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Moritz Geometry Editor


Interpolation and Nesting


Surfaces and bodies can be created by interpolating between objects, by nesting within a body or closed surface (including cylinders and cones), and by applying an offset to an existing object. These actions are performed from the Interpolate dialog.

Interpolation of a Sphere and a CylinderInterpolation can be between objects of the same type. Some types can be mixed as specified in the Table below. For example, interpolation can be between spheres and ellipsoids, as shown in the Figure at the right. Cylinders and cones must be in the same direction-a CX surface, for example, can be interpolated with CX, C/X, ECX, and EC/X surfaces. One object need not be contained within the other, such as shown below.
Ellipsoid Interpolation
BOX and WED interpolation is not permitted at the moment. While possible, the interpolated BOXs or WEDs often contain non orthogonal vectors. They would be acceptable as ARBs; we will add the ability to convert the interpolated bodies to ARBs in the future. There is no requirement that the interpolation results are useful for anything.

A Nested BoxNesting consists of adding a number of evenly spaced objects within an existing object. The Figure at the right shows nesting with a BOX body. All surfaces and bodies except for planes, SQ and GQ surfaces, and ARB bodies can be nested. When the Cell column ofTable 5 contains `X', cells can be automatically defined between the original and each nested object. Simple Cellnesting is a special form of nesting that can be applied to RPPs, RCCs, and RECs. It results in a further subdivision, such as shown in the Figure at the left. Cells created as a result of such nesting are simple cells that do not contain a union operator (:) in their descriptions.Nested RPP with Simple Cells

Offsetting is another form of nesting where the user specifies the distance between the original object and the offset objects. The Figure at lower left shows an example. The new objects can be added within or outside of the original. For internal offsetting, the number of objects to add and the offset thickness may result in some objects that are too small-for example spheres with negative radius. If this is the case for the first object to be added, Moritz issues a warning and does not do the offset. Otherwise, the offsetting is quietly terminated if another object cannot be added.Offset Torus

The results of the last interpolation, nest, or offset operation can be undone-all surfaces and cells that were created by the operation are destroyed. The undo stack is shared with the Translation and Duplicate dialogs. Using Undoon any of these dialogs will undo the last operation made with one of these dialogs, not necessarily the one made with the current dialog.


Surfaces and Bodies for Interpolation and Nesting

When Nesting
Object Interpolation Partner Cells Simple Cells
Plane Plane


Sphere Sphere, Ellipsoid
X

Ellipsoid Sphere, Ellipsoid
X

Cylinder Cylinder, Elliptical Cylinder in same direction


Cone Cone in same direction


Torus Torus
X

BOX BOX (under construction)
X

WED WED (under construction)
X

RCC RCC
X
X
REC REC
X
X
TRC TRC
X

RPP RPP
X
X





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