Evaluation points and interpolation points inside ray tracing steps.

The evaluation points, which are outside the control of the user, should not be confused with the interpolation points for displays, the number of which is specified by the user.

The evaluation points:

The Bulirsch-Stoer integration technique is used for ray tracing (that is, trajectory integration). The technique subdivides each step as many times as is necessary into 'evaluation points', to achieve the requested inaccuracy. The number of evaluation points is usually quite large (16) and it depends on the ray tracing inaccuracy that the user has chosen, but is otherwise outside the control of the user.

When the user chooses step lengths or times that are too small, giving too many steps, the total number of evaluation points can become extremely large, leading to long tracing times (but not higher accuracy).

The 'evaluation points' are not necessarily on the ray itself, and their coordinates are not retained. The only accurate ray coordinates that are available in this method are therefore those at the end points of the ray steps. These coordinates are output as data and are used in plotting

The interpolation points:

The rays appear on the screen before and after clicking on 'Ray tracing complete'.

Before clicking on 'Ray tracing complete'.

The user can specify a number of 'interpolation points' to be used in each step, to improve the appearance of the rays on the screen.

Before clicking on 'Ray tracing complete' the program interpolates extra points between the accurately calculated end points of the steps. The maximum number of interpolation points is 20. The values of the ray parameters at the interpolated points are evaluated by a 5-point interpolation using the 2 end points of the present ray step and the 3 previous steps (if these exist), giving a 5 point interpolation. The interpolation points have no effect on the accuracy of the ray tracing.

The routine that is used to give the interpolation points is also used to give the parameters at a 'test plane', but the results can be inaccurate if the plane is at or near the end of the ray (because the routine works best when there are at least 2 steps before and after the plane). This problem can be overcome by extending the length of the ray beyond the test plane.

If you ask for interpolated points then these points for step number n will be evaluated after step number n+1 has been traced. In other words, the interpolation occurs one step in arrears. A consequence of this is that the ray information will appear on the screen one step in arrears.

After clicking on 'Ray tracing complete'.

After clicking on 'Ray tracing complete', when the rays are displayed in 2D or 3D views, interpolation points are again used but the routine that is used (cubic spline) is different: it is faster and sometimes less accurate.

Return to general note on step lengths or times