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Parameters - Base1, Base2, Base3, Base4
Name: Base1, Base2, Base3, Base4
Type: quaternion
Read/Write: readable
Context: Transformation, Iteration, Coloring
Description:
In order to obtain the three dimensional sub space R3 of the 4 dimensional quaternion space R4 ChaosPro needs to create a basis of R4. The basis is an orthonormal basis, i.e. it consists of 4 vectors of R4, where each vector is orthogonal to each other and additionally has a length of 1.
The first vector of the basis is always the normal vector, which you can define in the quaternion parameter window. That vector gets normalized (i.e. expanded/truncated, so it has unit length 1). Then the other base vectors get created around this vector. The three dimensional sub space, which then ChaosPro actually uses, consists of those three other vectors. Perhaps you want to create a transformation, which uses that basis in order to distort the sub space: And for that purpose the basis is contained in these four predefined parameters.
A short example: If ChaosPro wants to examine the pixel (x,y,z) in R3, then that pixel corresponds to
the quaternion q = BasePoint+x*Base2+y*Base3+z*Base4.