TipAlternately, you can select the Project normal tool before selecting the surface on which you want to create curves-on-surface, and then click the Go button.
2. Click the Project normal icon, or choose Create CurvesOnSurface > Project normal from the Surface Edit palette menu.
3. Click the curve, isoparametric curve, or curve-on-surface you want to project.

   The curve is projected onto all picked surfaces along the surfaces’s normals.

   This operation can take some time depending on the complexity of the geometry. Press to cancel the operation.

4. You can now:
   • Continue to click curves to project.
   • Select new surfaces using a Pick tool and click the Project normal icon again.
   • Choose another tool.

To map a curve onto a surface to create a curve-on-surface

1. Figure out how you want the curve to map:
   • Check the parametric directions of the surface. Use the Reverse direction tool to display and reverse the surface direction if necessary.
   • Note which world space axes correspond to the U and V axes of the surface.
2. Set up the options.
3. Pick the surface on which to create curves-on-surface.
4. Click the Geometry mapping icon, or choose Create CurvesOnSurface > Geometry mapping from the Surface Edit palette menu.
5. Click the curve, isoparametric curve, or curve-on-surface you want to map.

   The curve is mapped onto the picked surface using the settings in the Geometry mapping option window.

6. You can now:
   • Continue to click curves to map.
   • Select a new surface using a Pick tool and click the Geometry mapping tool again.
   • Choose another tool.

Tips and notes

• Surfaces that have curves-on-surface are drawn with a dotted outline.
• You cannot intersect faces, but you can project and map them onto surfaces.
• If you are not using a vector with the Project tool and you are always using the same window, try creating a vector in the view direction of the window. That way, you won’t have to worry about which window is active.
• To minimize distortion when mapping, the size of the mapped area in world space should be proportional to the size of the surface.
• To insert edit points on curves where they intersect a surface or another curve, use the Curve Section tool.

Limitations

The following limitations apply to the Surface Edit > Create CurvesOnSurface > Project, Surface Edit > Create CurvesOnSurface > Intersect, and Evaluate > Cross section tools:

• Generally, intersection does not work if the intersecting surface passes exactly through ‘degenerate’ points, such as the pole of a sphere, where many CVs are placed on top of each other, or where a surface wraps back on itself. If this situation occurs, move one of the surfaces a bit (a minuscule amount will do), do the intersection, and move the surface back.
• Complex saddle point regions may cause problems for the intersection code.
• Occasionally, the order in which intersecting objects are picked can make a difference. To guarantee the simplest curve of intersection (the one with the fewest knots), pick the simplest object first. Usually, the order of picking does not make a difference.
• The curve-on-surface resulting from an intersection has multiple knots. This means that they are not as easily editable as other curves on surface might be.

  Troubleshooting trimmed surfaces

Options

Create

Curves-on-surface: The result of the projection are curves-on-surface.

Curves: The result of the projection are free curves.

Tolerance

The accuracy of the match between the original curve and the curve-on-surface. The smaller the value, the more accurate the projection, but the longer the calculation time required.

For example, if the Tolerance is 0.01, the curve-on-surface must match the original curve within 0.01 units at each point that Project normal checks.

Curve data factor

Number of times that each surface patch is subdivided to get an accurate result.

The default is 1, which is sufficient for most surfaces. Larger values increase calculation time. Only increase the value for very simple surfaces.

Match Original

This option is only available if Create is set to Curves.

If this option is checked, the edit points from the original curves will be projected on the surface(s), and the projected curves will interpolate them, resulting in a similar number of spans.

If this option is not checked, the resulting curves will be better approximations of the projected sections from the original curves, but will likely contain more spans.

Create History

Save the history of the projection for later editing. If you turn Create History on, you can modify the curves and surfaces that were used to create the projected curves, and the projected curves will update.