4.2 Intersection of 3D Surfaces with Cutting Planes

In addition to the standard controls that come with the VRML browser, Figure 3 shows a panel labeled ``Cutplane control" which gives the user additional capabilities. We used VRML to create files that would generate cutting planes through a 3D surface. By manipulating the panel controls, a user can study the change in the intersection as a plane is moved through a surface. Currently, the cutting planes are limited to planes perpendicular to the X and Y coordinate axes, but we are working on an extension to the Z direction. Future work will extend the capability to an arbitrary direction.

When the user clicks the X button on the Cutplane control panel, a bounding box appears around the figure along with a cutting plane that moves perpendicular to the X axis. The user moves the plane by clicking on the second row of buttons which operate like those of a VCR. The plane moves in sync with the projected intersection curve, displayed on opposite faces of the bounding box as shown in Figure 4. The controls operate similarly in the Y direction. We are working on the addition of a slider bar to the control panel to give the user more flexibility and make it easier to stop the plane at desired points.

Figure 4: VRML display with X direction cutting plane.

To implement the cut plane control, we used VRML reusable components called PROTO's. Our Cutplane PROTO displays the plane and searches the surface data to determine which points are closest to the specified plane. Linear interpolation is then used to obtain the coordinates for the intersection. All the surfaces we have done to date intersect the X or Y planes in continuous curves. If the surface contains holes, then the intersection curves will be disconnected at some locations, so we have to be careful about how we connect the points. Such a situation is the norm for the Z direction. The intersection of the Z direction plane with the surface is the contour curve for that level which, in general, is not a single continuous curve. Therefore, we are testing various packages for contour plotting to use in determining the Z direction intersection points. In testing the effectiveness of the packages on different machines we are finding that an acceptable speed for the VCR controls on one machine may actually be too fast on another. For that reason, we may decide that the slider bar, which gives the user more control, is a better choice.