This first section, describes the use of the three nonlinear transformations TAPERING, TWIST and BEND. For this intro a sierpinski like structure is used, which is transformed nonlinear in every iteration.

There you see Tapering, Twist and Bend in their simplest form. Tapering can be defined as a piecewise linear funktion, because it's fast and you can construct more complicated transformatons with a repeated use of tapering. The definition of Twist is also piecewise. For certain points along an axis you can specify the twist ratio. The other rotations are linear interpolated. Bend is defined with the startingpoint, the Endpoint, the Middle of Bend and the Bend radius.

At first we have Tapering. In the first picture the cones are transformed with the same tapering in every level. As a result every Cone is tapered three times. In the second picture you can see a tapering that's defined in three pieces.

These picture shows a recursivly tapered Thetrahedron. At the end the structure is twisted one time. The second picture is twisted relativly strong. The twisting-ratio increases with the hight of the object.

The thetrahedron is recursivly tapered, once twisted and at last bended. (The second picture is the same as above with one additional bend.)


My neat Raytracing Project ...