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Every point on an EdgeCAM surface is defined in terms of a 2-axis co-ordinate system. The axes of this system are called U and V. All co-ordinate values range from 0 to 1.
The U, V co-ordinate system is related to the World Axes (the x, y, z co-ordinate system) by three functions involving the u and v co-ordinates, or parameters, in “parametric space”, as follows:
x co-ordinate = X(u,v)
y co-ordinate = Y(u,v)
z co-ordinate = Z(u,v)
The exact function or mapping depends on the surface type (you do not need to know the exact mapping functions to use surfaces in EdgeCAM!).
Therefore, for every point in parametric space, there is a corresponding point in World Space, although the reverse is not true. This simply means that although every point on a given surface exists in World Space, not every point in World Space is located on this surface.
This diagram shows the same surface in both world and parametric space.
There are several reasons why it is convenient to use parametric space for surfaces:
Any point on the surface can be specified uniquely by a (u, v) pair.
All surface types can be treated in the same way by surface manipulation functions; for example, any surface type can be intersected or trimmed against any other. This is not the case with some CAD/CAM packages, which do not allow intersection between certain surface type combinations.
Parameter lines of constant u or v generally follow the contours of the surface. For this reason, it is often convenient to machine a surface by moving the tool in a constant U or V direction.