Use an Intersection Point 2D () or Intersection Point 3D () dataset, found under the More 2D Datasets and More 3D Datasets submenus, to enable evaluation of expressions at the intersection points of particle or ray trajectories and a surface or to evaluate intersection points with a more general surface. You can use the Intersection Point datasets with the following plot nodes and derived value nodes: Particle Trajectories and Ray Trajectories; Particle and Ray (1D plots); Particle Evaluation and Ray Evaluation; Point Trajectories; Histogram; Phase Portrait; Optical Aberration; and Aberration Evaluation.

From the Curve type list, you can specify that the intersection of the particle or ray trajectories with one of the following curves is taken:

For Line as the curve type, choose one of the following options from the Line entry method list:

If you want to create additional lines that are parallel to the line you defined, select the Additional parallel lines check box and enter the distances between each line in the Distances field, or click the Range button () to define a range of distances.

For Circle as the curve type, you define the circle by entering its center coordinates in the x and y fields under Center and the radius in the Radius field.

For Semicircle as the curve type, you define the semicircle by entering its center coordinates in the x and y fields under Center, an axis direction in the x and y fields for the axis vector components under Axis direction, and the radius in the Radius field. The axis direction defines the extent of the semicircle as the segments of the circle perimeter where the scalar product with the axis direction vector is positive. For example, with the default axis direction (0, 1), the semicircle consists of the circle perimeter where y > 0.

For defining a general curve, you enter a curve expression F(r). The intersection points will be evaluated on the curve F(r) = 0.

From the Surface type list, you can specify that the intersection of the particle or ray trajectories with one of the following surfaces is taken:

For Plane as the surface type, choose one of the following options from the Plane type list:

For a General plane type, also choose one of the following options from the Plane entry method list:

If you want to create additional surfaces (planes) that are parallel to the plane you defined, select the Additional parallel planes check box and enter the distances between each plane in the Distances field, or click the Range button () to define a range of distances.

For Sphere as the surface type, you define the sphere by entering its center coordinates in the x, y, and z fields under Center and the radius in the Radius field.

For Hemisphere as the surface type, you define the hemisphere by entering its center coordinates in the x, y, and z fields under Center, an axis direction in the x, y, and z fields for the axis vector components under Axis direction, and the radius in the Radius field. The axis direction defines the extent of the hemisphere as the parts of the sphere’s surface where the scalar product with the axis direction vector is positive. For example, with the default axis direction (0, 0, 1), the hemisphere consists of the part of a full sphere where z > 0.

For a general surface, you enter a surface expression F(r). The intersection points will be evaluated on the surface F(r) = 0.

Under Space variables (Intersection Point 3D only), you can change the name of the space variables x and y for the intersection surface’s coordinates from their default values (ip1x and ip1y, for example).

Under Normal variables, enter or edit the variable names for the components of the normal vector — nx, ny, and nz (Intersection 3D) or nx and ny (Intersection Point 2D). The default names are ipl1nx, ipl1ny, and ipl1nz, respectively.

Select an option from the Interpolation between time steps list: Linear (the default) or Cubic. If the expressions being evaluated at the intersection point are differentiable, the Cubic interpolation method will take into account the derivatives of these expressions at the time steps before and after the intersection point is reached. This allows expressions that do not vary linearly over time to be interpolated more accurately.