Scratching the Surface of Surfaces

31 Jan, 2002 By: John E. Wilson

This month, we continue our exploration of the 3D modeler Rhino as we look at its surface-making tools. If you do not currently use Rhino, you can find out about it at You can also download an evaluation version to try the operations described here.

Rhino can create both solid and surface models-a solid model completely encloses a space, while a surface model is open-but it does not separate them into two distinct object types. You will generally concentrate on surfaces as you construct 3D models with Rhino because its tools for making surfaces can create shapes midrange solid modelers such as Solid Edge and Inventor cannot. (In recognition of this, Solid Edge has a promotion in which purchasers of Solid Edge can receive a Rhino seat at no additional charge.)

A convenient way to access Rhino's tools for creating surfaces is from Surface in Rhino's menu bar. These tools can be separated into three categories: those that don't require curves to define a surface, those that create surfaces from a set of stationary curves, and those that create surfaces by moving one or more curves through space. Most of the curves used to create surfaces will be curve objects, but you can also use edges of existing surfaces as curves. Regardless of the tool used to create them, all surfaces are the same type of object, a NURBS surface. See the sidebar in my December 2001 column entitled, "There's Something About NURBS" to learn about NURBS. The tool you select for creating a surface depends on the shape you want to create and the curves available as a framework for the surface.

Surfaces That Do Not Require Curves
Figure 1 shows examples of surfaces you can make with the tools in this category.

Figure 1. By specifying point locations, you can create Rhino surfaces with either three or four edges.

Choose Point from the Surface menu to create a surface by specifying the locations of either three or four corner points. The surface will be a planar triangle when you specify three points, but you can create a folded surface by specifying four corner points. Selecting Rectangle from the Surface menu displays a secondary menu for creating rectangular planar surfaces. Table 1 provides a description of the choices in this secondary menu.

Table 1. Tools in Rhino's Surface/Rectangle Menu
ToolUser ActionResults
Corner to Cornerspecify two diagonally opposite corners of the surfacemakes the rectangular surface parallel to the current construction plane
3 Pointsdefine one edge of the surface by specifying two adjacent corners, and specify a third point to establish its widthmakes the rectangular surface parallel to the current construction plane
Verticalspecify two points on the construction plane to make one edge of the surface, and then specify the height of the surfacemakes the rectangular surface perpendicular to the current construction plane
Through Pointsselect three or more existing point objectsif you select just three points, the resulting surface passes through all of them; if you select more than three points, and they are not coplanar, the location of the rectangular surface is interpolated to lie between them
Cutting Planeselect one or more existing surfaces, and then specify one edge of the surface by selecting two pointsmakes the new surface perpendicular to the current construction plane and long enough to pass through the selected surfaces

Surfaces Based On Stationary Curves
Figure 2 shows examples of one surface. Choose Edge Curves from the Surface menu to use two to four existing curves as the boundary of a surface. The curves do not need to touch one another, and the order in which you pick them is not important. From Planar Curves in the Surface menu also uses a set of curves as the boundary of a surface. Any number of curves can be used, but they must all be planar and be in the same plane. Also, they must form a closed loop and their ends must touch one another (a loop within a loop creates a hole in the surface).

Figure 2. Here are some examples of Rhino surfaces made from sets of stationary curves. The curves on the left are the basis of the surfaces shown on the right.

To create a surface from two or more curves that are spaced apart, choose Loft from the Surface menu. You will be prompted to pick the curves that serve as cross sections of the surface in sequence from the beginning to the end of the surface. The curves can be either open or closed, but they must all be one or the other. If you use closed curves, their seam points must be aligned and they must all have the same direction to prevent kinks and twists in the surface. Rhino displays the seams and directions of closed curves, and you can adjust them before creating the surface. You can also begin or end the surface at a point. Options for specifying a loft style include having the surface pass exactly through all curves, allowing the surface to move away from the curves, and having straight surface sections between the curves.

Form Curve Network in the Surface menu creates a surface from three or more curves. You have considerable leeway in your choice of curves. The curves do not have to touch, and both open and closed curves can be included. If there is a closed curve, though, you must have another closed curve to go with it, and you must have a minimum of three open curves in the network. If all of the curves are open, the network must have at least four curves and they must, at least roughly, form a grid-like pattern. The order in which you select the curves is usually not important because Rhino automatically sorts them and determines how they should be used in creating the surface. If Rhino has trouble determining how some curves fit in the network, you will be prompted to reselect these one at a time and specify their direction.

Surfaces Based on the Movement of Curves
Figure 3 shows examples of these surfaces. Select Extrude from the Surface menu to define a surface by pushing a curve, which is often referred to as the profile, through space. A secondary menu listing the four extrusion options then displays.

Figure 3. Surfaces defined by the movement of curves through space are shown in this figure. The surfaces on the right were created from the curves shown on the left.

Select Straight to extrude one or more curves linearly. The curves can be open or closed, and they can also be non-planar. The direction of the extrusion is, by default, in the z-axis direction of to the current construction plane, and you can specify the extrusion distance by entering a distance value on Rhino's command line or by dragging the profile through space. Options include reversing the extrusion direction, and extruding the surface equally on both sides of the profile. When the profile is closed, you can taper the extrusion surface, round or chamfer its end corners, and even cap both ends of the surface to make a solid.

Along Curve in the Extrude menu uses a second curve as a path to set the direction and length of the extrusion. You can select just one profile curve and one path curve. The orientation of the profile does not change as it is extruded. Choose To Point in the Extrude menu to have the extruded surface taper to a point.

The shape of the surface created when you choose Ribbon from the Extrude menu is achieved by offsetting the profile curve and filling the space between the two curves with a surface. Rhino prompts you to specify the offset distance and direction.

Using Sweep 1 Rail from the Surface menu is like extruding a profile along a path, but you can place additional profiles along the path to further shape the surface, and you can control the angle and twist relationships between the profiles and the path. Rhino's prompts for creating a sweep surface use the term rail when referring to the path, and they refer to the curve, or curves, to be swept as cross section curves. Cross section curves can be either open or closed, but they must all be one or the other. An option allows you to make the ends of the surface taper to a point. By default, cross section curves that are not circular rotate as they are swept along the rail, which causes the surface to be twisted. You can select a sweep-style option, though, to prevent this rotation.

When you choose Sweep 2 Rails from the Surface menu, you will be prompted to select two rails, and then one or more cross section curves. The width of these curves automatically adjust to fit the rails as they are swept along. As with one-rail sweeps, both the rails and the cross-section curves can be open or closed, and you can taper the surface ends to a point.

Choose Revolve from the Surface menu to create a surface by revolving a cross section about an axis. The cross section can be open or closed and can consist of several separate curves. You specify the axis by selecting two points, and you can revolve the cross section through any angle greater than zero.

Rail Revolve in the Surface menu also creates a surface by revolving a cross section about an axis. However, the cross section stretches or compresses to conform to the shape of a rail curve as it's revolved. Rhino will issue a command-line prompt for you to select one cross-section and one rail curve, and then to specify the axis of revolution. The cross-section and rail curves can be open or closed.

Next month, we'll explore some other of Rhino's tools for creating surfaces and explain how you can analyze and modify them.



About the Author: John E. Wilson

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