MAPaint Technical Report:
Ray Tracing or ``Laser'' View

Ray Tracing or ``Laser'' View

With respect to a given section a continuous line on that section can be converted to a surface by considering the set of perpendicular rays through each point on the line. The view will correspond to a ``curtain'' view or prism generated by translating the curved line through 3D space in a direction perpendicular to the section. The term laser view has been termed because, in analogous fashion to the section view, this view of the data can also be used to cut existing domains. There is the constraint however that the laser view must pass right through the domain to be cut or be a closed curve.

To define the laser view a set of points at unit distance along the curve are selected and for each point, (x'_i, y'_i, z'_i), we know that z'_i = d. At each point the value of z' is allowed to vary in unit steps from d_min to d_max and the correspondig value r in the original image coordinates is calculated using equation 6. The grey value for that point can then be determined. By scanning in this fashion the grey-values over the entire laser view can be established. The individual line images are aligned by the points corresponding to z'_i = d.