Symmetry Types

Reflective symmetries can be defined as either unilateral or multilateral, and either approximate or enforced.

Unilateral symmetries

Have only one side that governs the others, but not vice versa. For example, handles created and morphs applied to handles on the positive side of the symmetry are reflected onto the other side or sides of the symmetry, but handles created or morphs applied to handles on the other side or sides of the symmetry are not reflected.

multilateral symmetries

All sides govern all other sides. For example, a handle created or a morph applied to a handle on any side is reflected to all the other sides.

Approximate symmetries

May contain handles that are not symmetric to other handles. For example, handles created on any side of the symmetry are not reflected to the other sides. This option is best for asymmetrical, but similar, domains or for a cyclical symmetry applied to a mesh that sweeps through an arc but not a full circle.

Enforced symmetries

Cannot contain handles that are not symmetric on all other sides. For example, handles created or deleted on any side of the symmetry are created or deleted on the other sides so that the symmetry is maintained. When a reflective symmetry is created with the enforced option, additional handles may also be created to meet the enforcement requirements.

Reflective symmetries are 1-plane, 2-plane, 3-plane, and cyclical.

One Plane

A mirror is placed at the origin perpendicular to the selected axis (default = x-axis).

In Figure 1, the mesh on the left is before morphing; the mesh on the right is after morphing. The icon for 1-plane symmetry is a rectangle perpendicular to the symmetry system's selected axis. You can think of this rectangle as a mirror. The highlighted handle is moved. Notice how only the handle at the lower left has been selected and how the handle on the upper left is automatically moved symmetrically. This type of symmetry is very useful for a wide variety of symmetric models.

Figure 1.

Two Plane

Two mirrors are placed at the origin perpendicular to the selected axis and the subsequent axis (that is x and y, y and z, z and x) (default = x and y-axis).

In Figure 2, the mesh on the left is before morphing; the mesh on the right is after morphing. The icon for 2-plane symmetry is two rectangles perpendicular to the symmetry system's selected axis and subsequent axis. You can think of these rectangles as mirrors. The highlighted handle is moved. Notice how only the handle at the lower left has been selected and how the other three symmetric handles are automatically moved symmetrically. This type of symmetry is very useful for objects symmetric across two perpendicular planes.

Figure 2.

Three Plane

Three mirrors are placed at the origin perpendicular to all three axes.

In Figure 3, the mesh on the left is before morphing; the mesh on the right is after morphing. The icon for 3-plane symmetry is three rectangles perpendicular to all three of the symmetry system axes. You can think of these rectangles as mirrors. The highlighted handle is moved. Notice how only the handle at the lower right has been selected and how the other seven symmetric handles are automatically moved symmetrically. This type of symmetry is very useful for objects symmetric across three perpendicular planes.

Figure 3.

Cyclical

Two mirrors are placed along the selected axis (default = z-axis) and run through the origin with a given angle in between that is a factor of 360. The result is a wedge that is reflected a certain number of times about the selected axis.

Figure 4 is an example of cyclical symmetry with a cyclical frequency of 8 (45 degrees per wedge). The mesh on the left is before morphing and the mesh on the right is after morphing. The icon for cyclical symmetry is a number of spheres lying perpendicular the symmetry system's selected axis and connected to the origin with lines. The number of spheres is equal to the number of symmetric wedges. Each cyclical wedge is identical to the others when rotated through an angle (in this case 45 degrees) about the selected axis. The highlighted handle is moved. Notice how only one handle has been selected and how the other seven symmetric handles are automatically moved symmetrically. This type of symmetry is very useful for objects that repeat at regular intervals about a central point.

Figure 4.

Generally speaking, the handles for a domain with non-reflective symmetry will act as if they are the shape of the symmetry type. For instance, a domain with linear symmetry causes handle movements to act on the domain as if the handle was a line in the direction of the x-axis. A domain with circular symmetry causes handle movements to act on the domain as if the handle was a circle centered around the z-axis. The edges of a domain affect how influences between handles and nodes are calculated. Non-reflective symmetries work best for domains that are shaped like the symmetry type and have a regular mesh. For example, a circular symmetry works best for a round domain with a concentric mesh.

Linear

Handle acts as a line drawn through the handle location parallel to the selected axis (default = x-axis).

In Figure 5, the mesh on the left is before morphing; the mesh on the right is after morphing. The icon for linear symmetry is two parallel lines extending along the selected axis. The highlighted handle is moved. Notice how the handles act on the mesh as if they were parallel lines. This type of symmetry is very useful for changing the shape of entire cross-sections by moving only a few handles.

Figure 5.

Circular

Handle acts as a circle drawn through the handle position about the selected axis (default = z-axis).

In Figure 6, the mesh on the left is before morphing; the mesh on the right is after morphing. The icon for circular symmetry is a circle at the origin of the symmetry system lying perpendicular to the selected axis. The highlighted handle is moved. Notice how the handles act on the mesh as if they are circles about the selected axis. This type of symmetry is very useful for keeping a circular part circular while manipulating its shape.

Figure 6.

Planar

Handle acts as a plane drawn through the handle location perpendicular to the selected axis (default = x-axis).

In Figure 7, the mesh on the left is before morphing; the mesh on the right is after morphing. The icon for planar symmetry is a shaded rectangle perpendicular to the symmetry system's selected axis. The highlighted handle is moved. Notice how the handles act on the mesh as if they were perpendicular planes. This type of symmetry is very useful for manipulating the shape of regular sections along their length without changing their profile.

Figure 7.

Radial 2D

Handle acts as a ray drawn through the handle position originating from and extending perpendicular to the selected axis (default = z-axis).

In Figure 8, the mesh on the left is before morphing; the mesh on the right is after morphing. The icon for radial 2-D symmetry is a flat cone with its vertex at the symmetry system origin and perpendicular to the selected axis. The highlighted handle is moved. Notice how the handles act on the mesh as if they were rays extending in a radial direction away from the selected axis. This type of symmetry is very useful for changing the shape of a part while keeping its radial profile intact.

Figure 8.

Cylindrical

Handle acts as a cylinder drawn through the handle position about the selected axis (default = z-axis).

In Figure 9, the mesh on the left is before morphing; the mesh on the right is after morphing. The icon for cylindrical symmetry is a cylinder parallel to the symmetry system's selected axis centered about the origin. The highlighted handle is moved. Notice how the handles act on the mesh as if they were cylinders. This type of symmetry is the equivalent of using both circular and linear symmetry together and is very useful for making circular changes to solid meshes.

Figure 9.

Radial + Linear

Handle acts as a plane drawn through the handle position extending from the selected axis (default = z-axis).

In Figure 10, the mesh on the left is before morphing; the mesh on the right is after morphing. The icon for radial+linear symmetry is a 3-D wedge lying perpendicular to the selected axis with its vertex at the symmetry system origin. The highlighted handle is moved. Notice how the handles act on the mesh as if they were planes parallel to and extending away from the selected axis. This type of symmetry is the equivalent of using both radial and linear symmetry together and is very useful for making radial changes to solid meshes.

Figure 10.

Radial 3D

Handle acts as a ray drawn through the handle position originating from origin.

Figure 11 is an example of radial 3-D symmetry. The model is a hollow sphere made with solid elements. The mesh on the left is before morphing; the mesh on the right is after morphing. The icon for radial 3-D symmetry is a cone with its vertex at the origin of the symmetry system. The highlighted handle is moved. Notice how the handles act on the mesh as if they were rays extending away from the origin. This type of symmetry is very useful for making radial changes to spherical objects.

Figure 11.

Spherical

Handle acts as a sphere drawn through the handle position centered on the origin.

In Figure 12, the mesh on the left is before morphing; the mesh on the right is after morphing. The model is a hollow sphere made with solid elements. The icon for spherical symmetry is a sphere centered at the symmetry system origin. The highlighted handle is moved. Note how the handles act on the mesh as if they were spheres centered at the origin. This type of symmetry is useful for changing the shape of spherical objects while keeping their spherical shape intact.

Figure 12.