3D Mapping

The 3D Mapping transformation maps a fractal onto a three-dimensional shape, such as a plane or a sphere. It is available as a transformation in Standard.uxf and as a transformation plug-in in Standard.ulb.

Once this transformation is in effect, normal zooming and panning will just move the 3D shape around with the fractal on it. If you want to zoom into the fractal as it is mapped onto the shape, use the Fractal Center, Fractal Magnification, and Fractal Rotation parameters.

To use the rotation and translation parameters effectively, you need to understand the left-handed 3D coordinate system used by the transformation. Here, the X-axis points to the left, the Y-axis points upwards, and the Z-axis points into the screen. So, if you use a positive Z-translation, the 3D shape will appear to move away, into the screen.

The following parameters are available:

Shape	Selects the type of 3D shape that the fractal is mapped onto. In the plug-in version of 3D Mapping, this is a plug-in parameter that lets you select any plug-in that implements a mapping shape.
X Rotation Y Rotation Z Rotation	Rotates the 3D shape around the X, Y, or Z axis. To predict the direction of rotation, hold up your left hand with your thumb pointing into the positive axis direction (for example, to the left for X rotation). Your (curled) fingers now show the direction of positive rotation around that axis.
X Translation Y Translation Z Translation	Moves the shape around in 3D space. You always need some positive Z translation to move the shape "into" the screen, otherwise you will be "inside" the shape and it won't be visible. With the plane shape, use a negative Y translation to look down upon it.
Fractal Center Fractal Magnification Fractal Rotation	Specifies the location of the fractal as it is mapped onto the shape. When adding the transformation, the current coordinates will be used (remember to reset the location to get a proper view of the 3D shape). The easiest way to specify a location is to copy the coordinates from the Location tab of a different fractal window that contains the same fractal formula without the 3D Mapping transformation.